Carnot’s Theorem

Nov 09, 2022, 16:45 IST

Carnot’s theorem, also known as Carnot’s rule, was developed by Nicolas Léonard Sadi Carnot in 1824, with the principle that there are limits on maximum efficiency for any given heat engine. It depends mainly on hot and cold reservoir temperatures.

Definition

Heat engines working between the two heat reservoirs are less efficient as compared to the Carnot heat engine operating between the same reservoirs. Irrespective of the operation details, every Carnot engine is efficient between two heat reservoirs.

Maximum efficiency is given as follows:

η_max = η_carnot = 1- T_c / T_H

Where,

T_C = absolute temperature of the cold reservoir.

T_H = absolute temperature of the hot reservoir.

η = the ratio of work done by the engine to heat drawn out of the hot reservoir.

Processes involved in thermodynamics can be carried out by the two ways:

Reversible Engine

The efficiency of all the reversible engines remains the same, which works between two same heat reservoirs.

Where,

ΔS = change in entropy

T = temperature

Irreversible Engine

No irreversible engine is more efficient as compared to the Carnot engine working between the two reservoirs.

Examples of an irreversible engines are:

• Plastic deformation
• Friction
• Spontaneous chemical reaction

Applications of Carnot’s theorem

• Carnot’s theorem finds the application in engines that convert the thermal energy to work.
• Refrigeration: The method of removal of heat from at a low temperature and dissipating it to a higher temperature. This is a reversible process.

Frequently Asked Questions (FAQs)

Q1. Can the efficiency of Carnot's engine be 0 or 1?

Ans. η is always less than 1 because T_L is less than T_H. This implies the efficiency cannot be 100%. It can be 1 or 100% only when T_L = 0K (absolute zero of temperature), which is impossible to attain practically.

Q2. Are fuel cells limited by Carnot efficiency?

Ans. The reason is due to the combustion irreversibility of the latter. This has led to the statement that fuel cell efficiency is not limited by the Carnot cycle.

Q3. Where is Carnot engine used?

Ans. The thermodynamic Carnot engine was initially derived to describe the conversion of heat to work. A Carnot engine in reverse operation also acts as a model for heat pumps (refrigerators).

Q4. How can you increase the efficiency of a Carnot cycle?

Ans. Hence, by decreasing the sink temperature and increasing the reservoir temperature. We can increase the efficiency of the Carnot.

Q5. Is Carnot reversible or irreversible?

Ans. Reversible