Thermodynamics: An Engineering Approach
9th Edition
ISBN: 9781260048766
Author: CENGEL
Publisher: MCG
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Chapter 4.5, Problem 13P
A gas is compressed from an initial volume of 0.42 m3 to a final volume of 0.12 m3. During the quasiequilibrium process, the pressure changes with volume according to the relation P = aV + b, where a = −1200 kPa/m3 and b = 600 kPa. Calculate the work done during this process (a) by plotting the process on a P-V diagram and finding the area under the process curve and (b) by performing the necessary integrations.
FIGURE P4–13
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1. A gas expands in a cylinder from 500 kPa and 0.1 m3 to a final volume of 0.5 m3. Determine the work done if the pressure distribution is determined to be:
P=C
PV=C
where V is in m3 and P in kPa.
(a) An ideal gas is taken through a quasi-static process described by P = aV², with a = 2.00 atm/m°, as shown in the figure.
The gas is expanded to twice its original volume of 1.00 m³. How much work (in MJ) is done on the expanding gas in this
process?
P= aV²
V
2.00 m³
1.00 m3
MJ
(b) What If? How does the work done in part (a) compare to the lowest and highest possible amounts of work that can be
done on this gas between the initial and final states if the pressure always remains between P, and P, and the volume
always remains between V, and V? (Enter your answers as percentages of the work done in part (a).)
lowest
x 100% =
%
W part (a)
highest
x 100% =
%
part (a)
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3. A piston is resting on stops in a frictionless piston-cylinder device. The system contains water
with a mass of 1 kg. The initial temperature is 30°C and the initial volume is 0.1 m³. The pressure
required to raise the piston is 100 kPa. Find the work done if we add heat until the water is
completely vapor (x=1). Find the heat added to the system. Draw and label the process on P-v
and T-v diagrams.
4. A frictionless piston-cylinder device contains 10 kg of water initially at 100 kPa and 100°C. If the
volume reaches 20 m³, the piston hits a set of stops and is restrained from further upward
travel. Heat is added until the temperature is 200°C. Calculate the pressure at this point. Also,
calculate the temperature when the piston first touches, but exerts no force, on the stops. Draw
and label the process on P-v and T-v diagrams.
Chapter 4 Solutions
Thermodynamics: An Engineering Approach
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