3.3.3 Work on a Gas

Concept:

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Doing work on a gas increases its temperature.

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Work Done Formula:

\text{Work Done} = \text{Force} \times \text{Distance} = \frac{\text{Force}}{\text{Area}} \times (\text{Area} \times \text{Distance}) = \text{Pressure} \times \text{Volume}\\ \text{Work Done} = \text{Pressure} \times \text{Volume}

Key Points:

Adding More Particles to a Fixed Volume:
Doing work on a gas means compressing or expanding the gas, so changing the volume.
Pumping more gas into the same volume means more particles are present, so more collisions occur per unit time with the walls, so pressure increases.
Energy is transferred to the particles when more gas is added to the fixed volume, so this heats the gas.

A Fixed Number of Particles for a Smaller Volume:
The particles collide with the wall which is moving inward.
The particles gain momentum, as the rebound velocity is greater than the approaching velocity.
As the particles have a greater velocity, the pressure increases as the particles collide with the walls more frequently (the time between collisions decreases).
And the temperature also increases, as the kinetic energy of each particle increases.

Scenario	Effect on Particles	Effect on Pressure
More particles in a fixed volume	More collisions with walls	Pressure increases
Fixed number of particles, smaller volume	Collide with moving inward walls, gain momentum	Pressure increases, higher frequency of collisions