A sample of gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma=3 / 2$. The work done by the gas in the process is : $(\mu=1 \mathrm{~mole})$

$5.6$ $liter$ of helium gas at $STP$ is adiabatically compressed to $0.7$ $liter$. Taking the initial temperature to be $T_1$, the work done in the process is

The pressure and density of a diatomic gas $(\gamma = 7/5)$ change adiabatically from $(P, d)$ to $(P', d')$. If $\frac{{d'}}{d} = 32$, then $\frac{{P'}}{P}$ should be

Air is filled in a motor tube at ${27^o}C$ and at a pressure of $8$ atmospheres. The tube suddenly bursts, then temperature of air is $[{\rm{Given}}\,\,\gamma \,{\rm{of}}\,{\rm{air}} = \,1.5]$

The pressure $P_{1}$ and density $d_{1}$ of diatomic gas $\left(\gamma=\frac{7}{5}\right)$ changes suddenly to $P _{2}\left(> P _{1}\right)$ and $d _{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes $......$ times of its initial temperature.$\left(\right.$ given $\left.\frac{ d _{2}}{ d _{1}}=32\right)$

During the adiabatic expansion of $2 \,moles$ of a gas, the internal energy was found to have decreased by $100 J$. The work done by the gas in this process is ..... $J$