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 temperature, at a constant pressure is

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

Answer 1

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


Heat supplied to the gas at constant volume,
$Q=n{C}_V\Delta T$
Heat supplied to the gas at constant pressure,
$Q^{\prime }=n{C}_P\Delta T$

$\therefore \frac{Q{}^{{}^{\prime }}}{Q}=\frac{C_P}{C_V}$

And we know, $\frac{C_P}{C_V}=\gamma$

For diatomic gas And we know, $\frac{C_P}{C_V}=\gamma =\frac{7}{5}$
$\Rightarrow Q^1=\frac{7}{5}Q$
Final answer: (𝑎)