A piston-cylinder device contains 2 kg of a gas at 200 kPa and 300 K. The intern

Question

A piston-cylinder device contains 2 kg of a gas at 200 kPa and 300 K. The internal diameter of the cylinder is 20 cm and the pressure is kept constant by placing a weight on top of the piston. The outside pressure is 100 kPa and g = 10 m/s2
(a). Determine the mass of the weight necessary to maintain a pressure of 200 kPa inside the cylinder if the atmospheric pressure is 100 kPa. Assume g = 10 m/s2.
(b). The gas is now heated by an external candle until the piston moves up (without any acceleration) by a distance of 1 m. Determine the boundary work transfer in kJ (magnitude only, no sign needed; you know the sign would be positive anyway ). 15

(c). Determine the change (final minus beginning) in the PE of the mass on top of the piston as it is lifted by a distance of 1 m
(d). Should the answers to part (b) and (c) be equal?

Explanation / Answer

a)

upward force = dP*A

dP = pressure difference

A = area of the piston = pi*r^

r = radius of the piston = D/2 = 10 cm = 0.1 m

down ward gravitational force = Fg = m*g

in equilibrium

m*g = dP*A

m = dP*A/g

m = ((200-100)*10^3*3.14*0.1^2)/10 = 314 kg

(b)

work done = dP*y = 100*10^3*1 = 10^5 J

(c)

PE = m*g*h = 314*10 = 3140 J

d)

NO

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