Chapters
12 & 13 & 14
Thermodynamics The Gas Laws
Boyle's
Law
Keeping
the temperature constant, the volume of a gas varies inversely with
the absolute pressure.
(3)
Charles's
Law
When
the pressure is kept constant, the volume of a given amount of
any gas varies directly with the thermodynamic temperature.
(4)
GayLussac's
Law
When
the volume is kept constant, the absolute pressure of a given
amount of any gas varies directly with the thermodynamic temperature.
(5)
Ideal
Gas Law
(6)
Where and
n is the number of moles.
or
(7)
Where
N is the number of molecules and the Boltzmann's Constant is .
Example
6
A
person's lungs might hold 6.0 L of air at body temperature (310 K)
and atmospheric pressure (101 kPa). Given that the air is 21% oxygen,
find the number of oxygen molecules in the lungs.
Solution:
Solve
the ideal gas law for the number of molecules:
Then
find 21% of this number:
Example
7
Feeling
a bit cool, you turn up the thermostat in your house or apartment.
A short time later the air is warmer. Assuming the room is well sealed,
is the pressure of the air (a) greater than, (b) less than, or
(c) the same as before you turned up the heat?
Solution:
(a)
The air pressure increases.
Example
8
A
cylindrical flask of crosssectional area A is fitted with an airtight
piston that is free to slide up and down. Contained within the flask
is an ideal gas. Initially the pressure applied by the piston is
130 kPa and the height of the piston above the base of the flask
is 25 cm. When additional mass is added to the piston, the pressure
increases to 170 kPa. Assuming the system is always at the temperature
290 K, find the new height of the piston.
Solution:
Example
9
Consider
again the system in the previous example. In this case the temperature
is changed from an initial value of 290 K to a final value of
330 K. The pressure exerted on the gas remains constant at 130
kPa, and the initial height of the piston is 25 cm. Find the
final height of the piston.
Solution:
Example
10
A
cylinder contains 12 L of oxygen at 20°C and 15 atm. The
temperature is raised to 35°C, and the volume is reduced
to 8.5 L. What is the final pressure of the gas in atmospheres?
Assume that the gas is ideal.
Solution:
Write
the initial and final states using the ideal gas law:
Divide
the final by the initial and solve for the final pressure:
Substitute
the numerical values:
The
Kinetic Theory:
The
temperature of an ideal gas is proportional to the average translational
kinetic energy of its molecules.
(8)
Speed
of Molecules in a Gas
(9)
Example
11
Find
the average kinetic energy of oxygen molecules in the air. Assume
the air is at a temperature of 21°C.
Solution:
Example
12
The
atmosphere is composed primarily of nitrogen (78%)
and oxygen (21%).
(a) Is the rms speed of (28.0
g/mol) greater than, less than , or the same as the rms speed
of (32.0
g/mol)? (b) Find the rms speed of and at
293 K.
Solution:
(a)
rms for nitrogen is greater because it has less mass.
(b)
On
to the Mechanical Equivalent of Heat
