Understanding Internal Energy in Thermodynamics: Definition and Equations"

[Greg Bernhardt]

Definition/Summary

In thermodynamics, internal energy, $U$, is the energy associated with the microscopic energies of a system, that is with the energy associated with the random motion of the molecules within a system.

More generally, while external energy is energy due to macroscopic motion (of the system as a whole) or to external fields, internal energy is all other forms of energy, including random motion (relative motion of molecules within the system) and dipole moments and stress.

Equations

First Law of Thermodynamics:

$$dU\,=\,dQ\,+\,dW$$

Central Equation:

$$dU\,=\,TdS\,-\,PdV$$

Internal energy plus pressure times volume equals enthalpy:

$$H\ =\ U\ +\ P\,V$$

Extended explanation

Above we define the internal energy as the energy associated with the microscopic energies of a system, that is the energy associated with the random motion of the molecules within a system.

So for a general fluid, the internal energy of a system is the sum of the translational kinetic energies, the rotational kinetic energies, the vibrational kinetic energies and the potential energies of all the molecules in that system.

The internal energy of a system is often erroneously referred to as the heat of a system.

Path independence:

One important point to note here is that dU is an exact differential, which means that the path integral

$$U = \int_\gamma dU$$

is path independent. In other words, at each equilibrium point, U is uniquely defined, irrespective of the path taken.

More physically, the change in internal energy between two states is independent of the process through which the change of state was made. Hence, internal energy is a state function.

Specific internal energy (s.i.e):

Specific internal energy (s.i.e) is internal energy per unit mass.

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[APhysicist]

I understand that internal energy is the energy associated with the microscopic motions of molecules in a system. It includes translational kinetic energies, rotational kinetic energies, vibrational kinetic energies and potential energies. Additionally, it is a state function, which means that the change in internal energy between two states is independent of the process through which the change was made. Specific internal energy (s.i.e) is the internal energy per unit mass.