A cube of ice is added to some hot water in a rigid, insulated container, which is then sealed. There is no heat exchange with the surroundings. What has happened to the total energy and the total entropy when the system reaches equilibrium?

Total energy decreases as well as total entropy.

Explanation:

Hello,

In this case, due to the effect of the high water's temperature, the ice will probably melt or at least, will decrease its initial temperature. In such a way, since no heat is exchanged with the surroundings, the system's equilibrium energy will be between the initial hot water's energy and the initial ice's energy, in other words, the total energy will decrease if the hot water's energy is larger than the ice's energy based on the first law of thermodynamics. Moreover, the total entropy of the system will decrease as long as during the aforesaid cooling process, the arrangement of system becomes less disordered (or more ordered) which is related with an entropy decrease, based on the second law of thermodynamics.

Best regards,

Total energy remain constant and total entropy Increases

Explanation:

Though in an ideal situation, there is no such system where the container will be completely airtight and there will be no exchange of heat with the environment. However, for the question, since there is no heat addition or removal in the system, there will be no change in total energy.

Entropy is a measure of the molecular disorderliness or randomness of a system. The hot water try to melt the ice in the container which increases the molecular disorderliness of the system and thereby increases the total entropy.