Molecular weight of nitrous oxide \(\left(\mathrm{N}_2 \mathrm{O}\right)=44 \mathrm{~g} / \mathrm{mol}\)
Number of moles of \(\mathrm{N}_2 \mathrm{O}=\frac{2.2}{44} \quad 0.05 \mathrm{~mol}\)
Specific heat capacity of \(\mathrm{N}_2 \mathrm{O}=880 \mathrm{~J} / \mathrm{g} . \mathrm{K}\)
\(\therefore\) Heat release on cooling from \(310 \mathrm{~K}\) to \(270 \mathrm{~K}\)
\(q=-2.2 \times 880 \times 40 \mathrm{~K}\)
\(q=-77.44 \mathrm{KJ}\)
Negative sign indicates heat released.
\(\therefore\) Work done by surrounding on system to compares the gas from \(217.1 \mathrm{ml}\) to \(167.75 \mathrm{ml}\) at constant pressure.
It means work done by surrounding is irreversible.
\(\begin{aligned} & \therefore W= P \times \Delta V \\ & =1.01 \times 10^5 \times(167.75 \quad 217.1 \mathrm{ml} l) \\ & =1.01 \times 10^5 \times 0.049 J \\ & W=4.95 k . J \end{aligned}\)
Using 1st Law of thermodynamics
\(\begin{aligned} & \Delta U=q+W \\ & \Delta U=-77.44 K J + 4.95 K J \\ & \Delta U=-72.49 K J \end{aligned}\).
$\therefore x = 72.$