Why is adiabatic process isentropic?

Why is adiabatic process isentropic?

• I have read that adiabatic process is isentropic because there is no heat exchange in an adiabatic process and thus no change in entropy. But my question is - Even in adiabatic process, work can be done. Let's take an example of an adiabatic vessel with a piston attached. That vessel does not exchange heat but work can be done by pulling in or out the piston. If the volume of the system changes, isn't entropy also changed, even in a reversible adiabatic process? EDIT : I know that change in entropy is defined as change in heat divided by temperature. Since there is no change in heat in an adiabatic process, the entropy is zero. My question is different - What I see entropy as - It is a measure of the different microstates in which a system can be. So, even if there is no change in heat energy, can't number of thermally achievable microstates increase if we increase the volume by doing work? Why is only heat considered as a measure of entropy?

• Answer:

  If I understand the question, you are wondering how to justify the statement that a (reverible) adiabatic process is isentropic from the point of view of statistical mechanics (the classical thermodynamics definition makes sense to you). Let us then start with the entropic fundamental relationship, S = S (U, V, N), where U stands for energy, V for volume, N for number of particles. In many a statistical mechanics texts you will find the explicit definition of S for a system of particles (under usual simplifying assumptions). Inyour example N is constant, but U and V are not: I would be glad to help further if needed, but if you looked at the expression for S as a function of V and N this would answer your question alone. I believe the discussion at http://physics.stackexchange.com/questions/52231/isentropic-processescold be useful.