Topic 3: Thermal Physics

3.1 Thermal Concepts3.2 Thermal Properties of Matter3.3 Kinetic Model of an Ideal Gas

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3.1 Thermal Concepts Physicists:

Observe, measure, explain.

Motion of bodies: Predict Velocity, Force, Acceleration

Holding objects: Some are hot and some are

cold.

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The Particle Model of Matter Greek Philosophers:

Smallest Part: Atom

Atoms (~10-10 m in diameter) Very small perfectly elastic balls.

Collision between atoms: Momentum and Kinetic Energy are

conserved.

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Elements and Compounds There are 117 different

types of atom, and a material made of just one type of atom is called an element.

Materials made from molecules that contain more than one type of atom are called compounds.

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The Mole

A mole of any material contains6.022 X 1023 atoms or molecules.

This number is known as Avogadro’s number.

Compare Hydrogen and Carbon.

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Three States of Matter

From observations we know that there are three states of matter:

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Example #1

If a mole of carbon has a mass of 12

g, how many atoms of carbon are

there in 2 g?

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Example #2

The density of aluminum is

2800 kg m-3 and the mass of a mole

of aluminum is 26.98 g.

What is the volume of 1 mole of

aluminum?

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Answers: Example 1 & 2

1. 1.004 X 1023 Atoms

2. 9.635 X 10-6 m3

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Exercise 1

The mass of 1 mole of copper is 63.54 g and its

density 8920 kg m-3.

A) What is the volume of 1 mole of copper?

B) How many atoms does one mole of copper

contain?

C) How much volume does one atom of copper

occupy?

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Internal Energy

Ponder Mechanics:

Energy and Work

velocity

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1 Is any work being done on the block by the force F?

2 Is energy being transfered to the block?

3 Is the KE of the block increasing?

4 Where is the energy going?

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Work Object Molecules move faster

The Internal Energy of the object has increased.

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Example #3

A car of mass 1000 kg is travelling at

30 m s-1. If the brakes are applied,

how much heat energy is

transferred to the brakes?

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Answer: Example 3

The thermal energy transferred to

the brakes is 450 kJ.

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Temperature

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Hotness and coldness

are the ways we

percieve differences

between objects.

We use temperature to

measure this difference.

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Temperature:

(T) is a measure of how hot or cold an object is.

Determines the direction of heat flow.

Is a scalar quantity, and is measured in degrees Celsius (°C) or kelvin (K).

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The Kelvin scale is based on the properties of a gas.

To convert Celsius to Kelvin:

T(K) = T(°C) + 273

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Thermometers

Temperature cannot

be measured directly,

so we have to find

something that

changes when the

temperature changes.

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Temperature and the Particle Model

Temperature is the average Kinetic Energy of the particles.

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Heat Transfer Pulling a block of wood along a rough

surface.

We can make a cold body hot by placing it next to a hot body.

If the cold body gets hot, then it received energy: Heat or Thermal Energy.

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Thermal Equillibrium

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Some definitions:

Temperature: Is a macroscopic concept that is

proportional to the average KE of the molecules of

the substance.

Heat: (Or thermal energy) is the energy that is

exachanged between two bodies as a result of a

temperature difference between them.

Internal Energy: The sum of the total random KE

and the total intermolecular potencial energy of the

molecules of a substance.

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Exercises

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1.

A hot body is brought into contact with a colder body

until their temperatures are the same. Assume that no

other bodies are around.

A) Is the heat lost by one body equal to the heat

gained by the other?

B) Is the temperature drop of one body equal to the

temperature increase of the other?

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2. A body at a given uniform temperature of

300 K and internal energy 8 X 106 J is split into two equal halves.

A) Has any heat been exchanged?

B) What is the temperature of each half?

C) What is the internal energy of each half?

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3.

The volume of 1 mol of hydrogen gas (molar mass

2 g mol-1) at stp (standard temperature and

pressure) is 22.4 L.

A) Find out how much volume corresponds to each

molecule of hydrogen.

B) Consider now 1 mol of lead (molar mass 207 g mol-

1, density 11.3 X 103 kg m-3). How much volume

corresponds to each molecule of lead?

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C) Find the ratio of these volumes (hydrogen and lead).

D) Hence determine that the order of magnitude of the ratio:

is 10.

Separation of hydrogen molecules

Separation of lead molecules

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Answers: Exercises

1. A) Yes, because of Energy Conservation.B) The changes in temperature are not necessarily equal.

2. A) No. B) 300 K. C) 4 X 106 J

3. A) 3.7 X 10-26 m3.B) 3.0 X 10-29 m3.C) Ratio = 1220

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3.2 Thermal Properties of Matter

Thermal Capacity

Specific Heat Capacity

Solving problems

Differences between the solid, liquid and gaseous phases

Specific Latent Heat

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Thermal Capacity

The actual increase in

temperature depends on

the body.

The thermal capacity (C)

of a body is the amount of

heat needed to raise its

temperature by 1°C. Units: J °C-1

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C: Thermal Capacity (J °C-1)

Q: Heat (Joules)

T: Temperature change (°C)

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QC

T

Example #4

If the thermal capacity of a quantity

of water is 5000 J °C-1, how much

heat is required to raise its

temperature from 20°C to 100°C?

Answer: 400 kJ

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Exercise 1

The thermal capacity of a 60 kg

human is 210 kJ °C-1. How much heat

is lost from a body if its temperature

drops by 2°C?

Answer: 420 kJ

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Specific Heat Capacity (c)

Depends only on the material.

The specific heat capacity of a

material is the amount of heat

required to raise the temperature of

1 kg of the material by 1°C.

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c: Specific Heat Capacity (J kg-1 °C-1)

Q: Heat (Joules)

T: Temperature change (°C)

m: Mass (kg)

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Qcm T

Example #5

A metal block of mass 1.5 kg loses

20 kJ of heat. As this happens, its

temperature drops from 60°C to

45°C. What is the specific heat

capacity of the metal?

Answer: 888.9 J kg-1 °C-1

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Exercise 2 (HW)The density of water is 1000 kg m-3.

A) What is the mass of 1 litre of water?

B) How much energy will it take to raise the temperature of 1 litre of water from 20°C to 100°C?

C) A water heater has a power rating of 1 kW. How many seconds will this heater take to boil 1 litre of water?

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Exercise 3 (900 J kg-1 °C-1) A 500 g piece of aluminum is heated with a

500 W heater for 10 minutes.

A) How much energy will be given to the aluminum in this time?

B) If the temperature of the aluminum was 20°C at the beginning, what will its temperature be after 10 minutes?

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Exercise 4 (440 J kg-1 °C-1) (HW) A car of mass 1500 kg travelling at 20 m s-1

brakes suddenly and comes to a stop.

A) How much KE does the car lose?

B) If 75% of the energy is given to the front brakes, how much energy will they receive?

C) The brakes are made out of steel and have a total mass of 10 kg. By how much will their temperature rise?

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Change of State

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Particle Model

Drawings

1. Molecules gain PE when the state changes.

2. A ball-in-a-box model of change of state.

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Boiling & Evaporation

Boiling takes

place throughout

the liquid and

always at the

same temperature.

Evaporation takes

place only at the

surface of the

liquid and can

happen at all

temperatures.

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Specific Latent Heat

The specific latent heat of a

material is the amount of heat

required to change the state of 1 kg

of the material without change of

temperature.

Units: J kg-1

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Latent means hidden.

L: Specific Latent Heat (J kg-1)

Q: Heat (J)

m: Mass (kg)

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QL

m

Example #6

The specific latent heat of fusion of

water is 3.35 X 105 J kg-1. How much

energy is required to change 500 g of

ice into water?

Answer: Q = 1.675 X 105 J

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Exercise 5

If the mass of water in a cloud is

1million kg, how much energy will be

released if the cloud turns from water

to ice?

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Latent heat of vaporization 2.27 X 106 J kg-1

Latent heat of fusion 3.35 X 105 J kg-1

Answer: 3.35 X 1011 J

Exercise 6

A water boiler has a power rating of

800 W. How long will it take to

turn 400 g of boiling water into

steam?

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Latent heat of vaporization 2.27 X 106 J kg-1

Latent heat of fusion 3.35 X 105 J kg-1

Answer: 1.135 X 103 s

HomeworkThe ice covering a 1000 m2 lake is 2 cm thick.

A) If the density of the ice is 920 kg m-3, what is the mass of the lake?

B) How much energy is required to melt the ice?

C) If the Sun melts the ice in 5 hours, what is the power delivered to the lake?

D) How much power does the Sun deliver per m2 ?

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Answers to Homework

A) 1.84 X 104 kg

B) 6.16 X 109 J

C) 3.42 X 105 W

D) 342 W m-2

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Kinetic Model of an Ideal Gas Pressure

Assumptions of the Kinetic Model

Temperature

Macroscopic behaviour of an ideal gas in terms of a molecular model.

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The Ideal Gas

Gaseous State has the simplest model.

Forces between molecules: very small.

Molecules move freely.

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Assumptions

The molecules are:

Perfectly elastic.

Spheres.

Identical.

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Assumptions

No forces between the molecules.

Constant velocity.

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Temperature of a Gas Temperature of a gas

is directly related to the average KE of the molecules.

If temperature increases:

The speed of the particles will increase.

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Pressure of a Gas

Let us apply what we know about particles to one molecule of gas.

Consider a single gas molecule in a box (perfectly elastic sphere bouncing off the sides).

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Pressure of a Gas

Change in:

Direction and Velocity.

Newton’s First Law of Motion: Particle at rest or moving with constant

velocity.

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The particle is experiencing a Force.

Pressure of a Gas

Newton’s Second Law: The force is equal to the rate change of

momentum.

The force will be greater if:

the particle travels with greater speed,

or hits the sides more often.

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Pressure of a Gas

Newton’s Third Law: FAB = -FBA

The wall exerts a force on the particle,

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“So the particle must exert a force on the wall.”

Pressure of a Gas If we add more molecules,

Then the particles exert a continuous force, F, on the walls of the container.

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Pressure of a Gas

ForceArea

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= Pressure

The particles exert a pressure on the container.

Properties of a Gas

Interactive Simulationhttp://phet.colorado.edu/en/simulation/gas-properties

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