Carnot Engine: Overview, Questions, Preparation

The Carnot engine is a thermodynamic cycle proposed by Leonard Carnot. A Carnot engine helps you estimate the maximum possible efficiency of a heat engine during the conversion of heat into work and, conversely, working between two reservoirs. This topic is important in Class XI Physics and has a weightage of around 20 marks along with Properties of Bulk Matter and Kinetic Theory of Gases. 

According to the Carnot Theorem – Any system that works between two given temperatures, hot reservoir (T1) and cold reservoir (T2), can never have an efficiency of more than the Carnot engine working between the same reservoirs, respectively.

The Carnot cycle is a thermodynamic cycle that involves four operations - isothermal gas expansion, adiabatic gas expansion, isothermal gas compression, and adiabatic gas compression. The Carnot cycle involves the steps mentioned below:

Step 1 (isothermal gas expansion) – In the first step, a cylinder is placed at the source so that the gas acquires the temperature. The amount of heat absorbed by the gas is qin from the heat source at a temperature of Th. The gas expands and works on the surroundings.

W1-2 = Q1 = µ x R x T1 x ln (v2 / v1)

Step 2 (adiabatic gas expansion) – In this step, the cylinder is removed and is placed on the insulating stand. The gas continues to expand and work on the surroundings; the temperature is lower TI. The work done by the gas is shown below:

W2-3 = µR / ʵ - 1 (T1 – T2)

Step 3 (isothermal gas compression) – The cylinder is removed from the insulating stand and placed in the sink. In this process, the heat loss qout when the surroundings do the work at the given temperature TI. The work done by the environment on the gas is shown below:

W3-4 = µR T2 ln (v3 / v4)

Step 4 (adiabatic gas compression) – In the last step, the cylinder is removed from the sink and is placed on the insulating stand again. The system is thermally insulated. The temperature rises back to Th as the surroundings work on the gas. The work done by the environment on the gas is shown below:

W4-1 = µR / ʵ - 1  (T1 – T2)

The principles of the Carnot engine apply to cyclical devices such as heat engines. The principles are as follows:

• The effectiveness of a heat engine that is irreversible is always lower than the efficiency of a reversible functioning of two similar reservoirs.
• The effectiveness of reversible heat engines working between two similar reservoirs is equal.

Carnot Cycle is usually used in thermal devices or thermal machines. Some examples of the Carnot cycle are heat pumps used to generate heat, refrigerators to cool, steam turbines used in ships, combustion engines in vehicles, and reaction turbines in airplanes.

Example 1. A Carnot Cycle operating between T1 = 500 K and T2 = 300 K produces around 2kJ of the mechanical work per cycle. Calculate the amount of heat transferred to the engine by the reservoirs?

Efficiency of a Carnot Engine η = 1 - (T2 / T1)

T1 = 500 K

T2 = 300 K

η = 1 - (300 / 500) = .4

Also, η = Output work / Heat Supplied = 2000 / x

Now, 2000 / x = .4

Thus, x = 5000J

Example 2. If the performance coefficient of a refrigerator is 5 and it operates at the room temperature of 300 K, calculate the temperature inside the refrigerator?

α = T2 / T1 - T2 

5 = T / 300 - T

Or T = 250 K

FAQs on Carnot Heat Engine

Q: What is a Carnot heat engine?

Ans: A Carnot heat engine is also known as a theoretical engine that operates on a reversible Carnot cycle. The Carnot engine has the maximum efficiency that a heat engine can have.

Q: What happens in the isothermal expansion process?

Ans: In the isothermal expansion process, the heat absorbed by the gas is equal to the work done.

Q: Which is the working fluid in Carnot’s cycle?

Ans: Ideal gas is the working fluid in a Carnot cycle.

Q: Which are the steps involved in the Carnot cycle?

Ans: The steps involved in a Carnot cycle are isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

Q: Which are the important parts of the Carnot heat engine?

Ans: The important parts of the Carnot heat engine are a cylinder, a reservoir, a heat-insulating stand, and a sink.