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Finding the entropy from the heat capacity

  1. Jan 11, 2016 #1
    Let's say that we have some canonical ensemble where I know that the heat capacity is given by

    ##C_{V}=\alpha(N,V) T^{n}##

    Since ##C_{V}=T\frac{\partial S(T,V)}{\partial T}## I know that

    ##S(V,T)=\frac{1}{n} \alpha(N,V) T^{n} + f(N,V) ##

    Where the function ##f(N,V)## has to do with the fact that I'm only taking the derivative wrt. to T and can lose such additional terms in general.

    I also know that ##S(V,0)=0## which means that ##f(N,V,)=0## which means I can always use this trick to find the entropy if the heat capacity is known. Obviously if ##C_{V}## is an uglier function of T we'd have to integrate and so on.

    ##QUESTION##: When is it okay to do such a reasoning and when isn't it?
     
  2. jcsd
  3. Jan 14, 2016 #2
    For an ideal gas, assuming CV is constant, ##S = N(C_vln(T) + R ln(V)+C)##. So this doesn't even work for an ideal gas. For real substances, there are phase changes that occur prior to getting to absolute zero that need to be included also.
     
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