# Question regarding change in enthalpy

1. Jan 18, 2014

### Marshillboy

This isn't a formal homework question so much as a conceptual question for my own edification.

I'm reading my textbook's section on enthalpy and energy, and given the expression:

ΔH=nCpΔT

It states that, "we can use this expression to represent the change in enthalpy when n moles of an ideal gas are heated, regardless of any conditions on pressure or volume."

I know that the ideal gas law stats that PV = nRT, and thus T is proportional to PV.

How can it be, then, that enthalpy change is only affected by temperature change and not affected by changes in pressure and/or volume?

2. Jan 18, 2014

### Staff: Mentor

First, that equation for enthalpy holds for constant pressure. At const. P, the volume will change when T changes of course. But it is taken care of by considering only T because P is fixed.

What the book mentions are "conditions" on P and V. This means that you do not need to know what P is, or what the initial and final volumes are. So long as you know ΔT, you can calculate ΔH.

3. Jan 18, 2014

### Staff: Mentor

What they are saying it that the enthalpy of an ideal gas is independent of pressure. If we regard the enthalpy (per unit mass) of a pure substance to be a function of pressure and temperature, the we can write:

H = H(T,P)

From this it follows that:

$$dH=\frac{\partial H}{\partial T}dT+\frac{\partial H}{\partial P}dP$$
But, by definition,
$$C_p=\frac{\partial H}{\partial T}$$
so
$$dH=C_pdT+\frac{\partial H}{\partial P}dP$$
For real gases in the limit of low pressures, it has been found experimentally that:
$$\frac{\partial H}{\partial P}→0$$
But real gases approach ideal gas behavior in the limit of low pressures. So, for ideal gases, the enthalpy is independent of pressure.

Last edited: Jan 18, 2014