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How do you work out work done on a gas?

Updated: 8/10/2023
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13y ago

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Mechanical work is defined as force times distance, F X D = W

In a system with a gas the pressure of the gas exerts some force per unit area. If the gas changes in volume then that force has acted over some distance. For small changes in volume dW = P * dV where dV is some infinitesimally small change in volume and dW is the infinitesimall small amount of work done on or by the system. To calculate work you can then integrate P*dV from the starting volume to the ending volume. Note that if P is a function of V, such as the ideal gas case where P = NRT/V then the integral becomes more complex, W = Integral(NRT/V * dV). This works out to W = NRT * ln(V2/V1) assuming positive work is work done on the system. In the case of gas expanding against atmospheric pressure P is constant so W = P * (V2-V1) again assuming positive work is work done on the system. If gas expands against a vacuum then the P being pushed against is zero so no work is done.

You can show that the units work out by analyzing the units involved:

P = Force / Area = Force / Distance ^2

V = Distance ^3

P*dV = Force / Distance ^2 * Distance ^3 = Force * Distance = Work

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Q: How do you work out work done on a gas?
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