Type:
Double
Date:________
Objective:
Kinetic Theory and the Gas Laws I
Kinetic Theory and the Gas Laws II
Homework: Do CONCEPT Q. # (4, 9),
Do PROBLEMS # (9, 14, 26) Ch. 14
AP Physics “B”
Mr. Mirro
Date: ________
Kinetic Theory and The Gas Laws I
An ideal gas is an “idealized” model for real gases that have sufficiently low densities. The condition
of low density means that the molecules of the gas are so f-a-r a-p-a-r-t that they DO NOT interact,
except during collisions that are effectively elastic.
The ideal gas law expresses the relationship among the
‰
‰
‰
‰
(I)
absolute pressure,
the Kelvin temperature,
the volume of the container and
the number of moles of gas.
Experiments reveal that a plot of gas pressure versus temperature is a “straight line.” The
graph indicates that the absolute pressure (P) of an ideal gas is “directly” proportional to the
Kelvin temperature (T). That is,
(P ∝ T)
(II) The relationship between gas pressure and number of
molecules is simple:
Experience indicates that it is possible to increase the
pressure of a gas by adding more molecules of gas,
ie. Pumping air into a flat tire increases the air pressure.
Thus, the absolute pressure of an ideal gas is “directly” proportional to the number of
molecules or moles (n) of the gas. That is,
(P ∝ n)
(III)
To see how the pressure of the gas depends on the volume of the container, look to a partially
filled balloon.
‰
‰
The partially filled balloon is initially soft because the pressure of the air is too low to
expand the balloon to its fullest.
However, if all the air in the balloon is squeezed into a small bubble, the balloon begins
to stretch and tighten up indicating an increase in pressure.
Since it is possible to increase the pressure of a gas by reducing its volume, the absolute
pressure of an ideal gas is “inversely” proportional to its volume (V). That is,
(P ∝ 1/V)
These THREE relations for the absolute pressure of an ideal gas, along with the universal gas constant,
form the basis of the Ideal Gas Law.
IDEAL GAS LAW
The absolute pressure (P) of an ideal gas is directly proportional to the Kelvin temperature (T)
and the number of moles (n) of the gas and is inversely proportional to the volume (V) of the gas.
PV=nRT
Where R is the universal gas constant of value 8.31 J/mol K
•
In many situations it is not necessary to use the Universal Gas Constant (R) at all ! Therefore, another
way to interpret the Ideal Gas Law is in terms of a “ratio.”
For example, many problems involve a change in
the pressure, temperature and volume of a fixed
amount (n) of gas. In this case:
PV = n R
T
⇒ Constant
If we let P1, V1 and T1 represent the appropriate variables initially and P2, V2 and T2 represent the
variables after the change is made, we can write the General Gas Law as follows:
P1V1 = P2V2
T1
T2
GENERAL GAS LAW
AP Physics “B”
Mr. Mirro
Date: ________
Kinetic Theory and The Gas Laws I
Ex 1: A spherical helium party balloon has a radius of 0.18 m. At a temperature of 20 °C (K = ??),
its internal pressure is 1.05 atm (N/m2 = ??). Find the number of moles of helium in the balloon.
Let Vsphear = 4/3 πr3 and 1 atm = 1.01 x 105 N/m2. [Giancoli13.12]
P N/m^2 =
k
TK =
Ex 2: A cylindrical container of radius 15 cm (m = ??) and height 0.30 m contains 0.6 mol of gas at
433 K. [PrincetonReview9.11mod]
a. What is the pressure of the gas confined
in the container ?
A=
V=
b. How much force does the confined gas exert on the lid of the container ?
FTBO⇒
Ex 3: A volume of 0.02 m3 of air at 27 °C and a pressure of 100,000 Pa is compressed until its pressure
becomes 250,000 Pa and its temperature is 102 °C. What is its new volume ? [Taffel14.4]
Ex 4: An automobile tire is filled to a gauge pressure of 200,000 Pa (Pabs = Pguage + Patm) at 10 °C
(K = ??). After driving 100 km, the temperature within the tires rises to 40 °C. If the volume
of air and number of moles remains constant, determine the absolute pressure within the tire
“now” ? [Giancoli13.13]
NEED:
Pabs =
T1abs =
T2abs =
AP Physics “B”
Mr. Mirro
Date: ________
Kinetic Theory and The Gas Laws II
When we consider the separate instances of constant temperature, pressure and volume respectively,
several special cases of the General Gas Law begin to emerge.
(I)
Ideal Gas at Constant Temperature Boyle’s Law states that:
The volume of a gas kept at constant temperature varies inversely
with the pressure exerted upon it.
Thus, the volume of a gas depends upon how much pressure
is exerted by a piston on the gas.
‰
‰
Consider a gas-tight piston pushing down on a sample of gas
in a sealed container.
2 atm
As the piston is pushed down, it exerts more pressure
on the gas and squeezes it into a smaller volume.
4 atm
twice the pressure
half the volume
Absolute Pressure
Therefore, if the absolute temperature of the gas is kept constant, then:
P1V1 = P2V2
(II)
Boyle’s Law
Ideal Gas at Constant Pressure Charles’ Law states that:
When a gas is kept under constant pressure, its volume varies
directly with absolute temperature.
Thus, when kept at the same constant pressure ALL gases expand or contract with changes
in temperature at approximately the same rate.
Therefore, if the absolute pressure of the gas
is kept constant, then:
V1 = V2
T1 T2
Charles’ Law
Absolute Temperature
(III)
Ideal Gas at Constant Volume Gay-Lussac’s Law states that:
When a gas is kept under constant volume, its absolute
pressure varies directly with absolute temperature.
Thus, when kept at the same constant volume ALL gases expend more or less pressure
according to changes in temperature.
Therefore, if the absolute pressure of the gas
is kept constant, then:
P1 = P2
T1 T2
Gay-Lussac’s Law
Absolute Temperature
AP Physics “B”
Mr. Mirro
Date: ________
Kinetic Theory and The Gas Laws II
Ex 1: A container contains 4000 m3 of Lithium (MLi = 6.941 u) gas at an absolute pressure of 1 atm
(1.01 x 105 Pa). If the temperature of the gas is at 300 K, [Cutnell14.9sim]
a. How many moles of lithium gas are present ?
b. Determine the number of Li molecules in the sample.
c. What is the mass of the gas in the container in kilograms ?
Ex 2: A sealed glass bottle at 27 °C (K = ??) contains air at atmospheric pressure and has a volume
of 30 cm3. The bottle is then tossed into an open fire. Assuming volume changes to be negligible,
What is the pressure (in atm) inside the bottle when the temperature of the air in the bottle reaches
200 °C ? [Serway10.8]
FTBO ⇒
Ex 3: A gas fills the right portion of a cylinder whose radius is 3.0 cm (m = ??). The initial pressure
of the gas is 1.01 x 105 Pa. A frictionless movable piston separates the gas from the left portion
of the cylinder that contains an ideal spring which essentially is in a vacuum, as shown. Initially,
while the piston is kept from moving by a stop pin, the spring is considered to be unstrained.
When the pin is removed the gas is allowed to expand, doubling the length of the gas-filled
chamber. If the initial and final temperatures are equal and the spring constant is 1500 N/m,
determine the amount of compression (in meters) that the spring experiences. [Cutnell14.26sim]