# Is enthalpy also valid for liquids and solids?

The definition of enthalpy is $$H=E+PV,$$ is it only valid for (ideal) gas? As this naturally comes from the first law of thermodynamics, $$dE=dQ+PdV$$ for a enclosed system of gas.

Can we talk about the enthalpy of (perfect) fluid and even solid (the pressure P seems uneasy to specify.)?

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For solids, as well as for liquids and gases, you can define a specific heat as

$$c_V \equiv \left(\frac{\partial U}{\partial T}\right)_V$$ and $$c_P \equiv \left(\frac{\partial U}{\partial T}\right)_P$$

For solids, however, $V$ is basically a constant, so that with excellent approximation

$$c_P \approx c_V \equiv c$$

and we can now define an internal energy $E$ as $$dE = c(T) dT\;.$$

We can proceed likewise with enthalpy:

$$dH = dE + d(PV) = c(T) dT + P dV + V dP$$

For a solid, $dV = 0$ for a fixed amount of matter, and furthermore $dE \gg V dP$, thus

$$H = E$$.

There is nothing wrong in these concepts (the thermodynamic potentials) for liquids and solids.

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Wonderful! Thank you so much, MariusMatutiae. – David Aug 13 '14 at 14:21
Why is $dE\ll VdP$? Is that specific for solids? – Kyle Kanos Aug 13 '14 at 14:34
@KyleKanos Sorry, typo, I meant $dE\gg V dP$. Yes, it is specific to solids and liquids, it is basically a restatement of the fact that $c_V \approx c_P$. – MariusMatutiae Aug 13 '14 at 14:46

The equation for enthalpy is valid for 'all' gases under normal conditions. It is because all the equations of thermodynamics (except ones which have ideal gas laws substituted in them) were experimentally confirmed under normal conditions. That is the reason why even enthalpy is an extremely useful tool in calculating the thermodynamic properties in any chemical experiment . However there is a limit beyond which this concept is defined. In the gaseous state, there is practically no interaction between neighbouring molecules. Therefore, most gases show common properties as compressibility. Thus, due to these common properties, they made a general enthalpy equation in view of gases. In liquids and gases, however, the interaction between neighbouring molecules comes into play. Each liquid may have a different way in which it's atoms interact. Therefore, there is no general enthalpy equation for liquids(I don't know what you mean by a perfect liquid).It is the same for solids; in fact, most solids are incompressible under pressures we are looking for. They also behave in a totally different manner under considerable pressure compared to gases. Hope it helped !

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Great! Thank you very much, FullBloodPhysicist. – David Aug 13 '14 at 14:16