Which of the following is/are mode/s of storage of internal energy in a system?

Which of the following is/are mode/s of storage of internal energy in a system?

a. Macroscopic energy mode
b. Microscopic energy mode
c. both a. and b.
d. none of the above

Correct Answer : c. both a. and b.

Explanation :

There are two modes in which energy can be stored in a system, macroscopic energy mode and microscopic energy mode.
In macroscopic energy mode, the kinetic energy and the potential energy of a system is considered. Let us consider a fluid element of mass m and a center of mass velocity is V. The macroscopic kinetic energy E_k of the fluid element is,
E_k = ½ mV²

If this fluid element is elevated to a certain height h from and arbitrary datum, the macroscopic potential energy E_p of the element,
E_p = mgh

The microscopic energy mode consists of an energy stored in molecular and atomic structure of the system. This energy consists of molecular translational kinetic energy, rotational kinetic energy, vibrational kinetic energy, chemical energy, electrical energy and nuclear energy.
If e represents the energy of one molecule then,

ε = ε_trans + ε_rot + ε_vib + ε_chem + ε_electronic + ε_nuclear

and if N is the total number of molecules in the system, the total microscopic internal energy will be,

U = Nε

Thus the total internal energy of the system will be,
E = E_k + E_p + U