[[Quasistatic process]]
# Work done by a gas during a quasi-static volume change
A volume change, 
i.e. the contraction or expansion of a container,
is a mechanical change —
and therefore any energy transferred due to this process will be **work**.
The amount of work due to an infinitesimal quasistatic volume change is
$$
\begin{align*}
\dj W &= -p \, dV
\end{align*}
$$
where $\dj W < 0$ for an expansion and $\dj W > 0$ for a compression.

> [!check]- Derivation
> Consider a container of an ideal gas expanding in one direction.
> The gas therefore exerts a force $\vab F$ due to pressure,
> resulting in a displacement $\vab s$ in that one direction.
> The total volume change will be $\vab A \cdot \vab s$, where $\vab A$ is the normal area vector:
> $$
> \begin{align*}
> \vab F &= p \vab A \\
> \dj W &= - \vab F \cdot d\vab s \\
> &= - p \vab A \cdot d \vab s \\
> &= - p d V
> \end{align*}
> $$
> 

![[work as area under p-v diagram.jpeg#invert|500]]


---
#state/tidy | #SemBr | #lang/en