Question

A gas is confined in a 0.80 m diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is 150 kg. The local acceleration of gravity is 9.813 m/s2 and atmospheric pressure is 101.57 kPa.
(a) What is the force in newtons exerted on the gas by the atmosphere, the piston, and the weight, assuming no friction between the piston and cylinder?
(b) What is the pressure of the gas in kPa?
(c) If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 0.83 m, what is the work done by the gas in kJ? What is the change in potential energy of the piston and weight?

Answer 1

For letter a)

Force exerted by piston and weight:

F = 150 kg * 9.813 m/s² = 1471.95 N

Force exerted by atmosphere:

P = F/A

F = P*A = 101570 Pa * (pi*(0.8^2)/4) m² = 51054.77 N

b) What is the pressure of the gas in kPa:

P = 101.57 kPa + (1471.95 N / (pi*(0.8^2)/4) m²) / 1000 = 101.57 kPa + 2.9283 kPa = 104.4983 kPa

c) If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 0.83 m, what is the work done by the gas in kJ? What is the change in potential energy of the piston and weight?

Work done by gas = 101570 Pa * 0.83 m * 0.502656 m2 = 42375.459 J = 42.375 kJ

Potential energy change = Mgh = 150 kg * 9.813 m/s2 * 0.83 m = 1221 J = 1.221 kJ