Consider the following figure. P(MPa) 10 8 V (m³) 12 6 8 10 (a) Determine the work done on a fluid that expands from i to f as indicated in the figure. | MJ (b) How much work is done on the fluid if it is compressed from f to i along the same path? | MJ

Consider the following figure. P(MPa) 10 8 V (m³) 12 6 8 10 (a) Determine the work done on a fluid that expands from i to f as indicated in the figure. | MJ (b) How much work is done on the fluid if it is compressed from f to i along the same path? | MJ

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter3: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 1CQ: Consider these scenarios and state whether work is done by the system on the environment (SE) or by...

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Question

Consider the following figure.
P( MPa)
10
8
4.
v (m³)
12
4
6
8
10
(a) Determine the work done on a fluid that expands from i to f as indicated in the figure.
MJ
(b) How much work is done on the fluid if it is compressed from f to i along the same path?
| MJ
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Expert Solution

Step 1

(a)

The work done on the fluid that expands from i to f by the area under the curve with volume can be determined as follows.

$\begin{array}{rcl} W_{i f} & = & [A r e a u n d e r t h e c u r v e] \\ = & [((9 MPa) (6 m^{3} - 3 m^{3}) + \frac{1}{2} (9 MPa - 3 MPa) (9 m^{3} - 6 m^{3}) + (3 MPa) (9 m^{3} - 6 m^{3}) + (3 MPa) (12 m^{3} - 9 m^{3}))] \\ = & 54 MJ \end{array}$

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