# Compression and Expansion Index

## Main Question or Discussion Point

Could anyone tell me what the compression and expansion is used for in a Thermodynamics situation?

What is the notation for Compression and Expansion in a formula?

I am trying to calculate work done by a heat engine.

Thanks

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Compression & Expansion basically relate to a change in Volume i.e. $\Delta V \ne 0$

Expansion is negative of Compression. Depending on your sign convention, either of them will be positive. Generally, $\Delta V$ is taken as $\Delta V = V_f - V_i$ and hence compression corresponds to a negative $\Delta V$ i.e. $-\Delta V_c > 0$

Also, if a conservative force is applied for either of the process, the work done for the same $|\Delta V|$ will have the same magnitude.

Under constant pressure, the work done in doing either of the process is given as:

$$W = P\Delta V$$

and for non-constant pressure, we express it in a differential equation. Note that here, Pressure will be some function of Volume and may also depend on Temperature which in turn maybe another function of Volume.

$$\int^{W}_0 dW = \int^{V_f}_{V_i}PdV$$

This holds only when there is no energy exchange from the system to the surrounding or vice versa in any form other than the force applied on the piston.