Answer to Question #241143 in Molecular Physics | Thermodynamics for hassan ihtisham

Question

During an adiabatic process pressure of gas is found to be proportional to the
cube of its temperature. The ratio of Cp/Cv is A. 2
B. 44319 C. 44257
D. 44289

Answer 1

$\frac{C_p}{C_V}=\gamma,$

$T^{\gamma}p^{1-\gamma}=const,\implies$

$p\sim T^{\frac{\gamma}{\gamma-1}},$ but

$p\sim T^3,\implies$

$\frac{\gamma}{\gamma-1}=3,$ where

$\gamma=\frac 32.$