The simplest model that retains the effect of gas-wall heat transfer is presented in the drawing. The mass of the ideal gas is m, the mass of the cylinder wall is M, and the specific heat of the wall material is c. Now consider the expansion from an initial volume V1 and pressure P1 to a final volume V2, and assume that at any instant during this process, the ideal gas and the wall material are always at the same temperature. The expansion process is sufficiently slow so that the process can be considered to be reversible. Furthermore, the combined system (ideal gas and cylinder material) does not exchange heat with its surroundings.
(a) By using an entropy balance for the whole system including the gas and wall and the entropy relations for the ideal gas and the cylinder wall modeled as an incompressible substance
(b) When the wall heat capacity (Mc) is very large compared to the heat capacity of the gas approximately what process does the gas follow?
(c) When the wall heat capacity is very small or thermal contact with the wall is poor approximately what process does the gas follow?