Question

Verify that pressure has units of energy per unit volume.

Final Answer

See the solution video for the dimensional analysis.

Solution Video

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This is College Physics Answers with Shaun Dychko.
We're going to show that pressure units are the same as energy per volume units. So the pressure is Newton's per square meter because the formula for pressure is force which is in Newton's divided by area which is in meter squared. And then we'll multiply top and bottom by meters which is the same as multiplying by one and since multiplying by one doesn't change things. We're allowed to do it. So we have Newton meters divided by meters cube. So this multiplying by one thing we see everywhere, multiplying by one changes the way things look and what it looks like on top is a force unit multiplied by distance unit which is our formula for work. And work has units of Joules. So Joules are Newton meters and on the bottom we have cubic meters which is units of volume. And so this shows, pressure has units of energy per volume