Two identical cylinders, each fitted with a movable piston of the...

For an isobaric process, the heat supplied is $Q = n C_p \Delta T$ and the work done by the gas is $W = n R \Delta T$.

From these, the work done can be expressed in terms of heat supplied as:
$W = Q \left(\dfrac{R}{C_p}\right)$

For the monatomic gas $A$, the molar heat capacity at constant pressure is $C_{p,A} = \dfrac{5}{2}R$.
Thus, $W_A = Q \left(\dfrac{R}{\dfrac{5}{2}R}\right) = \dfrac{2Q}{5}$

For the diatomic gas $B$, the molar heat capacity at constant pressure is $C_{p,B} = \dfrac{7}{2}R$.
Thus, $W_B = Q \left(\dfrac{R}{\dfrac{7}{2}R}\right) = \dfrac{2Q}{7}$

The work done by the gas in moving the piston by distance $x$ is $W = P \Delta V = P (\pi r^2) x$. Since the pressure $P$ and radius $r$ are identical for both cylinders, the displacement $x$ is directly proportional to the work done $W$.

Therefore, the ratio of displacements is:
$\dfrac{x_A}{x_B} = \dfrac{W_A}{W_B} = \dfrac{\dfrac{2Q}{5}}{\dfrac{2Q}{7}} = \dfrac{7}{5}$

Answer: $7 : 5$