Physics 12

Objectives Define pressure. State the assumptions of the kinetic model of an

ideal gas. State that temperature is a measure of the

average random kinetic energy of the molecules of an ideal gas.

Explain the macroscopic behavior of an ideal gas in terms of a molecular model.

State the equation of state for an ideal gas. Describe the difference between an ideal gas and

a real gas. Describe the concept of the absolute zero

temperature and the Kelvin scale of temperature Solve problems using the equation of state of an

ideal gas.

Activities

Lecture Quiz Computer simulation Graphical analysis

Gases

Compared to solids and liquids, gases behave quite differently, particularly in the volume that they occupy.

What are some factors that might affect the volume that a gas occupies?

Explain this behavior from a microscopic perspective.

Gases How would these factors affect the volume of a

gas?

Factor Effect on volume

increase in pressure

increase in temperature

increase in number of gas molecules

Gases

Because of the myriad of factors that affect the behavior of gases, it is valuable to determine a relationship between them.

The relationship between the volume, pressure, temperature, and mass of a gas is called an equation of state.

By state, we mean the equilibrium state of the system.

Gases

SI units for quantities involving gases

Quantity SI unit

volume m3

pressure Nm-2 or Pascal (Pa)

temperature K

**another unit for pressure, the atmosphere (atm) is often used:

1 atm = 1.01 x 10 5 Nm-2

Boyle’s law What is the effect of pressure on the volume of

a gas?

Factor Effect on volume

increase pressure

decrease pressure

Boyle’s law

For a given quantity of gas, it is found experimentally that the volume of a gas is inversely proportional to the absolute pressure applied to it when the temperature is kept constant.

V α 1/P Why is it important that we state that temperature is

constant?

Factor Effect on volume

increase pressure decrease volume

decrease pressure Increase volume

Boyle’s lawGraph of P vs. V (Boyle’s experiments)

• What are the implications of this relationship on the behavior of gases?

Charles’s law A century later, Jacques Charles performed

experiments on the effect of temperature on gases.

Factor Effect on volume

increase temperature

decrease temperature

• What is the effect of temperature on the volume of a gas?

Charles’s law

The volume of a given amount of gas is directly proportional to the absolute temperature when the pressure is kept constant.

V α T Can you think of any applications / examples of

this in the “real world”?

Factor Effect on volume

increase temperature increase volume

decrease temperature decrease volume

Absolute zero Recall the relationship between the Kelvin and

Celsius scales.

What kind of relationship is this?

Gay-Lussac’s law What is the effect of temperature on pressure?

Factor Effect on pressure

increase temperature

decrease temperature

Gay-Lussac’s law

At constant volume, the absolute pressure of a gas is directly proportional to the absolute temperature.

Factor Effect on pressure

increase temperature increase pressure

decrease temperature decrease pressure

The ideal gas law The three laws can be combined into ONE

general relationship between the three variables:

PV α T

There is one more factor that might affect pressure or volume that is not present; what is it?

The ideal gas law The amount of gas should also affect its volume:

PV α mT

The amount of matter is expressed in moles. 1 mol of a substance contains 6.02 x 1023 atoms

or molecules of the substance (Avogadro’s number).

Why don’t we use kilograms to express the amount of matter?

The ideal gas law But an expression of proportionality is not nearly as

useful as an equation, which brings us to the ideal gas law:

PV = nRT

Where: P is the pressure of the gas, V is the volume, n is the number of moles, and T is the temperature of the gas.

R is the universal gas constant (the constant of proportionality between all four factors:

R = 8.314 Jmol-1K-1

The ideal gas lawDetermine the volume of 1.00 mol of any gas at

STP (standard temperature, 0C, and pressure, 1.00 atm).

The ideal gas lawV = 22.4 L at STP

The ideal gas lawA helium party balloon, assumed to be a perfect

sphere, has a radius of 18.0 cm. At room temperature (20C), its internal pressure is 1.05 atm. Find the number of moles of helium in the balloon and the mass of the helium needed to inflate the balloon to these values.

The atomic mass of helium is 4.00 gmol-1

The ideal gas lawn = 1.066 mol

m = 4.26 g

Objectives Define pressure. State the assumptions of the kinetic model of an

ideal gas. State that temperature is a measure of the

average random kinetic energy of the molecules of an ideal gas.

Explain the macroscopic behavior of an ideal gas in terms of a molecular model.

State the equation of state for an ideal gas. Describe the difference between an ideal gas and

a real gas. Describe the concept of the absolute zero

temperature and the Kelvin scale of temperature Solve problems using the equation of state of an

ideal gas.

HomeworkGiancoli pg 381

# 29, 31, 33, 35, 39

Quiz next class on gas laws

Next lectures: Chapter 15-1 to 15-3