Define entropy. Give its units.

Hint: Thermodynamics deals with the study of heat, temperature, work and their relation with energy. For studying the states and energy of particles, one has to learn about the orientation of the particles in space and how this orientation affects the energy and work done on the system.

Complete step-by-step answer:
Entropy is defined as the measure of randomness of the particles in a system. Entropy is the thermal energy of the system per unit temperature that is unavailable to do useful work. This thermal energy cannot be exchanged to the surrounding. Systems with tightly packed atoms have less entropy and systems like gases have higher entropy. Mathematically, Entropy is the natural logarithm of the number of possible states of all particles of the system multiplied by the Boltzmann’s constant \[({{k}_{B}})\]
\[S={{k}_{B}}\ln \Omega \]
Entropy is denoted by S. Since it is the energy per unit temperature. The SI unit of energy is joules(J), that is, \[kg{{m}^{2}}{{s}^{-2}}\]. Hence the unit for entropy is in words joules per kelvin\[\left( \dfrac{J}{K} \right)\].
\[kg{{m}^{2}}{{s}^{-2}}{{K}^{-1}}\] is also possible.

Additional information:
A useful work in Thermodynamics is the work that can be transferred by the system to the surrounding. Entropy is a state function which means that the change in entropy can be found from the initial and final states of the system. If we keep the macroscopic quantities like the volume and pressure constant, we can estimate all the possibilities of the configurations of a system. These possibilities can be put together and are termed as microstates of the system. It is denoted by \[\Omega \].

Note:
1. Increase in energy allows the faster random movement of particles and hence increases the entropy.
2. The unit can be represented in different forms.
3. 1 Clausius is equal to \[4.1868\dfrac{J}{K}\].