Question

Two moles of a rigid diatomic gas does a work \(\frac{Q}{4}\) when the amount of heat supplied is \(Q\). In this process the total heat capacity of the gas is (\(R\) = gas constant)

• A. \(\frac{12R}{5}\)
• B. \(\frac{10R}{7}\)
• C. \(\frac{15R}{4}\)
• D. \(\frac{20R}{3}\)

Hint:

Use the first law to get the change in internal energy, then express heat supplied in terms of the temperature change.

Answer 1

The Correct Option is D

Step 1: Ratio of energies
$\dfrac{\Delta U}{Q}=\dfrac{3}{4}$.

Step 2: Express in terms of C
$\Delta U=5R\Delta T$ and $Q=C\Delta T$, so $\dfrac{5R}{C}=\dfrac{3}{4}$.

Step 3: Solve
$C=\dfrac{20R}{3}$, which is option (D).

Final Answer:
The heat capacity equals 20R by 3. \[ \boxed{\text{(D) }\dfrac{20R}{3}} \]