During an adiabatic process, the pressure is proportional to the cube of the temperature. Then ${C_p}/{C_v}$ is . . . . . . .

$5.6 \text{ liter}$ of helium gas at $STP$ is adiabatically compressed to $0.7 \text{ liter}$. Taking the initial temperature to be $T_1$,the work done in the process is

$V$ cc volume of a gas having $\gamma = \frac{5}{2}$ is suddenly compressed to $\frac{V}{4}$ cc. The initial pressure of the gas is $P$. The final pressure of the gas will be

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):

For an adiabatic expansion of an ideal gas,the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):

In a thermodynamic system,$\Delta U$ represents the increase in its internal energy and $dW$ is the work done by the system. Then,which of the following statements is correct?