Question

Consider the transfer of 10kJ of heat between thermal reservoirs at 500 and 400K. (a) Determine the magnitude, in kilojoules, and the direction of the availability transfer for two reservoirs. (b) Now, consider the transfer of 10 kJ of heat between thermal reservoirs at 280 and 250K. Determine the magnitude and direction of the availability transfers for these two reservoirs. (c) Compare the direction of heat transfer versus availability transfer for the two processes. The environmental temperature is 298K.

Answer 1

1.The availability of a given system is defined as the maximum useful work that can be obtained in a process in which the system comes to equilibrium with the surroundings or attains the dead state.

Suppose a certain quantity of energy Q as heat can be received from a body at temperature T.

The maximum work can be obtained by operating a Carnot engine (reversible engine) using the body at T as the source and the ambient atmosphere at T0 as the sink.

W=Q*(1-To/T)=Q-To|s|............Avialable energy at any state

Where, s is the entropy of the body supplying the energy as heat.

1. W1=10*(1-298/500)

W1=4.04 kJ

At state 400 K,

W2=10*(1-298/400)

=2.55 kJ

Thus change of avialable energy is=W1 -W2

=4.04-2.55

=1.49 kJ

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2. Case 2

entropy at state 1,T=280 K

s1=Q/T..............for finite body and constant temprature

s1=10/280

=.0357 kJ/k

W1=Q-Tos

=10-298*.0375

=-.6428 mJ

at state 2, T=250 K

s2=Q/T

s2=10/250

=.04 kJ/K

W2=Q-Tos

=10-298*.04

=-1.92

Note above result show availability is negative,but availability of system can not be negative becasue it is maximum obtainable work till dead state and in this problem system is already below the dead state.

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3.

heat transfer for problem 1. according to 2nd lwa of thermodynamic heat always flow from higher temprature to lower temprature untill and unless provided extrnal work, thus heat flow from 500k to 400k.

availability of system always deceases when its approches to dead state thus direction of availability decrease from 500k toward 400k.

heat transfer vs availability

at state 1 10kJ............>.........at state 2, 10kJ

at state 1 4.04 kJ............>......at state 2 ,2.55 kJ

conclusion: heat 10 kj at state 1 has heigher significance than at state 2.

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