* AVAILABILITY, UNAVAILABILITY AND IRREVERSIBILITY
AVAILABILITY, UNAVAILABILITY
AND IRREVERSIBILITY
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 irreversibility.
Irreversibility is inherent to every process.
It is due to some kind of energy or
potential loss or heat dissipation. There is
internal and external irreversibility.
Irreversibility is in every process.
Eating and cooking of food
are irreversible processes. Well known two
statements of the Second law of
Thermodynamics, by Planck’s and Clausius,
prove irreversibility in every process.
Irreversibility is reducible but is not
eliminated altogether. A reversible process
has zero irreversibility. 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

Mechanical work

Electrical energy

Potential energy

Kinetic energy

wind energy

water energy

Jet energy

Tidal energy
Low grade energy
Lowgrade energy is not fully convertible into useful work (Shaft Work). Second Law of Thermodynamics governs it.
Examples of Low Grade Energy are

Heat from nuclear fission or fusion

Heat from combustion of fossil fuels

Solar energy

Heat energy from any source
The highgrade energy is obtainable from lowgrade energy. The complete conversion of low grade energy into high grade (shaft work) is impossible. Thus there is irreversibility which vary from one process to another process.
Available Energy or Availability
The amount of lowgrade energy converted into high grade energy is available energy.
Unavailable Energy
The amount of lowgrade energy not converted into high grade energy is unavailable energy.
IrReversibility
It is the difference of available energy and the actual useful work obtained.
Theoretical Available Energy Between Two Reservoirs At Constant Temperatures

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 lowgrade energy converted into high grade energy is available energy.
Fig. 2 Availability and unavailability from a Finite Source
Total availability = area 12651
Net Available = W _{useful} = area 12341
Unavailability = area 45634
UNAVAILABILITY OR UNAVAILABLE ENERGY
The amount of lowgrade 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 NONFLOW PROCESS
Since availability is useful work. Therefore non flow process will be an expansion process up to atmospheric pressure p_{a}. Let V_{1 }and V_{a} are the initial and final volumes of the system. Therefore work not recovered is = P_{a }(V_{a}V_{1}). Since it is a nonflow process, there will be no flow work. Involve only initial and final internal energies.
Net Availability= W _{useful}= W _{max}—P_{a }(V_{a}V_{1})
Availability per unit mass will be = w _{useful}= w _{max} –T_{a }(s_{a}–s_{1})
For a nonflow process, W_{max }= (U_{1}U_{a})T_{a} (S_{a}S_{1})
AVAILABILITY FOR A FLOW PROCESS
In a flow process, flow work comes into existence. Thus it involves enthalpy.
Availability =W _{useful} = W _{max} = (H_{1}—H_{a}) – T_{a }(S_{a}—S_{1})
Availability per unit mass will be
=w _{useful}= w _{max =} (h_{1} –h_{a}) –T_{a }(s_{a}–s_{1})
Availability energy is exergy or work potential of a system. The body must come in equilibrium with the atmosphere after the process.
HIGHLIGHTS OF AVAILABILITYUNAVAILABILITY

Availability is the maximum work obtainable from a heat engine.

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

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

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

Any amount of heat transfer during a process decreases availability.

Gibbs function equation is
g = u + pv Ts
Maximum work done by a system under steady isothermal flow with heat exchange with surroundings.

Helmholtz function equation is a = uTs. It is the maximum work available. However, it is applicable only to a chemical and electrochemical processes.

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 irreversibility 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 (T2T1)
= 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/T_{1})
= 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 = 120075.96
= 1124.04 kJ
Salient features about availability

Maximum work obtained from a system.

Availability decreases with the heat transfer from a system.

Heat addition to a system increases availability.

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.