Internal energy

What is Internal Energy?

The internal energy is the thermodynamic property of the system. The internal energy is basically the total potential energy and the total kinetic energy of the particles involved in each system. It is denoted by symbol, E. If the particles kinetic energy and potential energy is high, the total kinetic energy of the system would be high.

In order to understand it, consider a system of ideal gas at temperature T. For ideal gas, there is no involvement of potential energy. At low temperature, the kinetic energy is small and at high temperature, the kinetic energy of the system is high. Thus the internal energy is higher in second case.

The internal energy $U$ of a system is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields. Internal energy principally refers to the kinetic energy of molecules and the chemical bonds between molecules. In summary, internal energy keeps account of the gains and losses of energy in the system due to changes in its internal state. Furthermore, internal energy can be defined by the formula:

$U=Q-W$

(1)

Where:

• $U$ is the change in internal energy.
• $Q$ is the heat added to the system.
• $W$ is the work done by the system.

Specific Internal Energy

The specific internal energy $\hat{u}$ is the internal energy per unit mass. It is defined under the formula:

$\hat{u}=U/m$

(2)

It can be related to the temperature and density through

$d\hat{u}=c_{v}dT+\frac{1}{{\rho }^2}\left[P-T{\left(\frac{\partial P}{\partial T}\right)}_{\rho }\right]d\rho$

(3)

If the fluid is incompressible, $d\rho =0$ and

$d\hat{u}=c_{v}dT$

(4)