A gas for which γ = 5 / 3 \ (γ = C_p / C_v ) is heated at constant...

Heat supplied at constant pressure is given by $\Delta Q = n C_p \Delta T$

Work done by the gas is given by $\Delta W = P \Delta V = n R \Delta T$

The fraction of heat used for external work is $\dfrac{\Delta W}{\Delta Q} = \dfrac{n R \Delta T}{n C_p \Delta T} = \dfrac{R}{C_p}$

Using Mayer's relation $C_p - C_v = R$ and $\gamma = \dfrac{C_p}{C_v}$, we have $C_p - \dfrac{C_p}{\gamma} = R$

$\dfrac{R}{C_p} = 1 - \dfrac{1}{\gamma} = \dfrac{\gamma - 1}{\gamma}$

Given $\gamma = \dfrac{5}{3}$, substituting this value:

$\dfrac{\Delta W}{\Delta Q} = \dfrac{\dfrac{5}{3} - 1}{\dfrac{5}{3}} = \dfrac{2}{5}$

Percentage of heat used for external work is $\dfrac{2}{5} \times 100\% = 40\%$

Answer: $40\ \%$