Question

Show that the entropy change in a process when a perfect gas changes from state 1 to state 2 is given by S₂ – S₁ = C_p lnT₂/T₁ + R ln P₁/P₂ .

Answer 1

Using clausius equality for reversible cycle,, we have

Let a control mass system undergoes a reversible process from state 1 to state 2 along path A and let the cycle be completed by returning back through path C, which is also reversible, then

Also we can move through path B and C then

The quantity  is independent of path A and B but depends on end states 1 and 2. Therefore this is point function and not a path function, and hence a property of the system.

Also; δq = T. ds (for reversible process) From first law