Question

When heat $Q$ is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $\Delta T$. The heat required to produce the same change in tempreture at a constant pressure is

• A. $\frac{7}{5}Q$
• B. $\frac{5}{3}Q$
• C. $\frac{3}{2}Q$
• D. $\frac{2}{3}Q$

Answer 1

The correct option is A $\frac{7}{5}Q$

Given:
According to the question, heat $Q$ produces the $\Delta T$ temperature rise at constant volume.
We know that,
Amount of heat required $\left(Q\right)$ to raise the temprature at constant volume
$Q=n{C}_P\Delta T..........\left(i\right)$
Amount of heat required $\left(Q_1\right)$ to raise the temprature at constant pressure
$Q_1=n{C}_P\Delta T..........\left(ii\right)$
Dividing equation $\left(ii\right)$ and $\left(i\right)$, we get
$\therefore \frac{Q_1}{Q}=\frac{C_P}{C_V}$

$\Rightarrow Q_1=\left(Q\right)\left(\frac{7}{5}\right)(\because \gamma =\frac{C_P}{C_V}=\frac{7}{5})$.

Hence option $\left(C\right)$ is correct.