Question

During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio \(\frac{C_{p}}{C_{v}}\) for the gas is
(A) \(\frac{3}{2}\)
(B) \(\frac{7}{2}\)
(C) \(\frac{5}{3}\)
(D) \(\frac{9}{7}\)

Answer 1

Ans: (A)
 \(P \propto T^{3}\)
or, \(\mathrm{P}=\mathrm{KT}^{3}\) or \(\mathrm{PT}^{-3}=\mathrm{K} \ldots \ldots\) (i)
For reversible adiabatic process
\(T^{\gamma} P^{1-\gamma}=K\)
\(\mathrm{PT}^{\frac{\gamma}{1-\gamma}}=\mathrm{K} \cdots \cdots\) (ii)
Comparing equation (i) and equation (ii)
\(\frac{\gamma}{1-\gamma}=-3\)
or \(\gamma=-3+3 \gamma\)
or \(\gamma=\frac{3}{2}\)

Answer 2

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Answer 3

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