Explain why each of the following processes is an example of increasing randomness: mixing hot and cold water; free expansion of a gas; irreversible heat flow; developing heat by mechanical friction. Are entropy increases involved in all of these? Why or why not?

The overall entropy of the system and its surroundings rises as a result of an irreversible process.

This process is making the system more random. The hot water loses heat at high temperatures; hence the entropy change is small. Whereas cold water gets hotter at low temperatures resulting in a high entropy change. The net entropy change is positive Therefore, the entropy of the system in this process is increasing.

This process is an irreversible process. Therefore, the entropy of the system in this process is increasing.

This process will increase the kinetic energy of the atoms, hence the randomness of the motion. Therefore, the entropy increases for irreversible (spontaneous) processes.

This process will increase the temperature of the atoms, hence the kinetic energy of the atoms. Which, in turn, increases the randomness of the motion. Therefore, the entropy of the system in this process is increasing.

Hence, the entropy increases involved in all of the processes.