Question 37. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \frac{C_{p}}{C_{v}} for the gas is :
(1) \frac{5}{3}
(2) \frac{3}{2}
(3) \frac{7}{5}
(4) \frac{9}{7}
Answer (2)
Explanation:
P \propto T^{3} \Rightarrow PT^{-3}=\mathrm{cons} \ tantPV^{\gamma}= constant
P\left(\frac{nRT}{P}\right)^{\gamma}=\mathrm{const}P^{1-\gamma} T^{\gamma}= constant
PT^{\frac{\gamma}{1-\gamma}}= constant
\frac{\gamma}{1-\gamma}=-3 \gamma=-3+3 \gamma 3=2 \gamma \gamma=\frac{3}{2}