40 Calorie of heat is needed to raise the temperature of 1 mole of an ideal monoatomic gas from ${20}^{0}C$ to ${30}^{0}C$ at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume.

$$\begin{gathered} given heat required raise the temperature of gas Q_p=40 calorie; number of mole \mu =1; change in temperature dT={10}^{0}C \\ {Q}_p=\mu C_{P}dT ; here C_P=specific heat at cons\tan t pressure \\ \Rightarrow Q_p=1x{C}_{p}x(30-20)=40\mathrm{cal}orie \\ \Rightarrow Cp = 4 Cal/mol-K \\ we know C_v - C_p = R; here C_v=specific heat at cons\tan t volume; R=Universal gas cons\tan t=2cal/mol-K \\ \Rightarrow C_v = C_p – R = 4 – 2 = 2 Cal/mol-K \\ heat required raise the temperature of gas Q_v = \mu C_{v}dT = 1 x 2 x (30-20) = 20 cal \end{gathered}$$