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is the same problem as temperature you
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is the same problem as temperature you
have to know which excitations you have
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have to know which excitations you have
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have to know which excitations you have
to deal with and you have to have a
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to deal with and you have to have a
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to deal with and you have to have a
model for them and you have to
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model for them and you have to
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model for them and you have to
equilibrate them okay um
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equilibrate them okay um
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equilibrate them okay um
where will most of that entropy come
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where will most of that entropy come
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where will most of that entropy come
from um typically we think of thermal
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from um typically we think of thermal
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from um typically we think of thermal
expansion uh largely caused by
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expansion uh largely caused by
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expansion uh largely caused by
vibrational entropy by phonon entropy so
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vibrational entropy by phonon entropy so
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vibrational entropy by phonon entropy so
um why does the entropy go up with
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um why does the entropy go up with
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um why does the entropy go up with
volume which is what gives you thermal
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volume which is what gives you thermal
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volume which is what gives you thermal
expansion because if you stretch a
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expansion because if you stretch a
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expansion because if you stretch a
material the bonds get slightly softer
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material the bonds get slightly softer