How does heating a gas in a vessel with a piston affect the pressure inside?

[AdityaDev]

If I fill a cylindrical vessel with a gas and put a piston of some mass on top of it and slowly heat the vessel, the piston will move up. But does the pressure inside the vessel change? ( vessel is insulated).if pressure doesn't change, how does the piston move up?

Pressure on piston : $P - p$ where P is atmospheric pressure and p is pressure exerted by gas.
Pressure on gas: $mg/A + P$

Also in W = PdV, does P denote external pressure or pressure exerted by gas?

 

[zoki85]

If pressure doesn't change piston will go up if the volume of the heated gas increase.

 

[Nugatory]

If I fill a cylindrical vessel with a gas and put a piston of some mass on top of it and slowly heat the vessel, the piston will move up. But does the pressure inside the vessel change? ( vessel is insulated).if pressure doesn't change, how does the piston move up?

This process proceeds by infinitesimal steps so that the system is always in equilibrium. The heat causes an infinitesimal increase in pressure, which lifts the piston infinitesimally, which increases the volume infinitesimally, which reduces the pressure so that it goes back to $mg/A$ with the piston at the new, slightly higher position and the system still in equilibrium. Then as heat continues to flow into the vessel the pressure increases again, moving the piston again... Imagine this process happening as an infinitely large number of infinitely small steps, and you'll see how the system can remain in equilibrium even as the piston moves and work is being done.
(If you've studied calculus and are familiar with the concepts behind integration, this may seem more natural).

It is also well to remember that when a thermodynamic system is in equilibrium, that doesn't mean that quantities such as pressure and temperature are fixed - they are constantly fluctuating around their equilibrium values. For any reasonably-sized system, these fluctuations are far too small to notice, but they provide a natural scale for the "small steps" that allow the system to change while remainingin equilibrium.

Also in W = PdV, does P denote external pressure or pressure exerted by gas?

They're the same, as the system is always in equilibrium.

 

[AdityaDev]

Thank you... i just solved 14 problems from Irodov's problems in general physics using that concept.