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Please correct me where my reasoning is wrong.

Consider a cylindrical piston in which an ideal gas is sealed. The gas is initially at temperature T. The piston is well insulated, so that all thermodynamic processes are at least adiabatic. Assume that the piston is massless and frictionless. Atmospheric pressure is assumed to be negligible.

Now the cross-section of the piston is A1. A block of mass M is placed on the piston and the cross-section of the block is A2. Immediately, due to the weight of the block, a downward force of Mg acts on the piston. This can equally be interpreted as a pressure of Mg/A2 (or is it Mg/A1 ? ).

On the other hand, the gas exerts an outward pressure on the piston much greater than that of the block, so that the piston begins to expand. As the piston expands, the gas's volume increases proportional to the height of the piston, since the cross-section of the piston is a constant.

Now as the gas's volume increases, its pressure must decrease. Eventually, its pressure must reduce to a value equal to the pressure exerted by the block. The piston is now in static equilibrium, since the gas pressure on it equally opposes the pressure due to the block's weight.

My question is, over this process, as the gas expands, can the work it does on the block be calculated? What about the work that the block does on the gas? Which of these is positive, and why?

Is the overall expansion process isothermal? One argument tells me that since the process is adiabatic (by assumption), nonzero work done must be accompanied by nonzero internal energy change (due to the first law), and thus nonzero temperature change (due to the relation between U and T). Thus the temperature must change and the process cannot be isothermal.

Another argument tells me that it is mathematically impossible to calculate the work done by the gas when both temperature and volume change?

So I appreciate all help in this helping understand this concept.

BiP