Molecular weight of nitrous oxide (N2O) = 44 g/mol
Number of moles of N2O = \(\frac{2.2}{44} = 0.05 mol\)
Specific heat capacity of N2O = 880 J/g.K
∴ Heat release on cooling from 310K to 270 K
q = -2.2 x 880 x 40 K
q = -77.44 KJ
Negative sign indicates heat released.
∴ Work done by surrounding on system to compares the gas from 217.1 ml to 167.75 ml at constant pressure.
It means work done by surrounding is irreversible.
\(\therefore W = -P \times \triangle V\)
\(= - 1.01 \times 10^5 \times (167.75 - 217.1 ml)\)
\(= 1.01 \times 10^5 \times 0.049 J\)
\(W = 4.95 kJ\)
Using 1st Law of thermodynamics
\(\triangle U = q + W\)
\(\triangle U = -77 .44 KJ + 4.95KJ\)
\(\triangle U = -72.49 KJ\)
Hence change in internal energy \(\triangle U = -72.49 KJ\)