When an ideal diatomic gas is heated at constant pressure, the fraction of heat energy supplied which increases the internal energy of the gas is:

$\begin{array}{rcl} & & amount of heat absorbed by gas at cons\tan t pressure is\\ & & {\text{dQ=nC}}_{\text{p}}\text{dT}\\ & & increase in internal energy of gas is\\ & & {\text{dU=nC}}_v\text{dT}\\ & & here m is mass of gas, \\ & & C is molar specific heat of gas,\\ & & dT is change in temperature\\ \therefore fraction of heat energy supplied which increases the internal energy of the gas is\frac{\text{dU}}{\text{dQ}}& =& \frac{{\text{C}}_{\text{v}}}{{\text{C}}_{\text{p}}}\\ \frac{\text{dU}}{\text{dQ}}& =& \frac{\text{5R/2}}{\text{7R/2}} substituting values for a diatomic gas\\ & & \frac{\text{dU}}{\text{dQ}}\text{=}\frac{5}{7}\text{.}\end{array}$