Carnot engine
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This document explains heat engines and the Carnot engine. It defines a heat engine as a device that converts heat into work via a cyclic process. It then describes the key components of a heat engine - a hot reservoir or source, a cold reservoir or sink, and a working substance within a cylinder. The document goes on to explain the Carnot cycle in detail, which consists of two isothermal and two adiabatic processes. It states that the Carnot engine has the maximum possible efficiency among heat engines operating between the same temperature limits. The efficiency of any heat engine is defined and the efficiency of the Carnot engine is derived.
Carnot engine
- 2. Objective is to explain what a heat engine is, and compute its thermal efficiency
- 3. Heat engine is a device by which a system is made to undergo a cyclic process that results in conversion of heat into work.
- 4. The different parts of heat engine are HOT RESERVOIR or Source is a material kept at high temperature and having infinite thermal capacity. Any amount of heat can be taken from it without changing its temperature.
- 5. COLD RESERVOIR or Sink is a material kept at low temperature and having infinite thermal capacity. Any amount of heat can be given to it without changing its temperature.
- 6. Working substance is a material which converts heat energy in to work. It is taken in a cylinder fitted with tight movable frictionless piston. The lower side of the cylinder will be thermally conducting.
- 7. It insulates the working substance from thermal contact with the surroundings. That is used for performing the adiabatic process.
- 8. Piston Cylinder Ideal Gas (working Substance) Source at Temp T1 Insulating Stand Sink at Temp T2
- 11. Carnot engine is an ideal heat engine whose efficiency is maximum. In carnot engine, carnot cycle is used. In carnot engine, ideal gas is the working substance and all the dissipative forces are absent.
- 12. Carnot devised an ideal cycle of operation for a heat engine and is know as carnot cycle. In one complete cycle of operation, there are four different thermodynamic processes.
- 13. At first, the working substance is kept in contact with the source. The piston of the cylinder is moved outwards. The gas expands at constant temperature. The amount of heat(Q1) is absorbed from the source to make the temperature constant. The volume increases and pressure decreases. This is called isothermal expansion. It is represented by the curve AB in the indicator diagram.
- 15. The lower conducting side of the cylinder is kept in contact with the insulating stand. The piston of the cylinder is moved outwards. The gas expands such that no heat enters the system or leaves from it. The volume increases and pressure decreases. The temperature is decreased from T1 to T2. This is called adiabatic expansion. It is represented by the curve BC in the indicator diagram.
- 17. The cylinder is kept in contact with the sink. The piston of the cylinder is moved inwards. The gas is compressed at constant temperature. The excess heat produced(Q2) will flow to the sink to make the temperature constant. The volume decreases and pressure increases. This is called isothermal compression. It is represented by the curve CD in the indicator diagram.
- 19. The cylinder is kept in contact with the insulating stand. The piston of the cylinder is moved inwards. The gas is compressed such that no heat enters the system or leaves from it. The volume decreases and pressure increases. The temperature increases from T2 to T1. This is called adiabatic expansion. It is represented by the curve DA in the indicator diagram.
- 22. We have the efficiency of heat engine, η = W/Q1 where ‘W’ is the work done and Q1 is the amount of heat absorbed from the source. Also W = Q1 – Q2 where Q2 is the amount of energy rejected to sink. There fore, η = ( Q1 – Q2)/Q1 = 1 – (Q2/Q1) For a carnot engine, it can be shown that η = 1 – (T2/T1) where T is the temperature of source and T2 that of sink. 1
- 23. Carnot engine is purely an imaginary engine. But all real engines are constructed based on carnot cycle. No other engine can have same efficiency as that of a carnot engine working between the same temperature range.