One mole of an ideal gas requires 207 J heat to raise it’s temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume the heat required to raise the temperature by 10 K for the same gas, will be : (given R=8.3 J/mol/K)

$\begin{array}{rcl}amount of heat required to raise the temperature of gas at cons\tan t pressure is Q_p& =& n{C}_p∆T\end{array}$

$\begin{array}{rcl}given Q_p& =& 207Joule;number of mole n=1;change in temperature ∆T=10K\end{array}$

$\begin{array}{rcl} & & \\ & & substitute the given values in above equation of Q_p\\ & & \text{207=1}\times {\text{C}}_{\text{p}}\times 10.........\left(1\right)\\ amount of heat required to raise the temperature of gas at cons\tan t volume is Q_v& =& n{C}_v∆T\\ given n& =& 1;∆T=10K, substitute in Q_v\\ & & {\text{Q}}_v\text{=1}\times {\text{C}}_{\text{v}}\times 10 ........\left(2\right)\\ & & subtract, eqn\left(1\right)-eqn\left(2\right),\\ & & \left({\text{207-Q}}_v\right)\text{=10}({\text{C}}_{\text{p}}-{\text{C}}_{\text{v}})\\ & \Rightarrow & {\text{207-Q}}_v\text{=10}\times \text{8.3=83}\\ & \Rightarrow & {\text{Q}}_v\text{=207-83}\\ & \Rightarrow & {\text{Q}}_v\text{=124\hspace{0.17em}J}\end{array}$