JEE Main 2022 — Thermodynamics (C) Question with Solution

$2.2 \mathrm{g}$ of nitrous oxide $\left({\mathrm{N}}_2\mathrm{O}\right)$ gas is cooled at a constant pressure of $1$ atm from $310 \mathrm{K}$ to $270 \mathrm{K}$ causing the compression of the gas from $217.1 \mathrm{mL}$ to $167.75 \mathrm{mL}$. The change in internal energy of the process, $△\mathrm{U}$ is $\text{'}-\mathrm{x}\text{'}\mathrm{J}$. The value of $\text{'}x\text{'}$ is _____.

[nearest integer]

(Given: atomic mass of $\mathrm{N}=14 \mathrm{g}{ \mathrm{mol}}^{-1}$ and of $\mathrm{O}=16 \mathrm{g}{ \mathrm{mol}}^{-1}$. Molar heat capacity of ${\mathrm{N}}_2\mathrm{O}$ is $100 {\mathrm{JK}}^{-1}{ \mathrm{mol}}^{-1}$)