In a thermodynamic process,if $\Delta W$ and $\Delta U$ are the work done and the change in the internal energy of a system respectively,then:

Initially,the pressure of $1 \text{ mole}$ of an ideal gas is $10^5 \text{ Nm}^{-2}$ and its volume is $16 \text{ litres}$. When it is adiabatically compressed,its final volume is $2 \text{ litres}$. Calculate the work done on the gas. [Given: Molar specific heat at constant volume $C_v = \frac{3R}{2}$] (in $\text{ kJ}$)

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $(P, \rho)$ to $(P^{\prime}, \rho^{\prime})$. If $\frac{\rho^{\prime}}{\rho}=32$,then $\frac{P^{\prime}}{P}$ is:

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 ........ $K$.

Slope of isotherm for a gas (having $\gamma = 5/3$) is $3 \times 10^5 \, N/m^2$. If the same gas is undergoing adiabatic change,then the adiabatic elasticity at that instant is ........... $\times 10^5 \, N/m^2$.