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Engineering and Tech / Fundamentals of Engineering Thermodynamics 7 / Chapter 3 / Problem 112P

Fundamentals of Engineering Thermodynamics | 7th Edition | ISBN: 9780470495902 | Authors: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

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Using Energy Concepts and the Ideal Gas ModelAir contained

Chapter 3, Problem 112P

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QUESTION:

Air contained in a piston-cylinder assembly, initially at \(2 \mathrm{bar}, 200 \mathrm{~K}\), and a volume of \(1 \mathrm{~L}\), undergoes a process to a final state where the pressure is 8 bar and the volume is \(2 \mathrm{~L}\). During the process, the pressure-volume relationship is linear. Assuming the ideal gas model for the air, determine the work and heat transfer, each in kJ.

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QUESTION:

Air contained in a piston-cylinder assembly, initially at \(2 \mathrm{bar}, 200 \mathrm{~K}\), and a volume of \(1 \mathrm{~L}\), undergoes a process to a final state where the pressure is 8 bar and the volume is \(2 \mathrm{~L}\). During the process, the pressure-volume relationship is linear. Assuming the ideal gas model for the air, determine the work and heat transfer, each in kJ.

ANSWER:

Solution 112P:

Step 1 of 5:-

Here we need to find the heat transfer and work done.

The piston-cylinder assembly contains air at a pressure of, ${P}_{1}=2\ bar=2\times{}1{0}^{5}\ Pa$ .

Temperature of air is: ${T}_{1}=200\ K$ .

And volume is: ${V}_{1}=1\ l=0.001\ {m}^{3}$ .

In the final state, the pressure reached to : ${P}_{2}=8\ bar=8\times{}1{0}^{5}\ Pa$ .

And the volume increased to: ${V}_{2}=2\ l=0.002\ {m}^{3}$ .

During the process, the pressure-volume relationship is linear.

So, $P=kV$ , where $k$ is a constant.

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