An ideal gas at $27^{\circ}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma = \frac{5}{3}$,then the rise in temperature is ........ $K$.

$A$ gas has pressure $P$ and volume $V$. If the gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume,what will be the new pressure? (Given: $(32)^{1.4} = 128$)

The following figure shows an adiabatic cylindrical container of volume $V_0$ divided by an adiabatic smooth piston (area of cross-section = $A$) into two equal parts. An ideal gas $(C_P/C_V = \gamma)$ is at pressure $P_1$ and temperature $T_1$ in the left part,and a gas at pressure $P_2$ and temperature $T_2$ is in the right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose $x$ = displacement of the piston):

At $27^\circ C$,a gas is suddenly compressed such that its pressure becomes $1/8$th of the original pressure. The temperature of the gas will be $(\gamma = 5/3)$.

For adiabatic processes $\left( \gamma = \frac{C_p}{C_v} \right)$,which of the following relations is correct?

$A$ van der Waals gas obeys the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$. Its internal energy is given by $U=C T-\frac{n^2 a}{V}$. The equation of a quasistatic adiabat for this gas is given by