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Chapter: Mechanical - Engineering Thermodynamics - The Second Law of Thermodynamics

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Available Energy, Availability And Irreversibility

The energy content of a system can be divided into two parts: · Available energy, which under ideal conditions may be completely converted into work · Unavailable energy which is usually rejected as waste.

AVAILABLE ENERGY, AVAILABILITY AND IRREVERSIBILITY

 

From second law of thermodynamics we found that complete conversion of heat into work is not possible in a continuous process. Also it has been proved that the most efficient cycle to produce work is a reversible power cycle (Carnot cycle). Even in carnot cycle, the efficiency of conversion can never be

unity and hence to establish a comparison of the work-energy conversion in actual processes, the maximum theoretical work obtainable with respect to some datum must be determined. This chapter is dedicated for this objective.

 

Available and Unavailable Energy

The energy content of a system can be divided into two parts

 

                 ·  Available energy, which under ideal conditions may be completely converted into work

 

·  Unavailable energy which is usually rejected as waste.

 

Consider Q units of heat energy available at a temperature T. Available part of energy can be obtained by assuming that the heat is supplied to a Carnot engine. Work obtained from the carnot engine


quantities can be represented as shown in the fig 6.1. The term T0 is the ambient temperature. Hence it can be concluded that the available and unavailable part of energy content of a system depends on the ambient conditions also.

 

Reversible Work In A Non-flow Process

From first law of thermodynamics

Qsys -W=U2-U1                         ...6.1

From second law of thermodynamics for a reversible process


This is also the maximum work in the process.

 

For a closed system, when undergoing change in volume, the work done against the atmospheric pressure:



Reversible Work In A Steady-state Control Volume

Steady flow energy equation for a constant volume is



From eqn 6.6 neglecting kinetic and potential energy changes


In an open system a fixed volume in space known as control volume is taken for analysis. Hence the atmospheric work term po(V1-V2) should not be considered. Therefore

 

Wrev= Wmax,useful for an open system

 

Availability

 

The maximum useful work that can be obtained from the system such that the system comes to a dead state, while exchanging heat only with the surroundings, is known as availability of the system. Here the term dead state means a state where the system is in thermal and mechanical equilibrium with the surroundings.

 

Therefore for a closed system availability can be expressed as

f=(U -Uo )+po (V -Vo )-To (S-So )

 

similarly for an open system

 

y=(H -Ho )-To (S-So )

 

In steady flow systems the exit conditions are assumed to be in equilibrium with the surroundings. The change in availability of a system when it moves from one state to another can be given as:

 

for a closed system

f1-f2 =(U1 -U 2 )+po (V1 -V2 )-To (S1 -S2 )             ...6.10

for an open system



Availability Change Involving Heat Exchange with Reservoirs

Consider a system undergoing a change of state while interacting with a reservoir kept at TR and atmosphere at pressure po and temperature To. Net heat transfer to the system


Qnet= QR-QO.      

From first law of thermodynamics   

Qnet- Wrev=U2-U1 ...6.12

From second law of thermodynamics, assuming the process to be reversible     

(Ds)Res+(Ds)atm+(Ds)sys=0


The negative sign for QR shows that the heat is removed from the reservoir.

 

By rearranging We get

 

Net heat transferred



 

Irreversibility

 

Work obtained in an irreversible process will always be less than that of a reversible process. This difference is termed as irreversibility (i.e) the difference between the reversible work and the actual work for a given change of state of a system is called irreversibility.

 

I=W  -W

rev  act

 

Let a stationary closed system receiving Q kJ of heat is giving out Wact kJ of work. From first law of thermodynamics.




Since (Ds)universe will be positive for an irreversible flow, irreversibility will be zero for a reversible process and will never be negative

I ³0 .

 

Similarly for a steady flow system




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