Two identical samples of a gas are allowed to expand $(i)$ isothermally $(ii)$ adiabatically. Work done is

At $N.T.P.$ one mole of diatomic gas is compressed adiabatically to half of its volume $\gamma = 1.41$. The work done on gas will be ....... $J$

Consider a cycle tyre being filled with air by a pump. Let $V$ be the volume of the tyre (fixed) and at each stroke of the pump $\Delta V$ $(< < V)$ of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from $P_1$ to $P_2$ ?

In an adiabatic process where in pressure is increased by $\frac{2}{3}\% $ if $\frac{{{C_p}}}{{{C_v}}} = \frac{3}{2},$ then the volume decreases by about

The slopes of isothermal and adiabatic curves are related as

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