Why Entropy of Carnot Engine is 0 & Heat Transfer in Refrigerator

[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??

 

[Andrew Mason]

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

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

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).]

Also in the refigerator section, why is Q_h coming into the heat reservoir when Q_c is the one being transferred??

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

 

[m2003]

The entropy of a Carnot engine being equal to 0 is a direct result of the Carnot cycle being a reversible cycle. In a reversible process, the change in entropy is equal to the heat transfer divided by the absolute temperature of the system. In the Carnot cycle, the heat transfer occurs at constant temperatures (the isothermal processes), and thus the change in entropy is equal to 0. This means that the entropy of the engine remains constant throughout the cycle, and at the end of the cycle, it returns to its initial value of 0.

In the refrigerator section, it is important to note that the heat transfer is occurring between two different systems - the refrigerant and the heat reservoir. The heat reservoir is at a higher temperature (Q_h) and is the source of the heat being transferred into the refrigerator. The refrigerant, on the other hand, is at a lower temperature (Q_c) and is the recipient of the heat being transferred. This is why Q_h is coming into the heat reservoir and Q_c is being transferred into the refrigerant. This transfer of heat is what allows the refrigerator to maintain a lower temperature inside while the heat from the heat reservoir is being removed.