A gas is confined in a 0.47 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 and atmospheric pressure is 101.57 kPa.

Question

(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

a. The force applied by the atmosphere (if the piston and weight were ‘massless’) would be the atmospheric pressure (101.57 kPa) times the cross-sectional area of the piston So, the force due to the atmosphere is The additional force applied by the piston and weight is Thus, the total force applied to the gas is about 19090 N.



b. The pressure of the gas is the total force found in (a) divided by the cross sectional area of the piston.





c. Since the mass of the piston and the pressure of the atmosphere don’t change in this process, the pressure of the gas inside the piston is constant as it expands, and the force applied by the piston and atmosphere to the gas is constant as the gas expands. We can compute the work either as the pressure times the change in volume or the force times the distance the piston moves. Since we’ve already computed the force in part (a), the simplest method is to multiply this force by the distance that the piston travels. W = Fl = 19090 N * 0.83 m = 15850 N m = 15850 J. The change in potential energy of the piston and weight is Thus, most of the work done by the gas goes toward ‘pushing back’ the atmosphere, not raising the piston and weight. This is a result of the fact that most of the pressure being applied to the gas is due to the atmosphere, and not to the weight and piston.