During the isothermal expansion of an ideal gas:

In an isothermal expansion of a gaseous sample, the correct relation is: (consider $\mathrm{w}$ (work) with sign according to new IUPAC convention)

[The reversible and irreversible processes are carried out between same initial and final states.]

Calculate magnitude of $\mathrm{\Delta U}$ of the reaction in $\mathrm{kcal} {\mathrm{mol}}^{-1}$ for the hydrogenation of acetylene to ethene at constant volume and at $77°\mathrm{C}.$ Given that ${\mathrm{\Delta H}}_{\mathrm{f}}\left({\mathrm{H}}_2\mathrm{O}\right)=-67.8 \mathrm{kcal} {\mathrm{mol}}^{-1}$; ${\mathrm{\Delta H}}_{\text{comb }}\left({\mathrm{C}}_2{\mathrm{H}}_2\right)=-310.1 \mathrm{kcal} {\mathrm{mol}}^{-1}, {\mathrm{\Delta H}}_{\text{comb }}\left({\mathrm{C}}_2{\mathrm{H}}_4\right)=-337.2 \mathrm{kcal} {\mathrm{mol}}^{-1}$.

Round off your answer to the nearest integer.