During an adiabatic process an object does $$100\,J$$ of work and its temperature decreases by $$5K.$$ During another process it does $$25\,J$$ of work and its temperature decreases by $$5K.$$ Its heat capacity for $${2^{nd}}$$ process is
A.
$$20\,J/K$$
B.
$$24\,J/K$$
C.
$$15\,J/K$$
D.
$$100\,J/K$$
Answer :
$$15\,J/K$$
Solution :
For adiabatic process, $$dU = - 100\,J$$ which remains same for other processes also.
Let $$C$$ be the heat capacity of 2nd process then
$$\eqalign{
& - \left( C \right)5 = dU + dW = - 100 + 25 = - 75 \cr
& \therefore C = 15\,J/K \cr} $$
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