Question

$70cal$ of heat are required to raise the temperature of $2$ moles of an ideal gas at constant pressure from $30^{\circ }C$ to $35^{\circ }C$. The amount of heat required in calories to raise the temperature of the same gas through the same range $\left(30^{\circ }C-35^{\circ }C\right)$ at constant volume is :

• A. 30 cal
• B. 50 cal
• C. 370 cal
• D. 90 cal

Answer 1

Answer: (B)

The heat required to raise the temperature of gas,
at constant volume $\left(C_V\right)$ is
$Q_V=C_V\Delta T\dots$ (i)
and at constant pressure is
$Q_P=C_P\Delta T\dots$ (ii)
Also, $\gamma =\frac{C_P}{C_V}\dots$ (iii)
From Eqs. (i), (ii) and (iii), we get
$\frac{Q_V}{Q_P}=\frac{C_P}{C_V}=\frac{1}{\gamma }$
For a diatomic gas $\gamma =\frac{7}{5}$
$\therefore Q_V=\frac{5}{7}\times 70=50cal$