When $2 \text{ moles}$ of a monatomic gas expands adiabatically from a temperature of $80^{\circ} C$ to $50^{\circ} C$,the work done is $W$. The work done when $3 \text{ moles}$ of a diatomic gas expands adiabatically from $50^{\circ} C$ to $20^{\circ} C$ is: (in $W$)

In an adiabatic process,the initial and final temperatures of $1 \, mol$ of an ideal gas are $T_1$ and $T_2$ respectively. The change in internal energy of the gas is .......

The mean kinetic energy of monoatomic gas molecules under standard conditions is $\langle E_1 \rangle$. If the gas is compressed adiabatically $8$ times to its initial volume,the mean kinetic energy of gas molecules changes to $\langle E_2 \rangle$. The ratio $\frac{\langle E_2 \rangle}{\langle E_1 \rangle}$ is

In a thermodynamic process,there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100 K$ and the universal gas constant $R = 8.0 J mol^{-1} K^{-1}$,the decrease in its internal energy,in Joule,is. . . . .

The $P-V$ diagram of a diatomic ideal gas system undergoing a cyclic process is shown in the figure. The work done during the adiabatic process $CD$ is (use $\gamma=1.4$) (in $J$):