One mole of an ideal gas expands adiabatically from $200 \,K$ to $250 \,K$. If the specific heat of the gas at constant volume is $0.8 \,kJ \,kg^{-1} \,K^{-1}$, then the work done by the gas is

Two moles of an ideal monoatomic gas at $27^{\circ}C$ occupies a volume of $V$. If the gas is expanded adiabatically to the volume $2V$,then the work done by the gas will be ....... $J$ $[\gamma = 5/3, R = 8.31 \text{ J/mol K}]$

When air of the atmosphere rises up,it cools. Why?

Consider a spherical shell of radius $R$ at temperature $T$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $E = \frac{U}{V} \propto T^4$ and pressure $P = \frac{1}{3} \left( \frac{U}{V} \right)$. If the shell now undergoes an adiabatic expansion,the relation between $T$ and $R$ is:

$A$ 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

The $P-V$ diagram for two adiabatic processes is given. Curves $1$ and $2$ correspond to: