# For change in entropy dS = dq/T, is T the temperature of system or surrounding or both?

For change in entropy dS = dqrev/T, is T the temperature of system or surrounding or both?

I am confused about Thot, Tcold, Tsys and Tsurr. If qrev, are we talking about the reversible cycle such as the carnot engine?

• Of the particular system of which you are trying to ascertain the entropy, of course.
– Danu
Sep 27 '14 at 18:11

Carnot engine involves isothermal and isentropic processes. For the isentropic process, $dS = 0$. For the isothermal process, because $T_{hot} = T_{cold}$, so $$dS_{tot} = dS_{sys} + dS_{surr}$$ $$dS_{tot} = \frac{Q_{rev}}{T} - \frac{Q_{rev}}{T} = 0$$ Since the same amount of heat gained by system is obtained from surroundings.
For a reversible process, $dS_{tot} = 0$.But it does not mean that no heat transfer has occured.