Question

Why we use dq(rev) and not dq(irr) to define entropy?
With temp randomness should increase, why ds=dq/T ?

Answer 1

Solution:

Entropy is a state function, hence the change in entropy is the same between any two states irrespective of the path.So, if you know the initial and final states of the process, you can assume a reversible process between them and calculate the change in entropy. The change in entropy (dS) is not equal to dq/T for all processes. This equation is only valid for reversible processes because the entropy of the system and the surrounding will remain a constant if the process is reversible. Therefore the correct equation would be dS = dq(rev) / T. The change in entropy in an irreversible process is always greater than dq/T because of entropy generation. Hence, entropy change is expressed in dq(rev) /T

The increase in temperature causes an increase in randomness. But for a reversible process, dS = dq /T = 0 because the total change in entropy is sum of the change in entropy of system and surrounding.

dS = dS (system) + dS(surrounding)

For a reversible process, dS(system) = + dq /T and dS(surrounding) = -dq /T, hence dS= + dq/ T - dq /T = 0

For an irreversible process, dS(system) = + dq /T and dS(surrounding) = 0, hence dS > dq/T

Since change in entropy is only expressed in reversible process, hence dS = dq /T