How does the volume of a gas change if the gas is doing work on the environment? If the environment is doing work on the gas?

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txmedteach | High School Teacher | (Level 3) Associate Educator

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To figure this out, you'll need to go back to the definition of work. Work is best definite in a one-directional sense as the integral over a distance of the force applied. More simply,

W = F*d

where W=work, F=force, and d=distance.

In thermodynamics, we often see the term P*Delta(V) to represent work (not always, but most of the time in most chem classes). If you think about it, that would be roughly the same thing as force*distance.

Now, how to apply it to this problem. In order for the environment to do work on a gas, it must "push" the gas back in on itself. In other words, the external environmnet is pushing the particles in the gas by a certain force over a certain distance into a smaller volume. Therefore, when the environment is doing work on a gas, the gas is decreasing in volume.

The opposite holds if we say the gas is doing work on the environment. The gas is "pushing" outward on the environment over a certain distance away from its initial volume. This would indicate that the volume of gas is increasing because the gas is expanding.

I hope that helps!