Question

The pressure P1 and density d1 of diatomic gas $\gamma = \frac{7}{5}$ changes suddenly to $P_2 > P_1$ and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes _____ times of its initial temperature.
(Given $\frac{d_2}{d_1} = 32$)

Answer 1

$P_1V_1^\gamma = P_2V_2^\gamma$

$\frac{P_1}{d_1^\gamma} = \frac{P_2}{d_2^\gamma}$

$\frac{d_1T_1}{d_1^\gamma} = \frac{d_2T_2}{d_2^\gamma}$

$T_2 = \left(\frac{d_2}{d_1}\right)^{\gamma-1} T_1$

$= (32)^{\frac{2}{5}} T_1$
$T_2 = 4T_1$