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During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:
A
$\frac{3}{2}$
B
$\frac{4}{3}$
C
2
D
$\frac{5}{3}$
Detailed Solution
$P \propto T^3$ and $PV = nRT$ give $PV^{3/2}$ = constant.
Comparing with $PV^\gamma$ = constant: $\gamma = \frac{C_p}{C_v} = \frac{3}{2}$
Comparing with $PV^\gamma$ = constant: $\gamma = \frac{C_p}{C_v} = \frac{3}{2}$