Question

\(70~\text{cal}\) of heat is required to raise the temperature of \(2\) moles of an ideal gas at constant pressure from \(30^\circ~\text{C}\) to \(35^\circ~\text{C}\). The amount of heat required to raise the temperature of the same gas through same range of temperature (\(30^\circ~\text{C}\) to \(35^\circ~\text{C}\)) at constant volume is
Given \((\gamma=7/5)\)

Answer 1

Heat absorbed at constant pressure to increase the temperature by \(\Delta T\),
\(Q_p=nC_p \Delta T~...(i)\)
\(C_p=\)molar heat capacity at constant pressure
\(\Rightarrow \)Heat required to raise the temperature of same gas by \(\Delta T\) at constant volume is,
\(Q_V=nC_V \Delta T~...(ii)\)
\(C_V=\)molar heat capacity at constant volume
\(\Rightarrow \dfrac{Q_V}{Q_p}=\dfrac{C_V}{C_p}\)
\( Q_V=Q_p \times \dfrac{C_V}{C_p}\)
\(Q_V=70 \times \dfrac{1}{\gamma}\)
\(\therefore Q_V=70 \times\dfrac{5}{7}=50~\text{cal}\)