SPSolution6-7

# SPSolution6-7 - Naik Sameer V Solution for Special Problem...

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Naik, Sameer V. Fall 2009 1000 Solution for Special Problem 6 Given: - Expansion of hydrogen inside a piston-cylinder device - Initial volume: 3 1 15 ft V = ; Final volume: 3 2 30 ft V = - Initial pressure: 1 14.7 psia P = - Area of piston: 2 3ft piston A = - Spring constant: lbf 15,000 ft k = Find: - Final pressure (psia) - P-V diagram - Work done during the expansion process (Btu) - Fraction of work done against the spring (Btu) System: Assumptions: - Quasistatic expansion process - Linear spring Basic Equation(s): spring Fk x = WP d v = Solution: (b) For a linear spring, the force varies linearly with displacement from the equilibrium position. As the spring is compressed from its equilibrium position owing to expansion hydrogen gas in the cylinder, the force exerted by the spring can be written as: () 3 21 2 lbf (30 15) ft 15,000 75,000 lbf ft 3 ft spring piston VV x k A == = × = . Hence, the pressure inside the cylinder increases. The final pressure will be given as: 22 lbf 75,000 lbf 14.7 in 3 ft spring piston F PP A =+ = + .

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SPSolution6-7 - Naik Sameer V Solution for Special Problem...

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