Higher Physics – Unit 1

1.6 – Gas Laws

Kinetic Theory of Gases

The kinetic model of matter explains the behaviour of gases using a model.

The model considers gases to be made up from a large number of very small particles which are far apart, move randomly at high speeds and collide (elastically) with everything they meet.Volume

The volume of a gas is taken as the volume of the container.

The volume occupied by the particles themselves is so small it is neglected.

Temperature

The temperature of a gas depends on the kinetic energy of the gas particles.

The faster the particles move the greater their kinetic energy and the higher the temperature.

Pressure

Pressure of a gas is due to the particles colliding with each other and the walls of the container.

The more frequent and harder the collisions, the greater the pressure.

Boyles Law

Pressure and Volume

The pressure of a fixed mass of gas is inversely proportional to its volume.

2211 V PV P

constantVP V1

P

This is used in the form:

pressure(Pa – Pascal)

volume(m3)

** NOT ON DATA SHEET **

Graphs of Relationship

pressure

volume

What remains constant throughout?

• temperature of gas,

• mass of gas.

volume1

pressure

Example 1

A sample of gas has a volume of 30 cm3 at a pressure of 2x105 Pa.

Calculate the new volume of gas when the pressure is increased to 5x105 Pa.

Pa 102P 51

31 cm 30V

Pa 105P 52

?V2

2211 V PV P

255 V10530102

256 V105106

5

6

2 105106

V

32 cm 12V

Worksheet – Boyle’s Laws

Q1 – Q5

Pressure Law

Pressure and Temperature

A fixed mass of gas at a constant volume is considered.

If the temperature is increased, the particles move with greater speed and kinetic energy. Collisions are more frequent and severe, causing pressure to increase.

When the temperature is decreased, the particles move with less speed and kinetic energy. Collisions are less frequent and severe causing pressure to decrease.

Graph of Relationship

The result is a straight line that does not pass through the origin.

p

T / oC-273

When the graph is extended back until the pressure reaches zero, it crosses the axis at -273°C.

This is known as absolute zero.

When the pressure is graphed against temperature in kelvin, the graph shows pressure to be directly proportional to temperature.

p

T / K0

NOT directly proportional

directly proportional

Relationship

The pressure of a gas is directly proportional to its temperature – IN KELVIN.

2

2

1

1

TP

TP

constantTP

TP

This is used in the form:

pressure(Pa – Pascal)

temperature(K)

** NOT ON DATA SHEET **

When using this equation – temperature must be in kelvin (K).

What remains constant throughout?

• volume of gas,

• mass of gas.

Absolute Temperature

The lowest possible temperature is -273°C.

This temperature is called absolute zero.

The absolute temperature scale calls -273°C, zero kelvin (K).

Converting °C to K

add 273

Converting K to °C

subtract 273

An increase of 5°C = an increase of 5 K.

No negative temperatures on the kelvin scale.

Pressure At Absolute Zero

At absolute zero, the pressure is zero.

This is because the particles do not move at absolute zero, so there are no collisions with the container walls.

Hence, there is zero pressure.

Pressure Law Problems

Example 1

A quantity of gas has a pressure of 2.5x105 Pa at a temperature of 20 °C.

(a) Calculate the new pressure when the temperature reaches 37 °C.

(b) State two important assumptions made in part (a).

(a)Pa 102.5P 5

1

C 20T1

?P2

2

2

1

1

TP

TP

273 20 K 293

C 37T2 273 37

K 310

310P

293

102.5 25

52 102.5310P293

2931077.5

P6

2

Pa 102.65P 52

(b)

Two important assumptions are that:

• the mass of gas is fixed,

• the volume of gas is fixed.

Worksheet – The Pressure Law

Q1 – Q7

Charles’ Law

Volume and Temperature

A fixed mass of gas at a constant pressure is considered.

If the temperature increases, the particles move with a greater speed and kinetic energy. The volume increases.

If the temperature decreases, the particles move with less speed and kinetic energy. The volume decreases.

Graph of Relationship

The result is a straight line which does not pass through the origin.

V

T / oC-273

When the graph is extended back until the volume reaches zero, it crosses the axis at -273°C.

When the volume is graphed against temperature in kelvin, the graph shows volume to be directly proportional to temperature.

V

T / K0

NOT directly proportional

directly proportional

Relationship

The volume of a gas is directly proportional to its temperature – IN KELVIN.

2

2

1

1

TV

TV

constantTV

TV

This is used in the form:

volume(m3)

temperature(K)

** NOT ON DATA SHEET **

When using this equation – temperature must be in kelvin (K).

Example 1

There is 50 cm3 of gas at 27 °C collected.

Calculate the volume of gas at 10 °C when the pressure is unchanged.

31 cm 50V

C 27T1

?V2

2

2

1

1

TV

TV

273 27 K 300

C 10T2 273 10K 283

283V

30050 2

50283V300 2

30014,150

V2

32 cm 47.2V

Worksheet – Charles’ Law

Q1 – Q7

Combined Gas Equation

Pressure, Volume and Temperature

In combining Boyle’s Law, the Pressure Law and Charles’ Law we can get one relationship that relates pressure, volume and temperature of a fixed mass of gas.

constantT

VP

2

22

1

11

TV P

TV P

pressure(Pa)

** NOT ON DATA SHEET **

When using this equation – temperature must be in kelvin (K).

This equation is used in the form:

temperature(K)

volume(m3)

Gas Laws and Kinetic Theory

Pressure and Volume (Mass and Temperature Constant)

• As volume decreases

• Gas particles are closer together

• Particles hit walls of container more often

• Over a smaller area

AF

P

So the pressure of the gas increases:

F ARepeat for volume

increase.

Pressure and Temperature (Mass and Volume Constant)

• As temperature rises

• The gas particles move faster

• They hit walls of the container more often and with greater force (harder)

AF

P

So the pressure of the gas increases:

F A unchanged

Repeat for temperature

decrease.

Volume and Temperature (Mass and Pressure Constant)

• As temperature rises

• The gas particles move faster

• They hit walls of container with greater force (harder)

• For constant pressure – volume must increase

• This gives bigger area

AF

P

The pressure of the gas remains unchanged:

F A

Repeat for temperature

decrease.

Worksheet – Combined Gas Equation

Q1 – Q10