Question

$5$ mole of oxygen are heated at constant volume from ${10}^{o}C$ to ${20}^{o}C$. What will be the change in the internal energy of gas? The molar heat of oxygen at constant pressure, $C_P=7.03cal$ ${mol}^{-1}{deg}^{-1}$ and $R=8.31J{mol}^{-1}{deg}^{-1}$.

Answer 1

$R=8.31J{mol}^{-1}{deg}^{-1}=\frac{8.31}{4.18}cal$ ${mol}^{-1}{deg}^{-1}$
$=1.99cal$ ${mol}^{-1}{deg}^{-1}$
We know that $C_P-C_V=R$
or $C_V=C_P-R=7.03-1.99=5.04cal$ ${mol}^{-1}{deg}^{-1}$
Heat absorbed by $5$ mole of oxygen in heating from ${10}^{o}C$ to ${20}^{o}C$
$=5\times C_V\times \Delta T=5\times 5.04\times 10=252cal$
Since, the gas is heated at constant volume, no external work is done,
i.e., $w=0$
So, change in internal energy will be equal to heat absorbed,
$\Delta U=q+w=252+0=252cal$