# What is the difference between internal energy and enthalpy?

1. Apr 1, 2014

### abi.ayan

could anyone explain me the fundamental different between internal energy and enthalpy? I searched and found the below definitions for both terms.
INTERNAL ENERGY:In thermodynamics, the internal energy is the energy contained by a thermodynamic system.

ENTHALPY:Enthalpy is a measure of the total energy of a thermodynamic system.

I really couldn't find the differences.Is enthalpy a subset of internal energy or internal energy a subset of enthalpy?

2. Apr 1, 2014

### UltrafastPED

Last edited by a moderator: May 6, 2017
3. Apr 1, 2014

### Andrew Mason

Enthalpy is defined as H = U + PV so the difference between H (enthalpy) and U (internal energy) is PV, the product of pressure and volume.

When a system changes thermodynamic state, there may be a change in Internal energy or a change in PV, or a combination of both.

The change in internal energy, dU, relates to the change in kinetic energy of the molecules plus their change in potential energy relative to each other if there are intermolecular forces.

The change in PV, d(PV), relates to the work done on or by the system (PdV) plus the volume x change in pressure (VdP) which is a kind of mechanical potential energy or mechanical stored energy. This VdP term can be confusing because it is actually included in the change in internal energy (dU)*.

Together these changes add up to the change in enthalpy. If there is no change in pressure (VdP=0) then by the first law of thermodynamics the change in enthalpy is the heat flow into or out of the system:

ΔHconstant P = ΔU + PΔV = Q

* [footnote: You have referred to a statement that enthalpy represents the total energy of the system (see, for example, the Wikipedia article referred to by UltrafastPED). This is not correct. The energy of the system is the internal energy. A change of this internal energy is equal to the change in enthalpy only if volume and pressure do not change. The change in enthalpy is equal to the energy flow into or out of the system during a thermodynamic process if pressure is constant. If pressure is not constant the change in enthalpy differs from the heat flow by that VdP term. For example, if volume is constant, the heat flow Q = ΔU and the change in enthalpy differs from the change in system energy by VΔP.

AM

Last edited: Apr 1, 2014
4. Apr 1, 2014

### Khashishi

One line definitions you can find online are typically oversimplified and wrong.

5. Apr 1, 2014

### dauto

Always try to understand and use the mathematical definitions. Wordy definitions such as "Enthalpy is a measure of the total energy of a thermodynamic system" are used to build intuition but are secondary to the mathematical definitions and are almost completely useless by themselves.

6. Apr 3, 2014

### Andrew Mason

The misinformation in the Wikipedia article has now been corrected. It no longer makes the incorrect statement: "Enthalpy is a measure of the total energy of a thermodynamic system.". The error was made in August 2010 and has persisted ever since, despite criticism in the Talk section of the article.

Thanks to the OP for the post pointing out the understandable confusion. Who knows how many others have been misled over the last 3 1/2 years!! This is a good example of why it is important not to rely only upon Wikipedia.

AM