Sample Problem
A gas in a cylinder occupies a volume of 0.065 m3atroom temperature (T = 293 K). The gas is confined by a pistonwitha weight of 100 N and an area of 0.65 m2. Thepressureabove the piston is atmospheric pressure.
(a) What is the pressure of the gas?
This can be determined from a free-body diagram of thepiston.The weight of the piston acts down, and the atmosphereexerts adownward force. These two forces are balanced by the upwardforcecoming from the gas pressure. The piston is in equilibrium, sotheforces balance. Therefore:
PA = PatmA + mg
Solving for the pressure of the gas gives:
P = Patm + mg/A
P = 101300 + 100/0.65 = 101450 Pa
The pressure in the gas isn't much bigger thanatmosphericpressure, just enough to support the weight of thepiston.
(b) The gas is heated, expanding it and moving the piston up.Ifthe volume occupied by the gas doubles, how much work has thegasdone?
Assume the pressure is constant. Once the gas has expandedandcome to a new equilibrium position the pressure will be thesamebecause the free-body diagram is the same. As long as theexpansiontakes place slowly, it is reasonable to assume that thepressure isconstant 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,thetemperature must also double.
Sample Problem
A gas in a cylinder occupies a volume of 0.065 m3atroom temperature (T = 293 K). The gas is confined by a pistonwitha weight of 100 N and an area of 0.65 m2. Thepressureabove the piston is atmospheric pressure.
(a) What is the pressure of the gas?
This can be determined from a free-body diagram of thepiston.The weight of the piston acts down, and the atmosphereexerts adownward force. These two forces are balanced by the upwardforcecoming from the gas pressure. The piston is in equilibrium, sotheforces balance. Therefore:
PA = PatmA + mg
Solving for the pressure of the gas gives:
P = Patm + mg/A
P = 101300 + 100/0.65 = 101450 Pa
The pressure in the gas isn't much bigger thanatmosphericpressure, just enough to support the weight of thepiston.
(b) The gas is heated, expanding it and moving the piston up.Ifthe volume occupied by the gas doubles, how much work has thegasdone?
Assume the pressure is constant. Once the gas has expandedandcome to a new equilibrium position the pressure will be thesamebecause the free-body diagram is the same. As long as theexpansiontakes place slowly, it is reasonable to assume that thepressure isconstant 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,thetemperature must also double.
