A gas is confined in a 1.25(ft) diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is The local acceleration of gravity is and atmospheric pressure is 30.12(in Hg).

Question

(a) What is the force in (lbf) 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 (psia)?

(c) If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 1.7(ft), what is the work done by the gas in What is the change in potential energy of the piston and weight?

Answer 1

a. The force exerted on the gas has two parts, the weight of the piston and the pressure of the atmosphere on the top of the piston. The force due to the weight of the piston is where m is the piston mass and g is the acceleration of gravity. We have to use to make the units work out right. The force due to the pressure of the atmosphere is PA where P is the pressure and A is the cross-sectional area of the piston. The cross-sectional area of the piston is So, the total force is:









b. The pressure of the gas is the force divided by the area





c. Because the weight of the piston, its cross-sectional area, and the pressure of the atmosphere on it all remain constant, the force on the gas and the gas pressure also remain constant. So, the work done by the gas can be computed as either F ?h or P ?V, using the pressure and force that we have already computed. Since we are given ?h = 1.7 ft, it is easiest to calculate it as



Most of this work is done against the pressure of the atmosphere, so only a small part of it changes the potential energy of the piston. The potential energy of the piston changes by