Heat engines and Refrigerators

Heat Engines and Refrigerators

Heat Engines:

The heat engine is a device which converts heat energy into mechanical energy. The main parts of a heat engine are:

(i) a hot body called source,
(ii) a working substance
(iii) an insulating stand and
(iv) a cold body called sink.

The working substance absorbs heat from the source, converts a part of it into useful work and rejects the rest to the sink. The working substance then returns to the original state. This series of processes is called a cycle. By repeating the cycle work can be continuously obtained.

Practical heat engine can be classified into

(i) external combustion engine and
(ii) internal combustion engine.

In an external combustion engine combustion takes place outside the cylinder of the engine. For example, steam engine is an external combustion engine. Its efficiency is very low; about 30%.
In an internal combustion engine, the combustion takes place inside the cylinder of the engine. Petrol engine and diesel engine are internal combustion engines. Efficiency of these engines is nearly 50%.

Canines heat engine:

Carrot realized a theoretical engine which is free from all defects of practical engines. Its efficiency is maximum it is an ideal heat engine which cannot be realized in practice.

Different parts of a Carnot’s engine

The essential parts of a Carnot's engine are
(1) Working substance
(2) Source
(3) Insulating stand
(4) Sink

1. Working Substance is an ideal gas contained in a cylinder with perfectly insulating wall and perfectly conducting base. It is closed with a tight fitting perfectly insulated an frictionless piston.

2. A hot body of infinite thermal capacity at higher temperature T1 serving as source.

3. A cold body of infinite thermal capacity at a lower temperature T2 serving as sink.

4. A perfectly insulating stand.

Carnot's cycle: The cycle of a Carnot's engine is completed in four operations.

1. Isothermal expansion:

The cylinder is placed on the source so that it acquires the same temperature T1 as that of the source. Let P1 and V1 be the pressure and volume of the ideal gas taken in the cylinder. Now the piston is slowly raised so that the working substance expands isothermally at constant temperature T1 till the pressure changes P2 and volume to V2. This process is represented by the curve AB on the indicator diagram. Let Q1 be the heat absorbed by the working substance during this isothermal expansion.

2. Adiabatic expansion

The cylinder is now transferred on to the insulating stand and the working substance is further allowed to expand adiabatically by raising the piston. Since no heat is supplied to the substance, its temperature falls. The expansion is continued till the temperature falls to T2. The adiabatic expansion is represented by the curve BC, where P3 and V3 are the final pressure and volume.

3. Isothermal compression

The cylinder is placed on the sink and the piston is pressed so that the gas gets compressed. Heat produced during compression is rejected to the sink and the temperature remains constant at T2. This isothermal compression is represented by the curve CD where the final pressure and volume are P4 and V4. Let Q2 be the heat rejected to the sink.

4. Adiabatic compression

The cylinder is again placed on the insulating stand and the gas is further compressed. This compression is adiabatic since no heat enters or leaves the working substance. The temperature rises to T1 and the point A is reached again, where the pressure and volume of the gas are P1 and V1 respectively. This compression is represented by the curve DA.

The external work done by the substance during the processes AB and BC are represented by areas ABB'A' and BCC'B' respectively.

Similarly the work done on the substance during the processes C D and DA are represented by areas CDD'C' and DAA'D' respectively.

Therefore, Net work done by the gas.

W = the difference between these two pairs of areas
     = area (ABB'A' + BCC'B') – area (CDD'C' + DAA'D') = area ABCD

Thus the area ABCD represents the net external work W done by the working substance in one complete cycle.

The net amount of heat absorbed by the working substance in one cycle = Q1 — Q2. Since the initial and final states are the same, there is no change in its internal energy. Hence from first law of thermodynamics,

W = Q1 — Q2 = Area of ABCD

Thermal efficiency

Thermal efficiency of a heat engine is the ratio of the net work done by the engine to the heat taken from the source during one complete cycle. If Q1 is the heat taken from the source and Q2 the heat rejected to the sink, work done in one complete cycle is given by,

W = Q1 — Q2

Efficiency , η = W/Q1 = (Q1 — Q2)/ Q1

For an ideal Carnot's engine it can be shown that, η = (T1 – T2)/ T1

where T1 and T2, are the temperatures of the source and the sink respectively.

From the above equation, it is clear that η always less than unity. As T1 > T2 the smaller the value of T2 greater is the efficiency. If T2= 0, then only the efficiency would be 100%. Since it is impossible to obtain a sink at absolute zero, an engine with 100% efficiency is a practical impossibility.

The Refrigerator—Reversibility of Carnot's cycle

Since Carnot's cycle is performed through steps which are perfectly reversible, it can he performed in the reverse order ADCBA. When the process is carried out this way we have a Carnots refrigerator. Here the working substance absorbs an amount of heat Q2 from the sink, the freezer compartment. An amount of work W is done by some external agency (generally an electric compressor). Then the working substance gives a large amount of heat Q1 to the source (generally the atmosphere). The working substance is called 'refrigerant'.

Therefore, Q1= Q2 + W

Coefficient of performance of a refrigerator (β)

It is defined as the ratio of the quantity of removed from the freezer compartment per cycle to the energy spent by the external agency per cycle to remove this heat.

β = Q2/W = T2/(T1 - T2)

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