# efficiency carnot engine | Efficiency of a carnot cycle |

## The Efficiency of a Carnot Engine: Exploring the World of Engine Cycles and the Carnot Theorem

Picture a world in which different engine cycles compete to be the most efficient at converting heat into work. In this world, a powerful theorem known as the Carnot theorem exists postulated by Sadi Carnot, a French engineer, which states that no cycle can surpass a reversible cycle that operates between the same temperature limits.

It’s like a race, in which the reversible cycle is the undefeated champion that sets the standard for all others to follow. But don’t lose hope, as every cycle can still strive to be the best of the rest. And just like in any competition, it’s important to know your opponent’s strengths and weaknesses. That’s why the Carnot cycle, with its two isothermal and two adiabatic processes, is the most popular contender for comparison. Let us know more about the efficiency carnot engine!

## General formula for Carnot engine efficiency

• Q1 = Heat supplied to the Carnot engine from the heat source
• Q2 = heat rejected by the Carnot engine to the sink

## Formula for carnot engine efficiency in terms of temperatures

• Delta T = T1 -T2
• T1 > T2

To solve problems related to the efficiency Carnot engine you need to know how it works, the different processes the Carnot engine will undergo to produce work and the P-V and T-S diagrams of a Carnot cycle.

## How Carnot engine produces work?

To produce work, the Carnot engine absorbs heat from the source and that heat is converted into work in the engine.

Wasted heat is rejected to the sink as shown in the schematic diagram

## P V diagram of a carnot cycle

In the PV diagram of a Carnot engine, the X-axis represents Volume and the Y- axis represents the pressure

a-b and d-c represent Reversible isothermal processes and b-c and d-a represent Reversible adiabatic processes.

Q1 is the heat supplied to the Carnot engine and Q2 is the heat rejected by the Carnot engine to the sink.

Area under the curve a-b-c-d represents net work done.

## T s diagram of a carnot cycle

In the TS diagram of a Carnot engine, the X-axis represents entropy and the Y- axis represents Temperature.

a-b and d-c represent Reversible isothermal processes and b-c and d-a represent Reversible adiabatic processes.

The area under the curve a-b-c-d represents net work output.

## Isothermal heat addition process (a-b)

• Heat is transferred reversibly and isothermally to the working substance from a high temperature reservoir.
• The high temperature reservoir is called the source, and its temperature T1 is infinitesimally higher than the working substance.
• Work is done by the system during this process, and the amount of work done is equal to the area underneath path a-b of the pressure-volume (p-V) diagram.

• The working substance undergoes a reversible adiabatic (or isentropic) expansion.
• The system is thermally insulated during this process.
• The temperature of the working substance decreases from the high temperature T1 to the low temperature T2.
• Work is done by the system during this process, and the amount of work done is represented by the area underneath path b-c of the p-V diagram.

## Isothermal heat rejection process (c-d)

• Heat is transferred reversibly and isothermally from the working substance to a low-temperature reservoir.
• Work is done on the system during this process.
• The amount of work done on the system is equal to the area underneath the path of c-d on the p-V diagram.

• The working substance is returned to its initial state at point a.
• The temperature of the working substance is raised from T2 to the initial high temperature T1.
• Work is done on the system and is equal to the area underneath path d-a of the p-V diagram.

## How to Improve the efficiency of a Carnot engine?

To achieve maximum efficiency in a Carnot engine, the temperature at which heat is supplied should be made as high as possible, while the temperature at which heat is rejected remains fixed. Since low temperature reservoir or sink is generally fixed by atmospheric or cooling water temperature.

## Limitation of a Carnot engine

The Carnot cycle has the highest possible efficiency between any two temperatures, but it is not suitable for use in engines that use gaseous working fluids due to its low net work output.