Available Energy

In order to determine that part of the energy which can be converted into work by an engine, we require consider a thermal reservoir at constant temperature T from which a quantity of energy Q is being absorbed as heat.

A Carnot engine may be operated between the reservoir at T and the surroundings at temperature T₀ to convert part of the energy into work. The amount or work that can be obtained is given by

(25.1)

Where is the change in the entropy of the reservoir that supplies the energy. The Carnot cycle is shown on a diagram (Figure 25.1)

Figure 25.1

The area 1234 represents the portion of energy delivered as work by the reversible engine and is called available energy .

The area 43BA represents the portion of the energy which is rejected to the atmosphere.

The portion of energy is not available for conversion into work is called unavailable energy . Therefore, the available energy represents the portion of the energy supplied as heat which can be converted into work by means of a reversible engine. It is also known as EXERGY .

The result is true also for the case of a finite body, which acts as a source, the temperature of which varies during the interaction.

Let us consider a finite body from which energy in the form of heat can be absorbed by a heat engine. As the energy is with drawn from the finite body, the temperature of the body keeps on decreasing. This process can be carried out using a large number of differential Carnot engine. For a differential Carnot cycle, let represent the energy absorbed at temperature T. The differential amount of work done by the engine is given by

(25.2)

Figure 25.2

If the Carnot engine works till the temperature of the body attains a value (Figure 25.2) the total work done by the reversible engine is given by

	(25.3)

Therefore, if a certain amount of energy, Q is absorbed as heat from a finite body, then represents the available portion of the energy which can be converted into work. The unavailable energy is also known as ANERGY.