NEET UG PHYSICS MCQ: THERMODYNAMICS

One mole of an ideal monatomic gas is taken from state $\mathrm{A}$ to state B through the process $P=(3 / 2) T^{1 / 2}$. It is found that its temperature increases by $100 \mathrm{~K}$ in this process. Now it is taken from state B to C through a process for which internal energy is related to volume as $U_{\text {int }}=(1 / 2) V^{1 / 2}$. Find the total work performed by the gas (in joule), if it is given that volume at $\mathrm{B}$ is $100 \mathrm{~m}^3$ and at C it is $1600 \mathrm{~m}^3$. (Use $R=8.3 \mathrm{~J} / \mathrm{mol} \mathrm{K}$.)