Reversibility of heat transfer

[kelvin490]

In the case of reversible heat exchange which the cooler body rises in temperature from T₁ to T₂, it requires that the temperature difference between the system and the heat source must be infinitesimal in every step. Usually the model is like that: Give a heat reservoir of temperature slightly higher than T₁, make a small amount of heat transfer, than the temperature of cold body rise a little bit. Then use another hotter reservoir and transfer another infinitesimal amount of heat, repeat the steps until the body is T₂.

The problem is: In every step the entropy decrease of hotter reservoir is smaller than the entropy increase of the cooler body. There is a net increase in entropy of the system. Although the increase is close to zero, we have done infinite number of step in order to increase the temperature to T₂. How can we ensure the overall increase in entropy is zero so that it is a reversible process?

 

[maajdl]

It is reversible only in the limit of dT = (T2-T1) → 0 .
There is no truly reversible process in nature, since such a process would take an infinite time.
Actual processes can at most be very close to reversible.
It is nevertheless a useful concept and it can even be useful as an approximation to actual processes.