Given data

• Gas is diatomic with $\gamma = 1.4$
• Work done in isobaric expansion: $W = 100\,\text{J}$
• We need heat supplied, $Q$

Use relation for an isobaric process

For an isobaric process, $W = nR\Delta T$

Also, $Q = nC_p\Delta T$

Therefore, $\frac{Q}{W} = \frac{C_p}{R}$

Find $C_p$ in terms of $R$ using $\gamma$

We know, $\gamma = \frac{C_p}{C_v} = 1.4$ and $C_p - C_v = R$

Using the standard relation, $C_p = \frac{\gamma R}{\gamma - 1}$

Substitute $\gamma = 1.4$: $C_p = \frac{1.4R}{1.4 - 1} = \frac{1.4R}{0.4} = 3.5R$

Now calculate $Q$

$\frac{Q}{W} = \frac{C_p}{R} = 3.5$

Hence, $Q = 3.5W = 3.5 \times 100 = 350\,\text{J}$

Match with options

• A: 150 J
• B: 490 J
• C: 350 J
• D: 250 J

So the correct option is C.