JEE Main 2018 — Thermodynamics

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $27^{\circ} \mathrm{C}$. The work done on the gas will be:

The value closest to the thermal velocity of a Helium atom at room temperature $(300 \mathrm{~K})$ in $\mathrm{ms}^{-1}$ is: $\left[\mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{~J} / \mathrm{K} ; \mathrm{m}_{\mathrm{He}}=7 \times 10^{-27} \mathrm{~kg}\right]$

One mole of an ideal monatomic gas is taken along the path $ABCA$ as shown in the $PV$ diagram. The maximum temperature attained by the gas along the path $BC$ is given by: 

One mole of an ideal monatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, ${27}^{o}C$ . The magnitude of work done on the gas will be:

Two moles of helium are mixed with n moles of hydrogen. If $\frac{{C}_{p}}{{C}_{v}}=\frac{3}{2}$ for the mixture then the value of $n$ is,

Two moles of an ideal monoatomic gas occupies a volume $V$ at ${27}^{o}C$ . The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ change in its internal energy.