Now let us apply the above results to evaluate the entropy of the universe when a system interacts with the surroundings. Refer to Figure 23.2.

Figure 23.2

Let Temperature of the surroundings

Temperature of the system

and,

(23.7)

If the energy exchange takes place, will be the energy transfer from the surroundings to the system.

(23.8)

(23.9)

(23.10)

[since ]

(23.11)

So,

(23.12)

If the system is isolated, that is, when there is no interaction between the system and the surroundings, then

(23.13)