Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \(\Delta Q : \Delta U : \Delta W\) is _______.

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: \(7 : 5 : 2\)