What is the meaning of internal Energy?

What is the meaning of internal energy. Is it the amount of energy that a body contains?

Answer

Standard Definition : The internal energy of a system is identified with the random, disordered motion of molecules; the total (internal) energy in a system includes potential and kinetic energy.

Since this molecular motion is primarily a function of temperature, the internal energy is sometimes called 'thermal energy'.

Total energy of the system $(E)$ = U (Thermal energy) + $E_{Kinetic\space of\space system}$ + $E_{Potential\space of\space system}$ ....

Here, the two terms viz, $E_{Kinetic\space of\space system}$ and $E_{Potential\space of\space system}$, are for the system and not the particles inside the system. For the particles the $KE$ and $PE$ is included in the internal energy.

In most of the cases, kinetic energy, potential energy, chemical energy of the system is constant, thus we conclude,

$\Delta{E}=\Delta{U}$

The proper form of the first law of thermodynamics is given by,

$\Delta E = q + W$,

but for the reasons stated above,

$\Delta U = q + W$.

Therefore, summing it up, Internal energy includes :

1). Translational KE

2). Vibrational and rotational kinetic energy

3). Potential energy from intermolecular forces