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Indigo5684
2025-09-30 13:19:30 -05:00
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docs/physics/thermal/1-energy.md
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@@ -138,4 +138,4 @@ Consider a piston with a compressable gas. In tthis case, with $\Delta x$ positi
We know that the force exerted by the piston is equal to the pressure times the area. Thus, $W = P A \Delta x$. But $A\Delta x$ is just volume (in this case, negative, as volume is decreasing). So, $W = -P \Delta V$. We know that the force exerted by the piston is equal to the pressure times the area. Thus, $W = P A \Delta x$. But $A\Delta x$ is just volume (in this case, negative, as volume is decreasing). So, $W = -P \Delta V$.
However, this assumes constant pressure. For a non-constant perssure, $P(V)$, we know that $W = \int F dx = - \int P(V) dV$. However, this assumes constant pressure. For a non-constant perssure, $P(V)$, we know that $W = \int F dx = - \int P(V) dV$.