Last updated on May 16th, 2022 at 09:01 pm

The **Carnot cycle** represents the *cycle of processes* for a *theoretical heat engine* with the maximum possible efficiency. Such an idealized engine is called a

**Carnot engine**. Here in this post, we present a brief idea of the

**Carnot cycle processes**, Carnot engine efficiency, and also we solve here a

*numerical problem related to the Carnot engine*.

## Carnot Cycle processes

The **Carnot cycle** represents the *cycle of processes* for a *theoretical heat engine* called a Carnot engine. This engine ideally is with the maximum possible efficiency.

Carnot cycle consists of an ideal gas undergoing the following processes: (refer to figure 1 for A, B, C, and D nodes of the Carnot cycle)

- Isothermal expansion (A →B)
- Adiabatic expansion (B →C)
- Isothermal compression (C →D)
- Adiabatic compression (D →A)

The area of ABCD provides the work done by the gas during the Carnot cycle.

## Efficiency of Carnot engine

*The temperatures of the hot and cold reservoirs fix the maximum possible efficiency that can be achieved.*

The efficiency of a Carnot engine can be shown to be: e_{c}= 1 – T_{C}/T_{H}, (Here, T in Kelvin)

% efficiency of a Carnot engine: %e_{c}= [1 – T_{C}/T_{H}] x 100%

## Numerical problem related to Carnot engine and Carnot cycle

**Q ) An engine operates at 300 °C and ejects heat to the surroundings at 20 °C. Find out the maximum possible theoretical efficiency.**

** Solution:**

T_{C} = 20 + 273 k = 293 K

T_{H} = 300 + 273 k = 573 k

The maximum possible theoretical efficiency = e_{c}= 1 – T_{C}/T_{H} = 1 – 293/573 = 0.49

Hence, %efficiency = 49%