During an adiabatic expansion of $2\, moles$ of a gas,the change in internal energy was found to be $-50\, J$. The work done during the process is ...... $J$.

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

Under an adiabatic process,the volume of an ideal gas gets doubled. Consequently,the mean collision time between the gas molecules changes from $\tau_{1}$ to $\tau_{2}$. If $\frac{C_{p}}{C_{v}}=\gamma$ for this gas,then a good estimate for $\frac{\tau_{2}}{\tau_{1}}$ is given by:

In an adiabatic change,the pressure and temperature of a monoatomic gas are related by the relation $p \propto T^{C}$,where $C$ is equal to

In the $P-V$ diagram shown,there are two adiabatic parts of the same gas intersecting two isothermals at $T_1$ and $T_2$. The ratio $\left(\frac{V_b}{V_a}\right)$ is equal to

During an adiabatic process, the pressure of a gas is proportional to the cube of its temperature. The value of $C_p / C_V$ for that gas is