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know if you sort of look at the scale
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know if you sort of look at the scale
here um it's pretty pretty amazing that
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here um it's pretty pretty amazing that
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here um it's pretty pretty amazing that
this effect comes out uh quite well
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but what about you know other things
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but what about you know other things
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but what about you know other things
remember that the
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the thermal expansion comes from how the
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the thermal expansion comes from how the
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the thermal expansion comes from how the
entropy changes with volume but that's
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entropy changes with volume but that's
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entropy changes with volume but that's
the total entropy the calculation I
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the total entropy the calculation I
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the total entropy the calculation I
showed you only had the vibrational
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showed you only had the vibrational
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showed you only had the vibrational
entropy in it okay okay so any other
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entropy in it okay okay so any other
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entropy in it okay okay so any other
level of excitations that changes with
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level of excitations that changes with
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level of excitations that changes with
volume can affect your thermal expansion
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volume can affect your thermal expansion
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volume can affect your thermal expansion
so you know an obvious one is the
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so you know an obvious one is the