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The incompressible-substance approximation

Liquids and solids often change volume very little over ordinary engineering pressure ranges. They can then be approximated as incompressible substances with

$$v\approx\text{constant}.$$

If the specific heat $c$ is also approximately constant,

$$\Delta u\approx c(T_2-T_1).$$

Since $h=u+pv$,

$$\Delta h\approx c(T_2-T_1)+v(p_2-p_1).$$

For a nearly isothermal liquid, this reduces to

$$\Delta h\approx v\Delta p,$$

which explains the familiar ideal pump-work estimate.

For example, water with $v\approx0.001\ \mathrm{m^3/kg}$ undergoing a pressure increase of $5\ \mathrm{MPa}$ at nearly constant temperature has

$$\Delta h\approx0.001(5000)=5\ \mathrm{kJ/kg}.$$

The approximation is excellent for many liquid processes but should not be used near strong density changes, phase transitions or highly compressible states.