3. A gas is confined in a 1.25 ft diameter cylinder by a piston, on which tests
ID: 883688 • Letter: 3
Question
3. A gas is confined in a 1.25 ft diameter cylinder by a piston, on which tests a weight. The mass of the piston and weight together is 250 lbm. The local acceleration gravity is 32.169 ft/s^2. The atmospheric pressure is 30.12 inch Hg. (a) What s the force in (lbf) exerted on the gas by the atmosphere, the piston and the weight? Assume no friction between the piston and the cylinder. (b) What is the pressure of the gas, in the unit of psi? (c) If the gas in the cylinder is heated, it expands and pushes the piston and weight upward. If the piston and weight are raised 1.7 if, what is the word done by the gas in ft.lbf? What is the potential energy of the piston and weight? Do you expect a temperature increase or decrease of the piston and weight?Explanation / Answer
a)
pressure = 30.12 in Hg = 2130.268 lbf / ft^2
Area = pi x d^2 / 4 = 3.14 x 1.25^2 / 4
= 1.226 ft^2
force = force exerterd by piston + force exerted by weight
= (pressure x area) + mg
= ( Patm x A ) + mg (g = 1)
= (2130.268 x 1.226) + 250 x 1
= 2613 + 250 x 1
= 2863 (lb f )
b)
Pressure of gas = Force /Area
= 2863 / 1.226
= 2335.23 lbf / ft^2
= 16.21 psi (1 lbf / ft^2 = 0.006944 psi)
c)
Work = F x d
= 2863 x 1.7
= 4867.1 ft lb f
Potential Energy = mgd
= 250 x 1 x 1.7
= 425 ft lb f
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