\(\therefore \,dQ = n{C_p}dT;\,where\,{C_p}\,is\,specific\,heat\,at\,constant\,pressure.\)
or \(dQ = n\left( {\frac{5}{2}R} \right)dT\)
\(Also,\,dW = PdV = nRdT\,\left( {PV = nRT} \right)\)
Required ratio\( = \frac{{dW}}{{dQ}} = \frac{{nRdT}}{{n\left( {\frac{5}{2}R} \right)dT}} = \frac{2}{5}\)