Entropy

The entropy postulate states that:

“If an irreversible process occurs in a closed system, the entropy of the system always increases, it never decreases.”

If the entropy is not equal to the energy of that entropy, it does not obey the law of conservation. The entropy always increases in irreversible processes.

In order to define the change in entropy of a system, we consider the following:

1. the system’s temperature and the gained or lose energy transferred as heat of the system; and
2. the ways in which the atoms or molecules that make up the system can be arranged.

The change in entropy of a system during a process that takes the system from an initial state i and final state f is defined as

$$\Delta S = S_f – S_i = \int \limits_i^f {dQ \over T}$$          (1)

where Q is the energy transferred as heat to or from the system during the process and T is the temperature of the system which is measured in kelvin. This implies that the change in entropy does not depend only on the energy transferred as heat but also on the temperature during the transfer of the energy occurred. The SI unit for entropy and so with the change in entropy is the joule per kelvin or J/K.

For isothermal expansion, the constant temperature T in equation (!) is taken outside the integral, that is,

$$\Delta S = S_f – S_i = {1 \over T} \int \limits_i^f dQ$$          (2)

Note that $$\int dQ = Q$$, which is the total energy transferred as heat during the process. Thus, equation (2) becomes

$$\Delta S = S_f – S_i = {Q \over T}$$          (3)

When the change in temperature is small compared to the temperature before and after the process, the change in entropy can be approximated as

$$\Delta S = S_f – S_i = {Q \over T_{avg}}$$         (4)

where $$T_{avg}$$ is the average temperature of the system in kelvin during the process.