#### Sample Problem

A gas in a cylinder occupies a volume of 0.065 m^{3} 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 m^{2}. The pressure above the piston is atmospheric pressure.

(a) What is the pressure of the gas?

This can be determined from a free-body diagram of the piston. The weight of the piston acts down, and the atmosphere exerts a downward force. These two forces are balanced by the upward force coming from the gas pressure. The piston is in equilibrium, so the forces balance. Therefore:

PA = P_{atm}A + mg

Solving for the pressure of the gas gives:

P = P_{atm} + mg/A

P = 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?

Assume the pressure is constant. Once the gas has expanded and come to a new equilibrium position 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 the work done is simply:

W = PDV

W = 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.