# Why Carnot's engine needs 4 cycles instead of only 2

1. Feb 11, 2012

### sangsang

I do not really understand the reason why Carnot ideal engine needs 4 cycles: isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression. Why cannot use only 2 cycles said isobaric expansion and isobaric compression, i.e. use a heat reservoir to expand the air inside the engine, then use a cold reservoir to compress the air?

I even checked the original paper of Carnot and it explains as below, but I am not very understand for the following 2 processes,

1) use hear reservoir to increase the temperature of air to expand
2) use compression to increase the temperature first, then use an isothermal expansion to expand

Why 1 is less efficiency then 2 as Carnot said?

[Since every re‐establishment of equilibrium in the caloric may be the cause of the
production of motive power, every re‐establishment of equilibrium which shall be
accomplished without production of this power should be considered as an actual loss.
Now, very little reflection would show that all change of temperature which is not due to a
change of volume of the bodies can be only a useless re‐establishment of equilibrium in the caloric.]

2. Feb 11, 2012

### Staff: Mentor

The net work done by one cycle equals the "area" enclosed by its path in a P-V diagram. Draw a diagram of the cycle that you described and calculate its area.

3. Feb 12, 2012

### Jano L.

You could do it by two isobaric compressions, but the second one would have to be at lower pressure (in order to extract some useful work). In order to do that without another 3rd process, after the first compression, you would have to make the pressure jump to lower value instantaneously, for example by releasing suddenly the load. But such a jump would be irreversible and in the end means loss of useful energy. Carnot has shown that in order to get maximum work form the reservoir, it is necessary to use reversible processes. Isotherms and adiabates in his cycle are reversible.

4. Feb 12, 2012

### chingel

What about having a piston on a crankshaft, then heating the air until the piston goes down from the increased pressure, then cooling it, making the pressure decrease and pull the piston back up?

5. Feb 12, 2012

### Jano L.

Chingel, by "heating the air" you mean heating the work fluid in the engine or the air outside the engine?

6. Feb 12, 2012

### Staff: Mentor

Er, yeah, perhaps you should list the 4 processes...

7. Feb 12, 2012

### chingel

I'm not really sure of the difference. Maybe I meant heating the work fluid.

8. Feb 12, 2012

### Andrew Mason

The Carnot cycle is as efficient as possible because the system is arbitrarily close to equilibrium with the surroundings (the reservoirs) at all times.

The only way you can get work out of such a system is to have heat flow from the hot to the cold.

The only way to do that AND have the system in equilibrium with its surroundings at all times, is to have heat flow occur isothermally with the system and surroundings at the same temperature (ie with the receiving body temperature lower by an infinitessimal amount).

The only way to have heat flows at two different temperatures (ie to have heat flow isothermally to/from reservoirs at two different temperatures) is to have the temperature changes occur adiabatically.

That, in a nutshell, is the Carnot cycle.

AM