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what we 're going to do in this video is think about how to visualize distributions of data , and then to analyze those visualizations , and we will eventually get to something known as a density curve . but let 's start with a simple example , just to review some concepts . let 's say i go to 16 students and i ask th... | if i were to ask you what percentage of the data is greater than three , well then you would be looking at this area , and it looks like it is about 50 % , but once again , i am estimating it . but you can start to see how , even with estimation , a density curve could be useful . in the real world , statisticians will... | can we always figure out the equations of the density functions or is it more practical to use rectangles instead ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | what i want to understand , in this video is , i have a subspace right here , v. i want to understand whether the transformation of the subspace -- and what did we call that ? we called that the image of our subspace , or our subset , either way . the image of v under t. in the last video , just to kind of help you vis... | what is the difference between a `` subspace '' and a `` subset '' ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | this is equal to the set of all the transformations of x . well all the transformations of x are going to be ax where x is a member of rn . so x is going to be an n-tuple , where each element has to be a real number . | please correct my understanding below about what are the matrices a , x , t ( x ) called ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | and that 's true of all subspaces . v -- let me write it this way -- the zero vector is a member of v. and it would be the zero vector with n components here , because v is a subspace of rn . and why i say that 's redundant , because if i say that any multiple of these vectors is also in v , i could just set the scalar... | why does the zero vector always have to be in a subspace v ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | and that 's true of all subspaces . v -- let me write it this way -- the zero vector is a member of v. and it would be the zero vector with n components here , because v is a subspace of rn . and why i say that 's redundant , because if i say that any multiple of these vectors is also in v , i could just set the scalar... | am i right that zero vector condition is not totaly redundand , and zero vector must be a member of subspace to prevent empty set { } from being a valid subspace ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | that is equal to , and we touched on this , or we actually talked about this when we introduced the idea . this is equal to the column space of a . or we just denoted it sometimes as c of a . | if we let matrix a=t then i want to know if the basis of column space is the basis of the image space ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | so if we write a -- let me write my matrix a . it 's just a bunch of column vectors , a1 , a2 . it 's going to have n of these , right ? | what is the difference between subset of vectors and set of vectors and subspace of vectors ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | so in order for it to be a subspace , if i take the transformation -- let me find two members of t. well clearly if i take the transformation of any members of v , i 'm getting members of the image . right ? so i can write this . | must have m amounts of values right ? |
let 's say that i have some set v that is a subspace in rn . and just as a reminder , what does it mean ? that 's just some set , or some subset of rn where if i take any two members of that subset -- so let say i take the members a and b -- they 're both members my subspace . by the fact that this is a subspace , we t... | and by the fact that it 's a subspace , we also know that if we multiply any member of our subspace by a scalar -- so the fact that those guys are members of our subspace -- we also know that if i pick one of them , let 's say a , and i multiply a by some scalar , that this is also going to be a member of our subspace ... | the closure under addition and the closure under scalar multiplication is only true when you are talking about a -- -linear -- - transformation , right ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | the average kinetic energy of the system went down . so the temperature would 've also gone down . and actually , just as a bonus point , what happened to the internal energy ? | since temp is the average k.e ( =1/2mv^2 ) , would n't the temp also increase ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | well , since it 's an isotherm , since the temperature did not change , what do we know about the internal energy ? did the internal energy change ? the temperature not changing told us that the kinetic energy did n't change . | i 'm still a bit confused why the fact that temperature is kept constant implies that the change in internal energy is 0 ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and the convention is that because we did work , but we were constant temperature , so our internal energy did n't change , we had to add energy to the system to make up for the work we did . so some heat must have been added to the system . and then what they do is they just put this little downward arrow and they wri... | explain the difference between temprature and heat ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so this is state 2 , this is state 1 . what i 'm claiming is that my path along this is going to be on some type of a rectangular hyperbola , or at least part of it . if i were to add rocks to it and compress it , i claim that my pv diagram would go like this . | why is the metal part at the back of the pencil cold ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so we did work . and so we changed some kinetic energy , or we transferred some kinetic energy , out of the system . that 's essentially what the work did . | what happens at the microscopic level when the kinetic energy of the ideal gas is transferred to the piston ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | that if i keep the temperature constant , that i 'm essentially moving along this hyperbola . well , let 's just take out the ideal gas formula . let me box off all this stuff over here . | what meant by tendency of a gas to acquire maximum `` randomness '' ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and then what they do is they just put this little downward arrow and they write a q right there . so some heat was put into the system during this isothermic process right there . and the value of that q is equivalent to the work we did . | if the process is isothermic , i suppose that no heat must be entered in the system so how is it possible that work done is equal to heat ( q ) ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | i should have done that first . nrt , it 's just a constant term . now , what 's the antiderivative of 1 over v ? | why does the fact that nrt is constant allow it to be equal to one ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so , if we look at this right here , temperature -- since we 're assuming we 're on an isotherm , is a constant . n and r are definitely constants . so we can rewrite this integral as the integral from v1 to v2 of 1 over v , dv . | would n't the nrt value depend on the n , r , and t values ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | nrt , it 's just a constant term . now , what 's the antiderivative of 1 over v ? it 's the natural log of v. so our work is equal to nrt times the natural log -- this is the antiderivative -- of v , evaluated at v2 minus it evaluated at v1 . so that is equal to nrt times , evaluated at v2 , so the natural log of v2 . ... | at 16 why ca n't we simply write 1/v dv as v^-1 dv and then integrate ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | this is my pressure . this is my volume . so this is my starting point right here . | which of the two will increase pressure adiabatic or isothermal process when the volume is reduced by 50 % of the initial volume ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | well , since it 's an isotherm , since the temperature did not change , what do we know about the internal energy ? did the internal energy change ? the temperature not changing told us that the kinetic energy did n't change . | what is the internal energy ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | well , think about it this way . some work was done , right ? our old ceiling was maybe some place around here . | i 'm aware of the area under the curve is work done , how integrating p is equal to the work done ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . | why dont sal include `` + c '' in his integration ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so even though if , i took two relative things of comparable size . that says , temperature a . this is temperature b . | why temperature decreases on removing pebbles ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | the isotherm assumption makes our math a little bit easier . because we know that pv is equal to nrt , ideal gas law . or we could say p , if we divide both sides by v , is equal to nrt , divided by v. so there we have it . | why does charles ' law not apply here ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | well , think about it this way . some work was done , right ? our old ceiling was maybe some place around here . | what is the difference in using w=p*deltav to calculate work done by an expanding gas , and w=nrt*ln ( vf/vi ) to calculate work done by an expanding gas ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and the convention is that because we did work , but we were constant temperature , so our internal energy did n't change , we had to add energy to the system to make up for the work we did . so some heat must have been added to the system . and then what they do is they just put this little downward arrow and they wri... | how can i add some heat on a system.if i increase temperature will the heat increase ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so even though if , i took two relative things of comparable size . that says , temperature a . this is temperature b . | then how come the temperature inside increases or decreases ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and , of course , i 'm doing these little pebbles , because i 'm going to remove them slowly . because i want to approximate a quasi-static process . or i want to approximate a system that 's always close enough to equilibrium that i 'm cool with defining our macro states , our pressure , our temperature , or our volum... | why should an isothermal process be a slow process ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | if temperature does n't change , internal energy wo n't change . if temperature goes up , internal energy goes up . if temperature goes down , internal energy goes down . and , of course , they 're not the same thing , though . | if the pressure goes down and the volume goes up , does n't that cancel each other out ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and for our simple system , where internal energy is represented by the kinetic energy of these molecules , that 's always going to be the case . if temperature does n't change , internal energy wo n't change . if temperature goes up , internal energy goes up . | does n't the internal energy of this adiabatic system not change by definition ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so temperature is just , by some scaling factor , a measure of kinetic energy . now , when i do some work , it 's essentially a transfer of kinetic energy . and i ca n't replace that energy with some heat because it 's adiabatic . there 's no heat going into or out of the system . | if the system is adiabatic , does n't that state that it is isolated from the world in terms of all transfer of energy , heat and work ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so in that situation , the kinetic energy of the system went down . the average kinetic energy of the system went down . so the temperature would 've also gone down . and actually , just as a bonus point , what happened to the internal energy ? | what would be the differences in behaviour between an isothermic and adiabatic system if i went on removing pebbles ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so a reservoir , you can kind of view as an infinitely large amount of something that is the temperature that we started off with . so this reservoir is t1 . so even though if , i took two relative things of comparable size . | can we also consider earth atmosphere as reservoir ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and actually i 'll add in a word right here . if it was an adiabatic process -- if it was adiabatic -- fancy word . all that means is , completely isolated from the world . | is there a way to define p ( v ) for an adiabatic process ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | well , think about it this way . some work was done , right ? our old ceiling was maybe some place around here . | decreasing temperature is a consecuence of the fact of doing work only right ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | it 's nrt natural log of v2 over v1 . this is v2 . this is v1 . | if i wil keep the temperature constant and increase its volume to v2 , what is the formula for v2 ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | well , since it 's an isotherm , since the temperature did not change , what do we know about the internal energy ? did the internal energy change ? the temperature not changing told us that the kinetic energy did n't change . | in isothermal reaction , why is change in internal energy zero ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and this is also equal to the heat put into the system . it 's also equal to q . so when you look at this , if we were to just draw this part of the curve -- let me redraw it just to make things neat . | why did sal scratch out the q [ heat ] at around ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | it also looks like that in the third quadrant , but we wo n't worry about that too much . so whenever you hold temperature constant , you 're on some rectangular hyperbola like this , like an isotherm . now , if the temperature was a different temperature , if it was a lower temperature , you 'd be on a different isoth... | how can the temperature go down if the situation is an isotherm ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | now , if this is 0 -- so we know that this did n't change , because the temperature did n't change . so that means 0 is equal to q minus w , or that q is equal to w. so this is the work done by the system . you 'll end up getting something in joules . | if internal energy =heat minus work done ( u= q-w ) , why would n't q decrease if temp is kept constant and system is performing work ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and actually i 'll add in a word right here . if it was an adiabatic process -- if it was adiabatic -- fancy word . all that means is , completely isolated from the world . | can an adiabatic process be isothermic ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | we pushed it up with some force for some distance . so we did work . and so we changed some kinetic energy , or we transferred some kinetic energy , out of the system . | hi , would an isobaric process do more work in gas expansion compared to an isothermal ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and , of course , they 're not the same thing , though . the difference between internal energy and temperature is the scaling factor , 3/2 times the number of molecules , times our ideal gas constant . so fair enough . | where does the 3/2nrt come from ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | so even though if , i took two relative things of comparable size . that says , temperature a . this is temperature b . | why does the temperature averages out when 2 bodies are kept in contact ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and what i 'm saying is , if i 'm doing an isothermic process , so i just keep removing these pebbles . so i start at this state right here . let me copy and paste it since i 've done so much art already here . | radiations start coming out from that substance ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | i inadvertently explained to you what an adiabatic process is , and why the temperature would naturally go down on its own if you did n't have this reservoir here . but the whole reason why i even thought about doing this video is because i wanted you get comfortable with this idea of , one , that a reservoir will keep... | i 'm confused why the reservoir is even needed to make this isothermic ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | and now we calculated the area under this , which is the work done , which was this value right here . let me write it there . it 's nrt natural log of v2 over v1 . this is v2 . | is it possible to write the equation as w=pv*ln ( v2/v1 ) ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | the difference between internal energy and temperature is the scaling factor , 3/2 times the number of molecules , times our ideal gas constant . so fair enough . i went through this whole exercise just to show you that if i was completely isolated , and if i removed a couple of these pebbles , that my temperature is g... | around 00 ; if the system is adiabatic , and the volume is increased , why does u goes down ? |
let 's start with our classic system that i keep using over and over again . and that 's because it tends to be very useful for instruction . it also tends to be the system that is most covered in classrooms . so hopefully it 'll be productive for you and your school work . so i have this container . it has a movable p... | if temperature does n't change , internal energy wo n't change . if temperature goes up , internal energy goes up . if temperature goes down , internal energy goes down . | so , if u goes down , where did the energy go to ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | p2 is also zero , so both of these are zero . remember , that 's the external pressure . p1 is the external pressure to the input to the pipe , and you can view this as a pipe . | why wouldnt the external pressure of the water leaving the hole be atmospheric pressure ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | the pressure would be the pressure that 's being exerted by the outside of the canister to contain the water , in which case , we would end up with no velocity . the water would n't spurt anywhere . but now we 're seeing the external pressure is zero . | in the last part of the video , should n't the volume of water coming out of the hole be a2*v2*time , since v2*time is the distance the water travels ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | i could redraw it as a pipe that looks like it has a big hole on the top , and it goes down to some level to a super-small hole like that . this would be a vacuum , and the fluid is just going in and it 's spurting out of this end . anyway , the pressure going into the pipe is zero , and we said since we put a hole , t... | even if this entire system is in a vacuum , would n't there still be pressure present in the system due to all the fluid behind a single fluid particle at point p2 ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | you can get rid of the area 1 on both sides , and then you 're saying that the velocity up here is equal to the rate at which the top of the surface moves down and is equal to 1/1,000 of the velocity of the liquid spurting out of this little hole . with that , we actually have the three variables for the left-hand side... | should n't there still be a rho ( p ) on the left side of the equation ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | this is an important thin . when we talk about bernoulli 's -- let me rewrite bernoulli 's equation . it 's p1 plus rho gh1 plus rho v1 squared over 2 is equal to p2 plus rho gh2 plus rho v2 squared over 2 . | when we talk about applications of bernoullis theoram say for example during a storm the roof of a house flies of , we talk about increase in air velocity and decrease in pressure .how does bernoullis equation explain this ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | with that said , what is the output velocity ? the velocity -- you just take the square root of both sides -- is the square root of 2gh . that is the output velocity . | is n't the final result v= root of 2gh called toricelli 's law ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | the pressure would be the pressure that 's being exerted by the outside of the canister to contain the water , in which case , we would end up with no velocity . the water would n't spurt anywhere . but now we 're seeing the external pressure is zero . | if the tube is tilted slightly at an angle what would be the effect on the speed of the water sprouting out ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | it 's a column of fluid that comes out , so per second , the length of the column of fluid will be the velocity times time , and then the cross-section of that column is equal to the output area . if i wanted to know the flow coming out , the flow coming out or the flux coming out would be equal to the hole 's area tim... | at the end of the video , are we not actually obtaining volumetric flow rate ( volume/time ) as opposed to flux ( volume/ ( area * time ) ) ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . | how can we consider a hole to be very very small.what will happen when the area of hole is increased by a greater amount and thus what will happen to the velocity of the fluid ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | but if we look at the water that 's spurting out of the hole , it 's not doing any work , because it 's not actually exerting force against anything so it 's not actually doing work . when we think about the pressure , the output pressure , it 's not the pressure at that depth of the fluid . you should think of it as t... | im confused , does the vacuum pressure p1 act as a sucking pressure preventing the water from leaving ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . | or does air bubbles enter the cup making p1=p2=1 atmosphere ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | the pressure would be the pressure that 's being exerted by the outside of the canister to contain the water , in which case , we would end up with no velocity . the water would n't spurt anywhere . but now we 're seeing the external pressure is zero . | if there is a vacuum both inside and outside the glass , would n't the fluid just stay stationary in a `` blob '' ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | it 's not exactly kinetic energy . it 's rho times v squared divided by 2 . one thing that we can immediately see is that we have all these rhos on both sides of the equation , so we can divide both sides by rho and get rid of all of those . | what if the surface are of fluid is not very much bigger than the hole the value of ( v^2/ ( suppose ) 20 ) ^2 will not be negligible ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | but if we look at the water that 's spurting out of the hole , it 's not doing any work , because it 's not actually exerting force against anything so it 's not actually doing work . when we think about the pressure , the output pressure , it 's not the pressure at that depth of the fluid . you should think of it as t... | i can`t understand that if water ( fluid ) if flowing out then the upper fluid will have to apply a force ( pressure ) on the lower fluid so that the water ( fluid ) flows out ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | i just substituted v2 over 1,000 for v1 . that equals the pressure at the hole , the external pressure at the hole , which is zero , plus h2 . this is h2 right here , which we said is zero . | why is the pressure at the hole not considered to be atmospheric pressure ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | now let 's figure out the things that we have to input here . what is the pressure at point two ? this is the important thing . | any one please tell me how to apply bernaulli in between to point inside the canister instead of the two point taken ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | the pressure would be the pressure that 's being exerted by the outside of the canister to contain the water , in which case , we would end up with no velocity . the water would n't spurt anywhere . but now we 're seeing the external pressure is zero . | would n't the velocity stay the same ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | that 's what the hole essentially creates . we 're going to say that p2 is zero , so this pressure was zero , because we 're in a vacuum . p2 is also zero , so both of these are zero . | what will be the effect if the portion on the top of the container is not vacuum ... say it is air ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | p2 is also zero , so both of these are zero . remember , that 's the external pressure . p1 is the external pressure to the input to the pipe , and you can view this as a pipe . | i 'm confused right now , what 's the pressure in bernoulli 's equation , is it the external pressure applied on the liquid or is it the pressure exerted by the fluid itself ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | one thing that we can immediately see is that we have all these rhos on both sides of the equation , so we can divide both sides by rho and get rid of all of those . then we can multiply both sides of the equation by 2 , and we get 2gh plus v2 squared over -- what 's 1,000 squared -- over 1 million . that is equal to v... | i know my algebra reasonably well ... but how did sal get 2gh instead of gh ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | this is an important thin . when we talk about bernoulli 's -- let me rewrite bernoulli 's equation . it 's p1 plus rho gh1 plus rho v1 squared over 2 is equal to p2 plus rho gh2 plus rho v2 squared over 2 . | does the pressure the same as the p ( density ) gh in the bernoulli 's equation ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | it 's not exactly kinetic energy . it 's rho times v squared divided by 2 . one thing that we can immediately see is that we have all these rhos on both sides of the equation , so we can divide both sides by rho and get rid of all of those . | i thought volumetric flux was v/ ( a*t ) = r ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | the pressure would be the pressure that 's being exerted by the outside of the canister to contain the water , in which case , we would end up with no velocity . the water would n't spurt anywhere . but now we 're seeing the external pressure is zero . | if the surface is not moving , then water does n't spurt out because of continuity equation ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | this is an important thin . when we talk about bernoulli 's -- let me rewrite bernoulli 's equation . it 's p1 plus rho gh1 plus rho v1 squared over 2 is equal to p2 plus rho gh2 plus rho v2 squared over 2 . we figured out all of these terms . | just like the pressure equation ( rho.gravity.height ) ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | let 's say that if we closed the hole , then at that point , sure . the pressure would be the pressure that 's being exerted by the outside of the canister to contain the water , in which case , we would end up with no velocity . the water would n't spurt anywhere . but now we 're seeing the external pressure is zero . | what is the principle of a firefighters nozzle which seems to have high water pressure and high water velocity ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | p2 is also zero , so both of these are zero . remember , that 's the external pressure . p1 is the external pressure to the input to the pipe , and you can view this as a pipe . | if external pressure is say 1 atm..will the ans change ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | we 're going to say that p2 is zero , so this pressure was zero , because we 're in a vacuum . p2 is also zero , so both of these are zero . remember , that 's the external pressure . | how are p1 and p2 zero ? |
where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . i said that the area of a2 is so small , it 's 1/1,000 of area 1 . then we used the continuity equation . we said the v... | where we left off , we had this canister , because it had a closed top and it had a vacuum above the fluid . the fluid on top had an area of a1 , and i poked a little hole with a super-small area a2 . | what is torricelli 's law ? |
- [ tutor ] so i 've got a binomial variable x and i 'm gon na describe it in very general terms , it is the number of successes after n trials , after n trials , where the probability of success , success for each trial is p and this is a reasonable way to describe really any random , any binomial variable , we 're as... | so what we 're gon na focus on in this video is well , what would be the expected value of this binomial variable ? what would the expected value , expected value of x be equal to ? and i will just cut to the chase and tell you the answer and then later in this video , we 'll prove it to ourselves a little bit more mat... | so say you have a table of values from x=0 to x=3 when x = 0,3 p ( x ) = 1/3 and x = 1,2 p ( x ) = 2/3 how do you use those values to find the expected value of x ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | let 's say it 's five dollars per flag -- five dollars per flag . so now what is the supply plus tax curve ? so the supplier / just to make the flags in china and ship them to united states and get the story here even to get that first flag done even if is that in the most efficient way possible looks do you need at le... | does an imposed tax always shift the supply curve ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | let 's say it 's five dollars per flag -- five dollars per flag . so now what is the supply plus tax curve ? so the supplier / just to make the flags in china and ship them to united states and get the story here even to get that first flag done even if is that in the most efficient way possible looks do you need at le... | is there a case in which a tax will shift the demand curve ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | so this right over here , this is almost perfectly elastic . if it was perfectly elastic , it would be completely horizontal . so this is almost almost almost perfectly -- perfectly elastic -- elastic demand . a very small change in price leads to a huge change in quantity . | why , when there is perfectly elastic demand , is the consumer surplus zero ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | and so what you have here is a very large , a high elasticity of demand . so this right over here , this is almost perfectly elastic . if it was perfectly elastic , it would be completely horizontal . so this is almost almost almost perfectly -- perfectly elastic -- elastic demand . a very small change in price leads t... | for a perfectly elastic curve there is no consumer surplus , is that right ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | [ i ] do n't like the idea of american flags being made in china . '' so they decide to tax american flags made in china . so what they do is that they place a tax , they place a tax -- and once again i 'll do a fixed dollar tax . it could be a percentage and if a percentage then it 'll change the sup -- the supply plu... | what would happen if the tax was on buyers ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | that is five dollars -- and then times eighteen thousand -- times eighteen thousand . so this right over here is the tax revenue . that right over there is a tax revenue . actually , let me draw a little bit more carefully so the tax revenue is this is going to be between this line right over here and five dollars . | the tax will affect the final price directly , right ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | [ i ] do n't like the idea of american flags being made in china . '' so they decide to tax american flags made in china . so what they do is that they place a tax , they place a tax -- and once again i 'll do a fixed dollar tax . | can america tax flags made in china ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | [ i ] do n't like the idea of american flags being made in china . '' so they decide to tax american flags made in china . so what they do is that they place a tax , they place a tax -- and once again i 'll do a fixed dollar tax . it could be a percentage and if a percentage then it 'll change the sup -- the supply plu... | when tax imposed on the flag , why the difference between the new price and the original price is not the amount of the tax ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | well , if the price goes slightly above that equilibrium price , people are going to say , `` well , i can go by the american flags made in taiwan , or even the ones made in america , or made in mexico , or made some place else . [ because ... ] `` people wo n't be able to tell the difference from a distance . '' so i ... | but is n't there a difference between marginal cost and incremental cost ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | let 's say it 's five dollars per flag -- five dollars per flag . so now what is the supply plus tax curve ? so the supplier / just to make the flags in china and ship them to united states and get the story here even to get that first flag done even if is that in the most efficient way possible looks do you need at le... | i 've seen a lot of comments say that it will be the same whether you make the demand + tax curve or supply + tax curve but i think it 's just the price that the same not the quantity in the new equilibrium can someone tell me whether it 's really right to make a demand+tax curve instead of supply+tax curve ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | so this right over here , this is almost perfectly elastic . if it was perfectly elastic , it would be completely horizontal . so this is almost almost almost perfectly -- perfectly elastic -- elastic demand . a very small change in price leads to a huge change in quantity . | who bears the burden of the tax when supply is perfectly elastic ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | so this right over here , this is almost perfectly elastic . if it was perfectly elastic , it would be completely horizontal . so this is almost almost almost perfectly -- perfectly elastic -- elastic demand . a very small change in price leads to a huge change in quantity . | how about in a case that taxes put it in perfectly elastic supply and perfectly inelastic supply ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | [ i ] do n't like the idea of american flags being made in china . '' so they decide to tax american flags made in china . so what they do is that they place a tax , they place a tax -- and once again i 'll do a fixed dollar tax . | how do us leaders place a tax on flags made in china ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | so this right over here , this is almost perfectly elastic . if it was perfectly elastic , it would be completely horizontal . so this is almost almost almost perfectly -- perfectly elastic -- elastic demand . a very small change in price leads to a huge change in quantity . | what are some examples of goods with ( nearly ) perfectly elastic demand ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | that is five dollars -- and then times eighteen thousand -- times eighteen thousand . so this right over here is the tax revenue . that right over there is a tax revenue . actually , let me draw a little bit more carefully so the tax revenue is this is going to be between this line right over here and five dollars . | when we buy big products like cars or stuff from other nations , we have to pay a tax to the government , right ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | let 's say it 's five dollars per flag -- five dollars per flag . so now what is the supply plus tax curve ? so the supplier / just to make the flags in china and ship them to united states and get the story here even to get that first flag done even if is that in the most efficient way possible looks do you need at le... | so does that make a tax+demand curve , seeing as the tax is imposed on the quantity consumed and not supplied ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | [ i ] do n't like the idea of american flags being made in china . '' so they decide to tax american flags made in china . so what they do is that they place a tax , they place a tax -- and once again i 'll do a fixed dollar tax . it could be a percentage and if a percentage then it 'll change the sup -- the supply plu... | does anyone know of work on oil/gasoline prices that predicts who would pay a $ 1 /gal gasoline tax , or a pahsed in tax ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | i 'm going to buy the ones that were made in china . '' and then the quantity demanded would be much larger . and so what you have here is a very large , a high elasticity of demand . so this right over here , this is almost perfectly elastic . | how must the quantity elasticity of inverse demand and the quantity elasticity of inverse supply be related for the impact of t on revenue to be zero ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | so this right over here , this is almost perfectly elastic . if it was perfectly elastic , it would be completely horizontal . so this is almost almost almost perfectly -- perfectly elastic -- elastic demand . a very small change in price leads to a huge change in quantity . | is it possible in our world to have a perfectly elastic demand curve ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | let 's say it 's five dollars per flag -- five dollars per flag . so now what is the supply plus tax curve ? so the supplier / just to make the flags in china and ship them to united states and get the story here even to get that first flag done even if is that in the most efficient way possible looks do you need at le... | what happens with the curve ? |
let 's think about how a tax on a product might affect it , if the demand for it is very , very , very elastic . so what i 've done here -- we 're going to think about flags -- the market for a certain type of flag that 's made in china . and to think about this flag -- think about it this way . if the price -- the pri... | so this right over here , this is almost perfectly elastic . if it was perfectly elastic , it would be completely horizontal . so this is almost almost almost perfectly -- perfectly elastic -- elastic demand . a very small change in price leads to a huge change in quantity . | this is some what random but what things are have perfectly elastic demand or is it just a theoretical state ? |
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