Carnot Theorem: Overview, Questions, Preparation

The Carnot's theorem was discovered by Nicolas Leonard Sadi Carnot in 1824. He stated that there are no limits for the efficiency of the heat engine; it can be as maximum as it could get depending upon the hot and cold reservoir temperatures.

Carnot's theorem states that:

1. Simple heat engines are less effective and efficient when they are between two heat reservoirs, whereas Carnot heat engines are more efficient operating between two heat reservoirs.
2. The Carnot engines are always efficient irrespective of their operations.
3. The formula of maximum efficiency is:

Nmax = nCarnot = 1 – Tc / TH

 Here, the TC is the temperature of the cold reservoir,

          T is the temperature of the hot reservoir,

         And n is the ratio of the work and the heat.

This states that the efficiency of reversible engines between the two same heat reservoirs is the same and equal. The formula of the reversible engine is illustrated below:

ΔS = ∫ ab d Qrev / T

Here, T is the temperature,

ΔS is the change in entropy, and

∫ ab is the path function.

The Carnot engine is the most efficient irreversible engine that works between the two same reservoirs. 

Some of the examples of the irreversible engine are as follows:

• Friction
• Chemical reactions
• Plastic deformation

The applications of the Carnot theorem are listed below:

1. One of the most significant applications of Carnot’s theorem is that it converts thermal energy into work.
2. The method of converting low temperature of heat into high temperature is called refrigeration and is a reversible process.

Carnot’s Theorem for Class 11

The chapter ‘Thermodynamics’ holds a weightage of 3 marks. It includes 2 questions in total consisting of one objective type question of 1 mark and one short question of 2 marks.

Example 1: Write the formula of Carnot’s maximum efficiency Theorem.

Answer: The formula of maximum efficiency is:

                  Nmax = nCarnot = 1 – Tc / TH

Here, the TC is the temperature of the cold reservoir,

                T is the temperature of the hot reservoir,

               And n is the ratio of the work and the heat.

Example 2: Write the formula of Reversible Engine.

Answer: The formula of Reversible engine is written below:

                  ΔS = ∫ ab d Qrev / T

Here, T is the temperature,

          ΔS is the change in entropy, and

          ∫ ab is the path function.

Example 3: Name the working fluid that is used in a Carnot Cycle.

Answer: The working fluid used in a Carnot cycle is an ideal gas.

Q: What are the examples of an irreversible engine?

Q: What is Carnot’s theorem?

Q: What do you mean by a reversible engine?

Q: What are the applications of Carnot’s Theorem?

Q: What do you mean by Diesel Cycle?