Placing a mass on a piston in a heat sink

Question

Imagine a problem with a piston filled with an ideal gas placed in a water bath. The gas is initially at a temperature equal to that of the water bath $T_1$ with volume $V_1$. A mass is then added to the piston. If the water bath is maintained at $T_1$ and the gas reaches a final volume $V_f$, what processes are involved in this sequence?

My initial thought was an adiabatic compression to the final state however I realised an adiabatic compression from $P_1,V_1$ to $P_2,V_f$ would result in a final temperature $T_f>T_1$ after which heat exchange would occur resulting in a different final volume.

My question is, what processes are involved the process of placing the mass on the piston, compressing the gas, and maintaining it at temperature $T_1$? Is it possible to assume this to be isothermal (ie. Heat exchange is instantaneous)?

Answer 1

what processes are involved in this sequence?

It is an irreversible constant external pressure process.

Although the temperature at the boundary between the gas and the bath is at the temperature of the bath, the compression will cause internal temperatures to initially rise so the process is not isothermal because temperatures will vary spatially within the gas.

For the process to be adiabatic during the compression, a very large mass would have to be applied to the piston so as to compress the gas so rapidly that there is no time for heat transfer to occur during the compression.

However, at the end of the compression it will no longer be adiabatic since the elevated internal temperatures will result in heat transfer from the gas to the bath until the gas reestablishes thermal equilibrium with the bath.

Hope this helps.

Answer 2

No. The surface of the gas remains T1, but the interior of the gas gets hotter, depending on the distance from the cylinder wall. So the gas gradually releases heat as the piston falls.