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In some process the temperature of a sub...

In some process the temperature of a substance depends on its entropy `S` as `T = a S^n`, where `a` and `n` are constants. Find the corresponding heat capacity `C` of the substance as a function of `S`. At what condition is `C lt 0` ?

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Here `T = a S^n` or ` S = ((T)/(a))^((1)/(n))`
Then `C = T(1)/(n) (T^((1)/(n) -1))/(a^(1//n)) = (S)/(n)`
Clearly `C lt 0` if `n lt 0`.
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