Question

5 moles of oxygen are heated at constant volume from $10{}^{\circ }Cto20{}^{\circ }C.$ What will be the change in the internal energy of gas?
(The molar heat of oxygen at constant pressure, $C_p=7.03$ cal mol${}^{-1}$ K${}^{-1}$ and $R=8.31J$ mol${}^{-1}{K}^{-1}$)

• A. $352cal$
• B. $252cal$
• C. $152cal$
• D. $452cal$

Answer 1

The correct option is B $252cal$

Given,
$R=8.31Jmo{l}^{-1}{K}^{-1}$
$=\frac{8.31}{4.18}calmo{l}^{-1}{K}^{-1}$
$=1.99calmo{l}^{-1}{K}^{-1}$
We know that, $C_p-C_v=R$
$\Rightarrow C_v=C_p-R$
$=7.03-1.99$
$=5.04calmo{l}^{-1}$
Heat absorbed by 5 mole of oxygen in heating from $10{}^{\circ }C$ to $20{}^{\circ }C$
$=5\times C_v\times △T=5\times 5.04\times 10=252cal$
Since, the gas is heated at constant volume, no external work i.e. change in internal energy wll be equal to heat absorbed,
$△E=q+w=252+0=252$ cal