What is the work for the free expansion of a gas into vacuum?

1 Answer

For an expansion into a vacuum, W=0W=0.

Explanation:

For a free expansion into a vacuum, a gas does no work, as there is no resistance on the gas as it expands, i.e. P=0P=0 and therefore the quantity -PDeltaV=0.

To say that W=-P_"atm"DeltaV is to say that the gas (the system) expands against an external pressure (applied by the surroundings), given specifically as atmospheric pressure P_"atm". This is not an expansion into a vacuum, simply by definition.

If we ignore the part about expanding into a vacuum and just think about the gas expanding, the sign of W should be negative from the perspective of the gas.

For an expansion we know that DeltaV is positive, as the final volume is greater than the initial volume (DeltaV=V_f-V_i) and P is always positive.

The work done by the system should therefore be negative for a regular expansion, as work is done by the system (the gas) onto the surroundings. The opposite is true for a compression (W > 0 for the gas).


Note that if you define W = PDeltaV, then it is from the perspective of the surroundings (around the gas), and not the system (the gas).