Work done by a gas

When we talk about the work done by a thermodynamic system, we often talk about the work done a gas confined to a container with a moving wall (a piston for example). This system is particularly interesting because it is the basis of all heat engines.

In this context, work is the amount of energy transferred by a system to its surroundings by a force that causes a displacement.

To calculate the work done by a gas we will start with the expression for the work done by a force and apply it to the situation represented in the following figure:

The left side of the upper figure represents a gas confined to a closed container. The gas exerts a force F on the moving wall, so that it moves a distance dx.

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The work done by F on the moving wall between states A and B is given by:

And, remembering the definition of pressure, we get:

The SI unit of work is the joule (J).

We can use a PV diagram to represent the process that the gas undergoes when it goes from state A to state B:

The work is the hatched area between states A and B under the curve which represents the process. The geometric interpretation of an integral is precisely the area under the curve, between VA and VB. If the work is done by the surroundings on the gas, a negative sign must be added.

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Sign criteria: The work done by an expanding gas on its surroundings is positive. When the gas compresses, the work it does is negative.

In the situation represented in the upper figure, the work done by the gas is positive.

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