A gas in a cylinder occupies a volume of 0.065 m³ at room temperature (T = 293 K). The gas is confined by a piston with a weight of 100 N and an area of 0.65 m². The pressure above the piston is atmospheric pressure.

(a) What is the pressure of the gas?

Draw a free-body diagram of the piston. The force of gravity on the piston points down, and the atmosphere exerts a downward force. The piston is in equilibrium, so these forces are balanced by the upward force from the gas pressure. Therefore:

PA = P_atmA + mg

Solving for the pressure of the gas gives:

P = Patm +

mg A

= 101300 +

100 0.65

= 101450 Pa

The pressure in the gas isn't much bigger than atmospheric pressure, just enough to support the weight of the piston.

(b) The gas is heated, expanding it and moving the piston up. If the volume occupied by the gas doubles, how much work has the gas done?

When a new equilibrium position is reached the pressure will be the same because the free-body diagram is the same. As long as the expansion takes place slowly, it is reasonable to assume that the pressure is constant during the expansion.

At constant pressure: W = PDV = 101450 * 0.065 = 6590 J

(c) What is the final temperature of the gas?

If the volume doubles while the pressure stays constant, the temperature must also double.