Find the temperature `T` as a function of the entropy `S` of a substance for a polytropic process in which the heat capacity of the substance equal `C`. The entropy of the substance is known to be equal to `S_0` at the temperature `T_0`. Draw the approximate plots `T (S)` for `C gt 0` and `C lt 0`.

Explanation

We know,
`S - S_0 = int_(T_0)^t (CdT)/(T) = C 1n (T)/(T_0)`
assuming `C` to be a known constant.
Then `T = T_0 exp ((S - S_0)/( C))`.
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