How the working of Carnot engine is explained in layman language?

 by  Maryam Hussain

How the working of a theoretical engine was proposed?

The theoretical heat engine was proposed by Sadi Carnot in 1824. Heat engines are devices that can convert heat into mechanical energy.

Like a Steam engine or Motor vehicle, the working principle of all heat engines is the same in which any working substance gas or vapor is brought back to the initial stage by going through different thermodynamic stages of a cyclic process. Carnot suggested that, if a heat engine goes through fixed thermodynamic stages of a specified process, then the efficiency of the heat engine may be 100% possible.

Ideally, this engine gives maximum efficiency. No other engine can be more efficient than this. The specified cyclic process suggested by Carnot is called the Carnot cycle.

The Carnot engine has four main parts:

1). First, an insulated, non-conducting stand, so that the transfer of energy is not possible.

2). Second, a hot reservoir with infinite heat capacity. Heat capacity is Infinite so that the temperature of the reservoir remains constant after taking any energy from it. It is also called a heat source.

3). Third, a cold reservoir. Its heat capacity is also infinite. So that any amount of heat is given, its temperature does not change. This is also called a heat sink.

4). Fourth, a cylinder in which the working substance can be kept. Working substances can be anything gas or liquid. A cylinder is fitted with a movable piston. The piston, cylinder walls, and base are made of non-conducting material making heat transfer impossible.

Carnot suggested that the Carnot engine goes through four different stages of the Carnot cycle:

1) Place the cylinder on the hot reservoir. Since the temperature of the reservoir is higher than the temperature of the gas, the heat flows from the heat reservoir to the gas forcing the gas to expand. Because the gas expands in direct proportion to the heat absorbed, the temperature of the gas remains constant. This process is called Isothermal expansion, as the gas expands, the volume of the gas increases and the pressure decreases.

2) In the next step, take off the cylinder from the hot reservoir and place it on the insulating stand. When doing so, the gas is contained to the heat insulator wall. Now Let the Piston to rise slowly upward due to which the gas continues to expand. But this time the gas is not getting any heat to expand. Such expansion is called adiabatic expansion. Since this expansion is taking place without heat, the temperature of the gas starts to decrease. Due to this expansion, the volume of the gas also increases and the pressure decreases.

3) In the next step, lift the cylinder from the stand and place it on the cold reservoir. Now press the Piston downward which causes compression of the gas. The reservoir absorbs whatever extra heat is produced due to the compression of the gas. In this way, the gas compresses at the same constant temperature. This is called isothermal compression. Due to this compression, the volume of the gas decreases and the pressure is increased.

4) In the final step, keeping the cylinder on the insulated stand again, press Piston downward. But now there is no cold reservoir to absorb the heat getting produced extra. Therefore, the temperature of the gas starts increasing. This compression is called adiabatic compression. Press the piston until the temperature of the gas rises back to equal that of the hot reservoir. This decreases the volume of the gas and increases the pressure. At the end of this step, the gas returns to its initial stage.

This complete cycle is called the Carnot cycle and the engine working on it is called the Carnot engine.

A Carnot engine's efficiency depends on the temperature of both reservoirs. Either raise the temperature of the hot reservoir to infinite kelvin or low down the temperature of the cold reservoir to zero kelvin. In both cases, the engine efficiency will be 100%. But it is not possible to do so.

Hence the Carnot engine is just a theoretical ideal engine.

The key to increase the efficiency of the practical engine, temperature difference between the two reservoirs must be kept as high as possible.

How to find out the efficiency of a Carnot Engine?

Illustration 1. A Carnot engine operates between two temperature reservoirs maintained at 250 ^oC and 22 ^oC, respectively. What should be the thermal efficiency of the Carnot Engine?

Solution:

A Carnot engine's efficiency is given by

Ƞ =  1 – (T_L / T_H)                                                             

Where,

Ƞ  = Thermal efficiency of an engine, this is normally known to us as a ratio of output by input

T_L = Temperature of a heat sink, (in absolute scale i.e. Kelvin or Rankine) a Low-temperature reservoir also mentioned as surroundings.

T_H = Temperature of heat source, (in absolute scale i-e Kelvin or Rankine) a High-temperature reservoir also mentioned as surroundings.

Now, converting the given temperatures to absolute temperatures

T_L =         22^oC       +             273         =             295^oK

T_H =        250^oC     +             273         =             523^oK

Then thermal efficiency is calculated as 43.6 %

How the increase in ambient temperature affects the thermal efficiency of a Carnot engine?

Illustration 2. Consider a Carnot engine operating between two temperature reservoirs maintained at 250 ^oC and 25 ^oC, respectively. 

a). What should be the thermal efficiency of the Carnot Engine?

b). Did the thermal efficiency of Carnot change Engine w.r.t that of illustration 1?

Solution:

A Carnot engine's efficiency is given by

Ƞ =  1 – (T_L / T_H)

                                                                   

Where,

Ƞ  = Thermal efficiency of an engine, this is normally known to us as a ratio of output by input

T_L = Temperature of a heat sink, (in absolute scale i.e. Kelvin or Rankine) a Low-temperature reservoir also mentioned as surroundings.

T_H = Temperature of heat source, (in absolute scale i-e Kelvin or Rankine) a High-temperature reservoir also mentioned as surroundings.

Now, converting the given temperatures to absolute temperatures

T_L =         25^oC       +             273         =             298^oK

T_H =        250^oC     +             273         =             523^oK

a). Then thermal efficiency is calculated as 43%.

b). We saw that the thermal efficiency of a Carnot engine decreased. It became 43 % from 43.6 % when T_L = Temperature of heat sink increased from 22^oC  to   25^oC.

How does a drop in ambient temperature affect the thermal efficiency of a Carnot engine?

Illustration 3. Suppose a Carnot engine operating between two temperature reservoirs maintained at 250 ^oC and 20 ^oC, respectively.

a). What should be the thermal efficiency of the Carnot Engine?

b). Did the thermal efficiency of the Carnot Engine change w.r.t that of illustration 1?

Solution:

A Carnot engine's efficiency is given by                                                              

Ƞ =  1 – (T_L / T_H)     

Where,

Ƞ  = Thermal efficiency of an engine, this is normally known to us as a ratio of output by input

T_L = Temperature of a heat sink, (in absolute scale i.e. Kelvin or Rankine) a Low-temperature reservoir also mentioned as surroundings.

T_H = Temperature of heat source, (in absolute scale i-e Kelvin or Rankine) a High-temperature reservoir also mentioned as surroundings.

Now, converting the given temperatures to absolute temperatures

T_L =         20^oC       +             273         =             293^oK

T_H =        250^oC     +             273         =             523^oK

a). Then thermal efficiency is calculated as 44 %.

b). We saw that the thermal efficiency of a Carnot engine increased. It became 44 % from 43.6 % when T_L = Temperature of heat sink decreased from 22^oC  to   20^oC.

How the decrease in source or hot reservoir temperature affects the thermal efficiency of a Carnot engine?

Illustration 4. A Carnot engine operates between two temperature reservoirs maintained at 230 ^oC and 22 ^oC, respectively.

a). What should be the thermal efficiency of the Carnot Engine?

b). Did the thermal efficiency of the Carnot Engine change w.r.t that of illustration 1?

Solution:

A Carnot engine's efficiency is given by

Ƞ =  1 – (T_L / T_H)                                                        

Where,

Ƞ  = Thermal efficiency of an engine, this is normally known to us as a ratio of output by input

T_L = Temperature of a heat sink, (in absolute scale i.e. Kelvin or Rankine) a Low-temperature reservoir also mentioned as surroundings.

T_H = Temperature of heat source, (in absolute scale i-e Kelvin or Rankine) a High-temperature reservoir also mentioned as surroundings.

Now, converting the given temperatures to absolute temperatures

T_L =         22^oC       +             273         =             295^oK

T_H =        230^oC     +             273         =             503^oK

a). Then thermal efficiency is calculated as 41.3%.

b). We saw that the thermal efficiency of a Carnot engine decreased. It became 41.3 % from 43.6 % when T_H = Temperature of heat source decreased from 250^oC  to   230^oC.