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a) The specific volume v of a gas can be expressed as a function of its pressure p and temperature T , as; KT p=- v - b a where Kis the gas constant, and a and b are constants. Show that the equation can be re- arrange into, f(v) = Av³ – Bv² +Cv – D=0,where A, B, C, and D are constants. Using Newton-Raphson method, find the specific volume v of the methane gas at a pressure of 2.1162 x10° Ibf / fi² and temperature 459.67° R with a = 4787.4 ft* – Ibf / lbm²; b = 0.0496 ft / Ibm, and K=96.35 ft – lbf / lbm –° R. Use the starting value of v = 0.0 and accuracy of ɛ = 0.001.

a) The specific volume v of a gas can be expressed as a function of its pressure p and temperature T , as; KT p=- v - b a where Kis the gas constant, and a and b are constants. Show that the equation can be re- arrange into, f(v) = Av³ – Bv² +Cv – D=0,where A, B, C, and D are constants. Using Newton-Raphson method, find the specific volume v of the methane gas at a pressure of 2.1162 x10° Ibf / fi² and temperature 459.67° R with a = 4787.4 ft* – Ibf / lbm²; b = 0.0496 ft / Ibm, and K=96.35 ft – lbf / lbm –° R. Use the starting value of v = 0.0 and accuracy of ɛ = 0.001.

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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a) The specific volume v of a gas can be expressed as a function of its pressure p and temperature T, as; KT p=- v -b a where Kis the gas constant, and a and b are constants. Show that the equation can be re- arrange into, f(v) = Av³ – Bv + Cv–D=0, where A, B, C, and D are constants. Using Newton-Raphson method, find the specific volume v of the methane gas at a pressure of 2.1162 x10'lbf / fi² and temperature 459.67° R with a= 4787.4 ft* – Ibf / lbm2, b = 0.0496 ft / Ibm, and K = 96.35 ft – lbf / lbm -° R. Use the starting value of v = 0.0 and accuracy of ɛ = 0.001.
Transcribed Image Text:a) The specific volume v of a gas can be expressed as a function of its pressure p and temperature T, as; KT p=- v -b a where Kis the gas constant, and a and b are constants. Show that the equation can be re- arrange into, f(v) = Av³ – Bv + Cv–D=0, where A, B, C, and D are constants. Using Newton-Raphson method, find the specific volume v of the methane gas at a pressure of 2.1162 x10'lbf / fi² and temperature 459.67° R with a= 4787.4 ft* – Ibf / lbm2, b = 0.0496 ft / Ibm, and K = 96.35 ft – lbf / lbm -° R. Use the starting value of v = 0.0 and accuracy of ɛ = 0.001.
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