Consider two solid blocks, one hot and the other cold, brought into contact in an adiabatic container. After awhile, thermal equilibrium is established in the container as a result of heat transfer. The first law requires that the amount of energy lost by the hot solid be equal to the amount of energy gained by the cold one. Does the second law require that the decrease in entropy of the hot solid be equal to the increase in entropy of the cold one

The statement is not correct because the decrease in entropy of the hot solid CANNOT BE equal to the increase in entropy of the cold one

Explanation:

Let us start by stating the second law of thermodynamics and it the second law of thermodynamics states that there is an entity called entropy and entropy will always increase all the time. Also, the second law of thermodynamics states that the change in entropy can never be negative. The second law of thermodynamics can be said to be equal to Change in the transfer of heat, all divided by temperature.

So, the first law of thermodynamics deals with the conservation of energy. But there is nothing like conservation of entropy.

Therefore, the decrease in entropy of the hot solid CANNOT BE equal to the increase in entropy of the cold one because entropy is not a conserved property.

Exactly; According to the second principle, when you have a system that goes from a state of equilibrium A to another B, the amount of entropy in the state of equilibrium B will be the maximum possible, and inevitably greater than that of the state of equilibrium A.

Explanation:

The second law of thermodynamics states that when a thermodynamic system passes, in a reversible and isothermal process, from state 1 to state 2, the change in its entropy is equal to the amount of heat exchanged between the system and the medium, divided by its absolute temperature.

Therefore if heat is transferred from the hot block to the cold block, so will entropy, in the same direction. When the temperature is higher, the incoming heat flux produces a smaller entropy increase. And vice versa.