2.49 A gas is contained is a vertical piston-cylinder assembly by a piston with

Question

2.49 A gas is contained is a vertical piston-cylinder assembly by a piston with a face area of 40 in.2 and a weight of 100 Ibf. The atmosphere exerts a pressure of 14.7 Ibflin,2 on top of the piston. A paddle wheel transfers 3 Btu of energy to the gas during a process in which the elevation of the piston increases. The change in internal energy of the gas is 2.12 Btu. The piston and cylinder are poor thermal conductors, and friction between them can be neglected. Determine the elevation increase of the piston, in ft

Explanation / Answer

Given data

Face area of piston = 40 in2

Weight = 100 lbf

Atmospheric pressure = 14.7 lbf/in2

Change in internal energy = 2.12 Btu

Let the increase in elevation of piston = X

Total work done = work done to push the piston + work done to increase the potential energy

= pressure * area * increase in elevation + weight x increase in elevation

= (14.7 lbf/in2 * 40 in2 * X ft) + (100 lbf * X ft)

= 588 X + 100 X

= 688 X lbf-ft * 1BTU / 778.16 ft-lbf

= 0.88 X Btu

Energy received by the gas = 3 Btu

Change in internal energy = 2.12 Btu

From the first law of thermodynamics

Change in internal energy = Energy received by the gas - total work done by gas

2.12 = 3 - 0.88 X

X = increase in elevation of piston = 1 ft

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