[A Level Physics] Relation of specific latent heat of vaporization and pressure.

So using △U=Q-W which is △U=mL-p△V, we know that the change in internal energy has to be the same for the vaporization of the liquid. So if pressure increases rearranging mL= △U+p△V mL would increase and since the mass is the same the specific latent heat increases. But my question is why is the change in volume the same as the change in volume found when calculating using the smaller pressure? I'm confused about whether the change in volume would vary with the pressure at a constant temperature or if is it the temperature that varies at a constant volume. https://bestexamhelp.com/exam/cambridge-international-a-level/physics-9702/2022/9702-s22-qp-42.php Third question here