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J co
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Homework Statement
Which of the following are not extensive functions:
S[1] = (N/V)[S[0]+[C][v] ln(T) + R ln(V)]
S[2] = (N)[S[0]+[C][v] ln(T) + R ln(V/N)]
S[3] = ([N][/2])[S[0]+[C][v] ln(T) + R ln(V/N)]
2. Homework Equations
I'm not really sure how to approach this problem. The definition that I find for extensivity states: "At fixed pressure and temperature, if the amount of a substance N is changed by a factor λ, the volume V is also changed by the same factor"
The corresponding example for the definition shows that if a system S(U,V,N) is combined with an identical system then the result should be 2U,2V,2N.
First - I get hung up on the language of these statements quite often which is pretty discouraging. When the definition says "fixed temperature and pressure" and the forumlae have ln(T), how can I say that the system has a fixed temperature?
Second - Should I be determining the extensivity by doubing S, for instance 2(S[1]), or should I consider if in the formula for the system N and V scale by the same factor?
3. The Attempt at a Solution
Once again, I'm not sure how to begin here.
If someone could simply point me in the right direction it would be greatly appreciated.
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