A diatomic gas ( γ = 1 . 4 ) does 200J of work when it is expanded...

For degree of freedom, we can write

$\gamma = 1 + \dfrac{2}{f} = 1 . 4 ⇒ \dfrac{2}{f} = 0 . 4$

$⇒ f = 5$

For isobaric process, $W = nR\DeltaT = 200J$.

Now, we can write

$Q = \left(\dfrac{f + 2}{2}\right)nR \Delta T$

$= \dfrac{7}{2} \times 200 = 700J$