• # question_answer 33) When two moles of oxygen is heated from $0{}^\circ C$ to $10{}^\circ C$ at constant volume, its internal energy changes by 420 J. What is the molar specific heat of oxygen at constant volume? A) $5.75\text{ }J\text{ }{{K}^{-1}}\text{ }mo{{l}^{-1}}$             B) $~10.5\text{ }J\text{ }{{K}^{-1}}\text{ }mo{{l}^{-1}}$C) $~21\text{ }J\text{ }{{K}^{-1\text{ }}}mo{{l}^{-1~}}$    D) $42\text{ }J\text{ }{{K}^{-1}}mo{{l}^{-1}}$

Since, the volume remains constant, dW= 0. Hence, $\Delta Q=\Delta U=420\,J.$But $\Delta Q=n{{C}_{v}}dT=2\times {{C}_{v}}\times 10$$(\because \,dT=10{{\,}^{o}}C=10\,K)$ or $20{{C}_{v}}=420\,or$ ${{C}_{v}}=21\,J{{K}^{-1}}mo{{l}^{-1}}$ Hence, the correction option is [c].