### Sample Problem

A gas occupies a volume of 0.065 m3 at room temperature (T = 293 K). The gas is confined by a piston of 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?

Use DID TASC. 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 below. Therefore:

PA = PatmA + mg

Solving for the pressure of the gas gives:
P = Patm +
 mg A
= 101300 +
 100 0.65
= 101450 Pa

The pressure in the gas is slightly larger than atmospheric pressure, just enough to support 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 is done by the gas?

As long as the expansion is sufficiently slow, the pressure remains constant.

At constant pressure: ΔW = PΔV = 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.