1. Use the first law of thermodynamics

For any thermodynamic process, $Q = \Delta U + W$ where:

• $Q$ = heat absorbed
• $\Delta U$ = change in internal energy
• $W$ = work done by the gas

Given: $W = 10\,\text{J}$

2. Internal energy change for a diatomic rigid gas

For a diatomic gas with rigid molecules, the degrees of freedom are: $f=5$ So, $C_V = \frac{f}{2}R = \frac{5}{2}R$

At constant pressure, $W = nR\Delta T$ Thus, $nR\Delta T = 10$

Now, $\Delta U = nC_V\Delta T = n\left(\frac{5}{2}R\right)\Delta T = \frac{5}{2}(nR\Delta T)$ Substitute $nR\Delta T = 10$: $\Delta U = \frac{5}{2}\times 10 = 25\,\text{J}$

3. Calculate heat absorbed

Using $Q = \Delta U + W$ $Q = 25 + 10 = 35\,\text{J}$

4. Check options

• A: $35\,\text{J}$ ✅
• B: $30\,\text{J}$ ❌
• C: $25\,\text{J}$ ❌
• D: $40\,\text{J}$ ❌

Therefore, the correct answer is A.