Engine with a single reservoir

Problem

A physicist claims: “I’ve found a machine that absorbs heat from a single hot reservoir and produces work, without giving up heat to any other reservoir.” Discuss whether this is possible in principle. Which formulation of the second law explicitly denies this device?

Solution

The device is impossible: it would be a perpetual motion machine of the second kind. Entropy analysis of one cycle: after a cycle the machine returns to its initial state, so $\Delta S_\text{macchina}=0$. The only body whose entropy changes is the reservoir, which gives up heat $Q$ at temperature $T$: $\Delta S_\text{univ}=\Delta S_\text{serb}=-\frac{Q}{T}<0$ A negative change in the entropy of the universe violates the second law. This is exactly what the Kelvin–Planck statement denies: it is impossible for a cyclic transformation whose sole result is the complete conversion into work of heat absorbed from a single source. $\ev{\text{Kelvin–Planck}}$

Collegamenti

Argomenti: Entropy and the second law Concetti: Second law of thermodynamics Competenze: Limiting-case and thought-experiment analysis Oggetti: Heat engine