Answered: Exergy balance for a closed system when…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Exergy balance for a closed system when the direction of heat transfer is taken to be to the system and the direction of work from the system.

Expert Solution

Step 1

Let's consider the total internal energy of the system under consideration are: latent heat energy and sensible heat energy.

The exergy balance is based bo the consideration that how much heat is converted into work.

Now calculate the work done by the system by using the equation, $d W = P d V$

$\begin{array}{rcl} d W & = & P d V \\ = & (P - P_{0}) d V + P_{0} d V \end{array}$

Where the term $(P - P_{0}) d V$ is the maximum useful work that can be produced by the piston.

The term $P_{0} d V$ represents the loss of heat in the atmosphere due to the change in volume.

Step 2

A reversible heat engine is used to transfer the heat reversibly from temperature ' $T$ ' to the ambient temperature, ' $T_{0}$ '.

Now derive the work done by the heat engine as follows:

$\begin{array}{rcl} d W_{H E} & = & η_{t h} d Q \\ = & (1 - \frac{T_{0}}{T_{1}}) d Q \\ = & d Q - \frac{T_{0}}{T_{1}} d Q \\ = & d Q - \frac{T_{0}}{T_{1}} (- T d S) \\ = & d Q + T_{0} d S \end{array}$

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