Question

Give the lower bound for the change in entropy of a process which occurs at constant temperature. This lower bound is achieved when the process is __________?

Answer 1

For an isothermal process in an ideal gas

There are two arguments for why the entropy change of the surroundings must be zero in this case. First argument. Since w = q = 0, there is no interaction between system and surroundings, the state of the surroundings does not change, and all thermodynamic functions of the surroundings remain constant, including entropy S'. Second argument. To maintain the condition of constant temperature in the system, we have

and additionally the surroundings need to have special properties which allow us to consider that heat transfer q' is independent of path. Then we can use the actual value q' for this process to calculate

where, as always, heat leaving system enters surroundings: q' = -q.