# Heat Engines/Entropy

1. May 13, 2007

### AznBoi

Can someone explain why the entropy of a cyclic carnot engine is equal to 0?

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Also in the refigerator section, why is Q_h coming into the heat reservoir when Q_c is the one being transferred??

2. May 13, 2007

### Andrew Mason

Entropy is 0 because the heat flow occurs when the system and surroundings are at the same temperature.

$$dS_{sys} = dQ_{sys}/T_{sys}; dS_{surr} = dQ_{surr}/T_{surr} = - dQ_{sys}/T_{surr}$$

The total entropy change is:

$$dS = dS_{sys} + dS_{surr} = dQ_{sys}\left{(}\frac{1}{T_{sys}} - \frac{1}{T_{surr}}\right{)}$$

So if the system and surrounding temperatures are infinitessimally close while heat flows, there is no entropy change. [There is no heat flow during the reversible adiabatic expansion and compression so there is no entropy change during the adiabatic processes (ds=dQ/T = 0/T = 0).]

A refrigeration cycle takes heat from the cold reservoir and delivers it to the hot reservoir. So Qh (the heat flow from the hot reservoir) is negative and Qc (the heat flow from the cold reservoir) is positive.

AM

Last edited: May 13, 2007