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Heat capacity intuition

  1. Jun 8, 2013 #1
    So heat capacity is the change in the mean value of the internal energy when the temperature is changed: C = d<E>/dt
    But I would like a little more intuition than that. T^(-1) = dS/d<E>, so going back to the intuition that the inverse of the temperature is a measure of how disordered the system becomes when we change the energy, what does this tell us that heat capacity is a measure for?
    The reason Im asking is I got an exercise, where the heat capacity goes from 0 to a max and then back to sorry for T=[0,∞). Im asked to interpret the meaning that C=0 for T=0 or T=∞, but I can't get the right intuition in terms of microstates etc.
  2. jcsd
  3. Jun 8, 2013 #2
    Look for an equation where you are expressing C in terms of S and T rather than anything to do with E. (Hint: Multiply your two equations together)
  4. Jun 8, 2013 #3
    well all I could get from that is:

    dU = TdS
    C=T dS/dT which is just the chain rule for dU/dT=C

    Was this what you were looking for? This doesn't for me give a lot of new insight.
  5. Jun 9, 2013 #4
    I could also ask another way. Why is it intuitively that solid materials have C=0 at T=0?
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