* AVAILABILITY, UNAVAILABILITY AND IR-REVERSIBILITY

AVAILABILITY

, UNAVAILABILITY

AND IR-REVERSIBILITY

The portion of low grade energy

 converted into useful work is

availability. Whereas the portion of low

grade energy not converted

into useful work is unavailability. The

difference between total availability and

useful work obtained is ir-reversibility.

Ir-reversibility is inherent to every

process. It is due to some kind of energy

or potential loss or heat dissipation.

There is internal and external ir-

reversibility. Ir-reversibility is in every

process. Eating and cooking of food

are ir-reversible processes. Well known

two statements of the Second law of

Thermodynamics, by Planck’s and

Clausius, prove ir-reversibility in every

process. Ir-reversibility is reducible but is

not eliminated altogether. A reversible

process has zero ir-reversibility. But it is

only a theoretical concept as it cannot be

achieved in actual practice.

Grades of Energy

There are two grades of energy available from the various sources.

High grade energy

High grade energy is fully convertible into useful work (Shaft Work). Second Law of Thermodynamics is not applicable. Examples of High Grade Energy are

1. Mechanical work

2. Electrical energy

3. Potential energy

4. Kinetic energy

5. wind energy

6. water energy

7. Jet energy

8. Tidal energy

Low grade energy

Low-grade energy is not fully convertible into useful work (Shaft Work). Second Law of Thermodynamics governs it.

Examples of Low Grade Energy are

1. Heat from nuclear fission or fusion

2. Heat from combustion of fossil fuels

3. Solar energy

4. Heat energy from any source

The high-grade energy is obtainable from low-grade energy. The complete conversion of low grade energy into high grade (shaft work) is impossible. Thus there is ir-reversibility which vary from one process to another process.

Available Energy or Availability

The amount of low-grade energy converted into high grade energy is available energy.

Unavailable Energy

The amount of low-grade energy not converted into high grade energy is unavailable energy.

Ir-Reversibility

It is the difference of available energy and the actual useful work obtained.

Theoretical Available Energy Between Two Reservoirs At Constant Temperatures

1. First reservoir at constant temperature but at a higher temperature than the atmospheric temperature

(II) Second reservoir is atmosphere at constant temperature.

Theoretical Available Energy

It is the amount of useful work available up to atmospheric temperature and pressure.

NOTE: No energy is convertible into useful work below the atmospheric conditions.

Theoretical Unavailable Energy

Equal to the product of atmospheric temperature and the change of entropy of the system during a process. Atmospheric temperature is the lowest temperature of heat rejection.

Theoretical Available Energy Between Two Finite Sources

Finite source is one where temperature is variable. In this case, there will be decrease in the availability as compared to the case of two constant temperature reservoirs.

AVAILABLE ENERGY OR AVAILABILITY

The amount of low-grade energy converted into high grade energy is available energy.

 

 

 

Fig. 2  Availability and unavailability from a Finite Source

Total availability = area 1-2-6-5-1

Net Available = W _useful = area 1-2-3-4-1

Unavailability = area 4-5-6-3-4

UNAVAILABILITY OR UNAVAILABLE ENERGY

The amount of low-grade energy not converted into high grade energy is unavailable energy.

T_h is the absolute high temperature of a body and T_a is the absolute atmospheric temperature in Fig.1. No energy is convertible into useful work below the atmospheric conditions.

T1 and T2 are the absolute temperatures of a finite source and T4 is the absolute atmospheric temperature in Fig.2.

AVAILABILITY FOR A NON-FLOW PROCESS

Since availability is useful work. Therefore non flow process will be an expansion process up to atmospheric pressure p_a. Let V₁ and V_a are the initial and final volumes of the system. Therefore work not recovered is = P_a (V_a-V₁). Since it is a non-flow process, there will be no flow work. Involve only initial and final internal energies.

Net Availability= W _useful= W _max—P_a (V_a-V₁)

Availability per unit mass will be = w _useful= w _max –T_a (s_a–s₁)

For a non-flow process, W_max = (U₁-U_a)-T_a (S_a-S₁)

AVAILABILITY FOR A FLOW PROCESS

In a flow process, flow work comes into existence. Thus it involves enthalpy.

Availability =W _useful = W _max = (H₁—H_a) – T_a (S_a—S₁)

Availability per unit mass will be

=w _useful= w _{max =} (h₁ –h_a) –T_a (s_a–s₁)

Availability energy is exergy or work potential of a system. The body must come in equilibrium with the atmosphere after the process.

HIGHLIGHTS OF AVAILABILITY-UNAVAILABILITY 

1. Availability is the maximum work obtainable from a heat engine.

2.  A heat engine always rejects some heat. Thus, total work recovery is not possible.

3. The work not recovered because of heat rejection to the surroundings is the unavailability.

4. On heat addition to a system, both available and unavailable energy increase.

5. Any amount of heat transfer during a process decreases   availability.

6. Gibbs function equation is

g = u + pv -Ts

Maximum work done by a system under steady iso-thermal flow        with heat exchange with surroundings.

7. Helmholtz function equation is a = u-Ts.  It is the maximum work available. However, it is applicable only to a chemical and electro-chemical processes.

8. The availability of a non flow process (or closed system)

Maximum work the system gives to some alternative                             system other than the surroundings. But there is no mass and heat transfer during the process in the control volume.

9.The availability of a flow process (or open  system)

Maximum work the system gives to some alternative system               other than the surroundings. But there is heat and mass                     transfer during the process in a control volume. Further, it is               in contact with the environment.

10. Every process in nature is irreversible. This ir-reversibility decreases the availability or the work recoverable from a system increases.

11.  Process efficiency is the ratio of actual work to maximum work possible. Thus, effectiveness of any irreversible process is less than unity. However the effectiveness of a reversible process will be unity. It is only theoretical. It can non achievable in actual practice.

12. Availability increases by reduction of the heat transfer and other ir–reversibility’s in a certain process.

Problem 1

Calculate the available and unavailable energy of a system. The available heat is 10000 kJ from a heat source at 400 K temperature. The surroundings is at 300 K temperature.

 Solution

Entropy Change

ds = Q/T

=10000/400

=25 kJ / K

Unavailable useful work

T ds =300 X 25

=7500 kJ

Available useful work

Q — T ds =10000 –7500

=2500 kJ

 PROBLEM 2

0.8 kg of air initially at 600 K temperature receives 1200 kJ of heat reversibly

at constant pressure. Determine the available energy and unavailable energy

of the heat added. Take the temperature of surroundings as 300 K.

Take Cp = 1.005 kJ / kg K

Solution

Let T2 be the temperature of air after the addition of heat at constant pressure.

Then

1200 = m Cp (T2-T1)

= 0.8 X 1.005 (T2 –600)

=0.804 T2 -462.28

T2      = (1200+462.28)/0.804

=2067.5  K

Change in entropy

ds = m Cp ln ( T2/T₁)

= 0.8 X 1.005 ln ( 2067.5/600)

= 0.2532 kJ / K

Unavailable work

T ds = 300 X 0.2532

= 75.96 kJ

Available work

Q- T ds = 1200-75.96

= 1124.04 kJ

Salient features about availability

1.  Maximum work obtained from a system.

2. Availability decreases with the heat transfer from a system.

3. Heat addition to a system increases availability.

4. Process effectiveness is ratio of useful work to the maximum work obtainable. Effectiveness of a reversible process is unity . The effectiveness of a irreversible process is less than unity.