Answer
Yes, entropy increases in all.
Work Step by Step
Mixing hot and cold water- The KE of the water molecules gets spread out more uniformly resulting in an increase in entropy. The hot and cold water molecules are originally separated and in order but as they mix, they become randomly spread out.
Free expansion of a gas: In this process, the gas molecules spread and occupy a much bigger volume resulting in an increase in entropy. The gas molecules were originally stuck to a smaller volume and were in order but as they expand, they become more random.
Irreversible heat flow: In this process heat flows from a hotter object to a less hotter or colder object without any external work being done on the system. This results in an increase in entropy as the heat becomes more random. Initially, the heat energy was ordered because of the temperature gradient, but as the heat flows, it becomes more random.
Developing heat by mechanical friction: The kinetic energy of its molecules increases when heat is developed by mechanical friction, which causes an increase in entropy. This increase in temperature results in an increase in the random motion of molecules which leads to entropy increase.
Entropy increase happens in all these processes as the particles become more randomly distributed than before.
