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= ²p. piston head D The work done by the gas when the volume expands from volume V, to volume V₂ is as follows. W · 1²0 *PdV In a steam engine the pressure and volume 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 140 lb/in² and a volume of 500 in³ and expands to a volume of 800 in³. (Round your answer to two decimal places.) W = ft-lb
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= ²p. piston head D The work done by the gas when the volume expands from volume V, to volume V₂ is as follows. W · 1²0 *PdV In a steam engine the pressure and volume 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 140 lb/in² and a volume of 500 in³ and expands to a volume of 800 in³. (Round your answer to two decimal places.) W = ft-lb
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 = r²P.
piston head
i
The work done by the gas when the volume expands from volume V₁ to volume V₂ is as follows.
-V₂
W =
X
P dV
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 140 lb/in² and a volume of 500 in³ and expands to a volume of 800 in³. (Round your answer to two decimal places.)
W =
ft-lb
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