In four experiments, blocks Aand B, starting at different initialtemperatures, were brought together in an insulating box and allowedto reach a common final temperature. The entropy changesfor the blocks in the four experiments had the following values (injoules per Kelvin), but not necessarily in the order given.Determine which values for Ago with which values for B.

In the given four experiments, blocks A and B brought together in an insulating box to reach a final temperature have four entropy values in each experiment.

This problem is based on the concept of the second law of thermodynamics which is an extended postulate to the concept of entropy. The law states that if a process occurs in a closed system, the entropy of the system increases for irreversible processes and remains constant for reversible processes. It never decreases.

Formula:

The entropy change of the system,$\Delta S⩾0$

As per the given concept and equation (i), the entropy change of the system of two blocks A and B with entropy changes $∆S_1$and $∆S_1$can be given as:

$$\begin{gathered} \Delta S⩾0 \\ \Delta S_1+\Delta S_2⩾0 \\ \Delta S_1⩾-\Delta S_2 \end{gathered}$$

Thus, there must exist either a negative equal entropy value of entropy change of block B or a lower negative value of entropy change of block B for every entropy value of block A.

Thus, the values of A and B that match the condition are$(8,-8),(5,-5),(3,-3),\text{(9,}-\text{2)}$.