Question 10: What is meant by Carnot Cycle and Carnot Engine?

ANSWER

### Carnot Cycle

A number of processes after the completion of which the properties of the system returns to the original state is called a *cycle*.

The operating cycle of a Carnot cycle consists of the following four processes.

#### 1. Isothermal Expansion

Consider a Carnot heat engine, which consists of a gas cylinder with perfectly insulating walls and perfectly conducting base, having an insulated, weightless and frictionless piston.

Let the initial pressure, volume and temperature of the system are P_{1},V_{1} and T_{1}, respectively. Place the cylinder on a high temperature reservoir (HTR). The gas absorbs some amount of heat (+ Q1). With the heat thus provided, the gas expands and the volume increases and pressure decreases. Thus, the temperature remains constant. After the absorption of heat (+Q_{1}) and the resultant expansion, the state of the gas is described with pressure P_{2}, volume V_{2} and temperature T_{1}(which is constant). Therefore, the process is isothermal represented by the isotherm A-B in the figure.

#### 2. Adiabatic Expansion

The cylinder is then placed on a heat insulation stand so that the heat can neither enter nor leave the system. The gas is allowed to expand under these conditions and let the new volume is V_{3}. With this expansion, the temperature of the gas in the cylinder falls down. Say, it is T_{2} now. Similarly, the pressure decreases from P_{2} to P_{3}. The process is an adiabatic expansion and represented by the adiabat B-C in the figure.

#### 3. Isothermal Compression

The gas cylinder is now placed on cold reservoir (LTR) at temperature T_{2}. The gas is compressed by increasing the load on the piston. Heat (-Q_{2}) is rejected by the gas to the LTR and in this way the temperature remains constant. However, the volume decreases from V_{3 }to V_{4} and pressure goes from P_{3} to P_{4}. The process is an isotherm shown by C-D in the figure.

#### 4. Adiabatic Compression

The gas cylinder is placed on the insulating stand and compressed to the initial stage of P_{1}, V_{1} and T_{1}. The process is represented by the adiabat D-A in the figure.

The four processes thus complete a Carnot cycle.

In one complete cycle, a Carnot heat engine performs a net amount of work ΔW, and absorbs a net amount of heat Q_{1} – Q_{2} in the process, represented by the area ABCDA.

### Efficiency

Efficiency is defined as,

Since Q and T are proportional, therefore,

This equation says that the efficiency of a heat engine can never reach to 100%, because T_{2}/T_{1}must have some positive numerical value and when subtracted from 1 will make the efficiency η < 1.

Pingback:index-cq10-p11