Heat is supplied to a diatomic gas at constant pressure. Then the...

For a diatomic gas, the number of degrees of freedom is $f = 5$.

The molar heat capacity at constant volume is $C_v = \dfrac{f}{2}R = \dfrac{5}{2}R$.

The molar heat capacity at constant pressure is $C_p = C_v + R = \dfrac{7}{2}R$.

At constant pressure, the heat supplied is $\Delta Q = nC_p\Delta T = n\left(\dfrac{7}{2}R\right)\Delta T$.

The change in internal energy is $\Delta U = nC_v\Delta T = n\left(\dfrac{5}{2}R\right)\Delta T$.

The work done by the gas is $\Delta W = nR\Delta T = n\left(\dfrac{2}{2}R\right)\Delta T$.

The ratio $\Delta Q : \Delta U : \Delta W$ is $\dfrac{7}{2} : \dfrac{5}{2} : \dfrac{2}{2} = 7 : 5 : 2$.

Answer: $7 : 5 : 2$