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Consider a cylindrical piston in which an ideal gas is sealed. The piston is well insulated, and it is assumed that all points in the gas are at temperature T and this temperature is fixed throughout the experiment.

Assume that the piston is weightless and frictionless. Also assume that there is no mass on the piston and that atmospheric pressure is 0.

Since the gas pressure is P, and the external pressure is 0, the gas will expand against the piston, and its volume will increase. Simultaneously, its pressure will decrease.

This process will technically occur for ever since the pressure P will never reach 0.

But what will be the work done by the gas from volume V1 (initial volume) to V2 assuming that the gas undergoes expansion ? Will it be positive or negative or even zero? What about the work done by the surroundings on the gas in this same process? Will it be positive or negative?

One argument tells me that the work done by the gas will be positive, because the gas pressure is directed against the piston, and the displacement of the piston is parallel to the gas pressure. Another argument tells me that the work done is zero, since the piston is weightless to begin with. Yet another argument tells me that the work done is positive, since the gas molecules themselves are being propelled in the direction of the gas pressure. Which of these is correct?

What about the work done by the gas as it expands from volum V1 to a volume of infinity? If this number can be expressed as a definite integral, does the integral diverge in this case?

These are all questions that are hindering but at the same time exciting my knowledge of physics. I appreciate all the help offered. Thanks!

BiP