Table of Contents
Carnot Cycle
Carnot Heat engine (based on Carnot Cycle) was a concept developed by Nicolas Leonard Sadi Carnot (1796-1832, a French Military Engineer and Physicist) so that one can visualize a reversible heat engine in practice.
Carnot engine is a reversible heat engine which works on Carnot cycle.
P-V Diagram
Carnot cycle comprises of four processes.
- Reversible isothermal process of heat addition (Process A-B)
- Reversible adiabatic process of expansion (Process B-C)
- Reversible isothermal process of heat rejection (Process C-D)
- Reversible adiabatic process of compression (Process D-A)
T-S Diagram
Carnot Heat Engine
Now we understand Carnot engine physically in the following way.
Process A-B
In this process heat is released from the hot reservoir and is absorbed by the ideal gas particles within the system. Thus, the temperature of the system rises. The high temperature causes the gas particles to expand hence pushing the piston upwards and doing work on the surroundings.
Process B-C
In this process expansion continuous, however there is no heat exchange between the system and the surroundings. Thus, the system is undergoing adiabatic expansion. The expansion allows the ideal gas particles to cool, decreasing the temperature of the system.
Process C-D
In this process surroundings do work on the system which causes heat to be released. The temperature within the system remains the same. Thus, isothermal expansion occurs.
Process D-A
No heat exchange occurs in this process however, the surroundings continue to do work on the system. Adiabatic compression occurs which raises the temperature of the system and puts the piston back to its original state (Prior to process A-B).
Below are P-V and T-S Diagrams of the Carnot Cycle.
We know T4 = T1, say it be TA and T3 = T2, say it be TB.
Below is the table which shows heat and work interactions of the Carnot cycle, along with the change in the internal energy.
| Process | Change in Internal Energy | Work Interaction | Heat Interaction |
| Process 1-2 | CV(T2-T1) | CV(T1-T2) | 0 |
| Process 2-3 | 0 | RTB ln(V3/V2) | RTB ln(V3/V2) |
| Process 3-4 | CV(T4-T3) | CV(T3-T4) | 0 |
| Process 4-1 | 0 | RTA ln(V1/V4) | RTA ln(V1/V4) |
Note: Negative value of heat interaction indicates heat rejected by the system and positive value of heat interaction indicates heat added to the system. Positive value of work interaction indicates work done by the system and negative value of work interaction indicates work done on the system.
Efficiency of Carnot Cycle
Efficiency of the Carnot Cycle is the ratio of work output to the heat input.
Work output = RTA ln(V1/V4) – RTB ln(V2/V3)
Heat Input = RTA ln(V1/V4)
Efficiency = Work Output/Heat Input
After putting values of heat input and work output in the above formula, we get
η = 1 – [(RTB ln(V2/V3))/(RTA ln(V1/V4))] … (1)
Also, V1/V4 = V2/V3
It means
η = 1 – (TB / TA)
Image attributions:
T-S Diagram: By Original:PAR~commonswikiVector:Smieh – This file was derived from: CarnotCycle1.png:, CC0, https://commons.wikimedia.org/w/index.php?curid=20068191
Images of Carnot’s Engine: By BlyumJ – Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=64937239