Homework SourseA pistoncylinder device contains 2 kg of a gas at 200 kPa an
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. Please double check your answer as you will need this answer in part (c)
B) The gas is now heated by an external candle, the temperature increases and the piston starts moving up (without any acceleration). The heating stops and the piston comes to an equilibrium after traversing 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 ).
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)
E)
| A physics student looks at this problem and says, \"the gas does work against the piston, which in turn raises the weight. So the answers to part (b) and (c) must be equal.\" Irrespective of what answers you got for parts (b) and (c), do you agree with his statement? | ||||
|
Solution
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
e) Qin is more than Wout
