Question

The molar specific heat of oxygen at constant pressure is $C_{p}=\text{7.03} \, cal \, mol^{- 1} \, K^{- 1}$ and $R=8.31 \, J\text{ mol}^{\text{-1}} \, \, \text{K}^{\text{-1}}$ . The amount of heat taken by $5$ moles of oxygen, when heated at constant volume from $10 \,{}^\circ C$ to $20 \,{}^\circ C,$ will be approximately

• A. $25 \, cal$
• B. $50 \, cal$
• C. $253 \, cal$
• D. $500 \, cal$

Answer 1

Answer: (C)

Given, $C_{p}=7.03 \, cal \, mol^{- 1} \, K^{- 1} \, ,R=8.315 \, J \, mol^{- 1} \, K^{- 1}$
$n=5 \, moles$ , $T_{2}=20^{ \, o}C, \, T_{1}=10^{ \, o}C,$
$\Delta Q= \, ?$
$\therefore \, \, $ Heat, $\Delta Q=nC_{V}\Delta T$
$=n\left(C_{p} - R\right)\Delta T$ $\left[\because C_{p} - C_{v} = R\right]$
$=5\left[7.03 - \frac{8.31}{4.2}\right]\times \left(20 - 10\right)$
$\sim eq253 \, cal$