$\Delta Q=n C_{p} \Delta T$

$\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}$

From first law of thermodynamics

$\Delta Q=\Delta U+\Delta W$

$\Delta \mathrm{W}=\Delta Q+\Delta \mathrm{U}$

$\Delta \mathrm{W}=\mathrm{nR} \Delta \mathrm{T}$

As $\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$

$\frac{\Delta W}{\Delta Q}=\frac{n R \Delta T}{n C_{P} \Delta T}=\frac{R}{C_{P}}=\frac{R}{\frac{5}{2} R}=\frac{2}{5}$