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When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the volume V: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = r²P. V X piston head i The work done by the gas when the volume expands from volume V₁ to volume V₂ is as follows. W = [ 1² POV dV JV₁

When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the volume V: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = r²P. V X piston head i The work done by the gas when the volume expands from volume V₁ to volume V₂ is as follows. W = [ 1² POV dV JV₁

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the volume V: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = πr²P. piston head W = ·V2 V The work done by the gas when the volume expands from volume V₁ to volume V₂ is as follows. P dV X i) In a steam engine the pressure and volume of steam satisfy the equation PV1.4 = k, where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work done by the engine during a cycle when the steam starts at a pressure of 160 lb/in2 and a volume of 500 in3 and expands to a volume of 1000 in 3. (Round your answer to two decimal places.) W = ft-lb
Transcribed Image Text:When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the volume V: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = πr²P. piston head W = ·V2 V The work done by the gas when the volume expands from volume V₁ to volume V₂ is as follows. P dV X i) In a steam engine the pressure and volume of steam satisfy the equation PV1.4 = k, where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work done by the engine during a cycle when the steam starts at a pressure of 160 lb/in2 and a volume of 500 in3 and expands to a volume of 1000 in 3. (Round your answer to two decimal places.) W = ft-lb
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