1. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA 1

2. Carnot Heat Engine Carnot Cycle Sajjad Ahmed Memon Senior Scientist NIMRA

3. Carnot Het Engine Carnot heat engine is an ideal heat engine which converts heat energy into mechanical energy. A heat engine acts by transferring energy from a warm region to a cool region of space and in the process, converting some of that energy to mechanical work. This process may be reversible. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

5. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded upon by Benoît Paul Émile Clapeyron in 1834. Rudolf Clausius in the 1857s and 66s, drawn out it mathematically from which the concept of entropy was developed. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

6. Working of Carnot Engine It consists of a cylinder and a piston. The walls of the cylinder are non-conducting while the bottom surface is the conducting one. The piston is also non-conducting and frictionless. It works in four steps. Which are as follows. 1.Isothermal Expansion 2.Adiabatic Expansion 3.Isothermal Compression 4.Adiabatic Compression Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

7. 1. Isothermal Expansion: First of all, cylinder is placed on a source and allow to move upward as a result temperature and pressure of the working substance decreases, while volume increases. In order to maintain temperature we have to supply more amount of heat from source to the cylinder. Since in this expansion temperature is kept constant. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

8. 2. Adiabatic Expansion: Secondly cylinder is placed on an insulator and piston is allow to move upward as a result temperature and pressure of working substance will decrease. While volume will increase but no heat is given or taken of the cylinder. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

9. 3. Isothermal Compression: In this state cylinder is placed on a sink and piston is allow to move downward as a result temperature and pressure of the working substance will increase while volume will decrease. In order to maintain temperature we have to reject extra heat from cylinder to the sink. Since in this compression temperature is constant. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

10. 4. Adiabatic Compression: Finally cylinder is placed on an insulator and piston is a flow to move downward, when we do so neither temperature nor pressure or volume is constant. But no heat is given or taken out of the cylinder. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

11. Reversible isothermal expansion (T H = constant) Reversible adiabatic expansion (Q = 0, T H  T L ) Reversible isothermal compression (T L =constant) Reversible adiabatic compression (Q=0, T L  T H ) Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

12. Carnot Cycle By combining the four processes Isothermal Expansion, Adiabatic Expansion, Isothermal Compression and Adiabatic Compression which are carried out in carnot engine, then we get a cycle knows as Carnot cycle. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

15. If we want to increase the efficiency of any heat engine then for this purpose we have to increase temperature of source as maximum as possible and reduce the temperature of sink as minimum as possible. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

16. Carnot's Theorem No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs. This maximum efficiency is defined by the formulas: Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

17. or Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

18. Here W is the work done by the system (energy exiting the system as work) and W = Q H - Q C Also W = T H - T C Q H is the heat energy entering the system Q C is the heat energy exiting the system T C is the absolute temperature of cold reservoir T H is the absolute temperature of hot reservoir Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

19. Carnot realized that in reality it is not possible to build a thermodynamically reversible engine, so real heat engines are less efficient than indicated by above equations. In addition, real engines that operate along this cycle are rare. Above equations are extremely useful for determining the maximum efficiency that could ever be expected for a given set of thermal reservoirs. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

21. Example 1: Consider a Carnot heat engine operating between a high temperature source at 900 K and rejecting heat to a low temperature reservoir at 300 K. Determine the thermal efficiency of the engine. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

23. Example 2: Calculate the work done by a carnot engine which is operating between at high temperature source of 500 K and the efficiency of the engine is 80%. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

25. Example 3: Calculate the heat energy entering the system in a carnot engine, energy exiting the system is 300 J with efficiency of 70%. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA