Energy

Pupil Notes

Name: _________

Wallace Hall Academy Physics Department

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Learning intentions for this unit ✓ ? ✘

Be able to state the law of conservation of energy

Be able to perform energy calculations when energy is transformed from one type

to another

Be able to state that pressure is force per unit area

Be able to perform calculations using P = F/A

Be able to convert temperatures between Celsius and Kelvin

Be able to perform calculations using P1T1/V1 = P2T2/V2

Be able to state that temperature is a measure of the mean kinetic energy of the

particles in a substance

Be able to describe how the kinetic model of a gas explains the pressure of a gas

Be able to describe hoe the kinetic model of a gas explains the relationship

between pressure, temperature and volume

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CONSERVATION OF ENERGY

Law of conservation of energy

The law of conservation of energy states that energy can neither be created nor destroyed,

just changed from one type of energy to another.

During the Dynamics, Electricity and Space topics you have already encountered many types of

energy. In the box below list the types of energy you know about alongside any equations that are

relevant.

While it is true that energy can neither be created nor destroyed, it can be wasted. When

transferring from one type of energy to another, energy is often wasted as heat or sound. In many

questions you will be asked where the wasted energy has gone and you will need to evaluate the

problem and state that energy is wasted due to friction as heat energy or by some other means.

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Examples

1. Oranges hang from a branch of a tree. An orange has a mass of 200 g and is at a height of 7 m

above the ground. The orange falls to the ground.

a. Calculate the gravitational potential energy it has when it is hanging from the tree.

b. Assuming that air resistance is negligible, calculate the kinetic energy of the orange just before

it hits the ground?

c. Calculate how fast the orange will be travelling just before it hits the ground.

d. Explain whether the actual speed of the orange would be smaller than, equal to or bigger than

the value calculated in part c.

2. A model rocket is fired straight up with an initial speed of 8 ms-1. the rocket has a mass of 0.2 kg.

a. Calculate the initial kinetic energy of the rocket.

b. The mass of the rocket does not change. The rocket reaches its maximum height. Calculate the

gravitational potential energy gained by the rocket.

c. Use your answer from b to calculate the maximum height reached by the rocket.

d. Explain whether the actual height reached by the rocket would be smaller than, equal to or

bigger than the value calculated in part c.

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3. A car is being driven along a road at 15 ms–1. The total mass of the car and driver is 900 kg.

a) Calculate the kinetic energy if the car and driver.

b) The brakes are applied and the car is brought to rest over a distance of 45 m. Calculate the

average frictional force applied by the brakes.

c) The brakes are made of 1.3 kg of a new carbon infused steel alloy with a specific heat capacity

of 490 J kg-1 oC-1. Calculate the final temperature of the brakes once the car comes to rest if

their initial temperature was 19 oC.

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Pressure

Pressure is defined as the amount of force per unit area.

P =

F =

A =

Examples

1. A cube of side 3m is sitting on a bench. If the mass of the cube is 27kg, calculate the pressure

on the bench.

2. A man of mass 70kg is standing still on both feet. The average area of each foot is 0.025 m2.

a) Calculate the force the man exerts on the ground (his weight in N).

b) Calculate the pressure exerted by the man on the ground.

c) If the man now stands on only one foot, calculate the pressure this time.

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3. A man of mass 60 kg is standing on a block of wood measuring 0.28 m × 0.08 m. Calculate the

pressure on the ground.

4. A woman of mass 60 kg stands on one high heeled shoe. The area of sole in contact with the

ground is 1.2×10–3 m2. The area of the heel in contact with the ground is 2.5×10–5 m2. Calculate

the pressure on the ground.

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GAS LAWS

Kinetic theory of gases

Particles in a gas have large gaps between them and

the particles move about in the gas freely. The kinetic

energy and velocity of the individual particles is linked

to the temperature of the gas. The higher the

temperature, the higher the kinetic energy and velocity

of the particles. When sealed in a container the

particles will hit the inside of the container walls with a

force which will create a pressure based on the force

the particles hit with and the area of the inside of the

container (P = F/A). Obviously the temperature of the

gas (kinetic energy of the particles), the volume of the

gas (area of the inside of the container) and the

pressure exerted by the gas on the walls of the

container (pressure) are all linked. The links between

the three are explained by the gas laws.

Examples

1. Air molecules exert an average force of 6 × 105 N on a wall. The wall measures 2 m × 3 m.

Calculate the air pressure in the room.

2. Hydrogen molecules at low pressure exert an average force of 3 × 104 N on one wall of a cubic

container. One edge of the cube measures 2 m. Calculate the pressure of the hydrogen.

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Pressure variation with temperature at constant volume experiment

Aim: To determine the relationship between pressure and temperature at constant volume.

Diagram:

Method:

Results:

Pressure (Pa) Temperature (oC)

In a group of 2 or 3 discuss what you think will happen to the pressure of the gas as the temperature is increased.

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As you will see the graph does not go through the origin. This is because we plotted temperature in oC rather than in Kelvin.

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Kelvin scale of temperature

We use the Celsius scale of temperature as it is convenient for everyday use with water freezing at

0 oC and boiling at 100 oC giving us an easy frame of reference to compare and understand different

temperatures. In Physics, however, it is more useful to use the Kelvin scale of temperature which is

referenced to 0 K which means there is no such thing as negative values of Kelvin so any

experiment involving temperature should provide a graph going through the origin. To convert from

Celsius to Kelvin or from Kelvin to Celsius use the following conversions,

K = C + 273

C = K - 273

The diagram shows two thermometers to

allow you to compare some commonly known

temperatures listed in Kelvin and in Celsius. It

is worth noting that the size of 1 oC is equal in

size to 1 K. This means a temperature

increase of 34 oC is exactly the same as a

temperature change of 34 K. It is just the

starting points that are different. The Celsius

scale starts at -273 oC and the Kelvin scale

starts at 0 K. 0 K is also known as absolute

zero where particles have zero kinetic energy.

Redo your table from the previous page with a

third column as shown below and then plot the

graph again with Pressure plotted against

temperature in Kelvin.

Pressure (Pa) Temperature (oC) Temperature (K)

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Conclusion:

Evaluation:

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Volume variation with temperature at constant pressure experiment

Aim: To determine the relationship between volume and temperature at constant pressure.

Diagram:

Method:

Results:

Volume (cm) Temperature (oC) Temperature (K)

In a group of 2 or 3 discuss what you think will happen to the volume of the gas as the temperature is increased.

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Conclusion:

Evaluation:

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Pressure variation with volume at constant temperature experiment

Aim: To determine the relationship between pressure and volume at constant temperature.

Diagram:

Method:

Results:

Volume (cm3) Pressure (Pa)

In a group of 2 or 3 discuss what you think will happen to the pressure of the gas as the volume is increased.

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The graph above looks like an inverse relationship so complete the table below and try to plot

pressure versus the inverse volume.

Volume (cm3) Pressure (Pa) 1/Volume (cm-3)

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Conclusion:

Evaluation:

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Gas law calculations

An increase in temperature causes an increase in pressure at constant volume.

An increase in temperature causes an increase in volume at constant pressure.

An increase in volume causes a decrease in pressure at constant temperature.

We can calculate how these changes affect the pressure, volume and temperature of a gas using

the relationship below.

P1 =

V1 =

T1 =

P2 =

V2 =

T2 =

Examples

1. 100 cm3 of air is contained in a syringe at atmospheric pressure (1×105Pa). If the volume is

reduced to 20 cm3, without a change in temperature, calculate the new pressure.

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2. A cylinder of oxygen at 27 oC has a pressure of 3×106 Pa. Calculate the new pressure if the gas

is cooled to 4 oC?

3. 120 litres of a fixed mass of air is at a temperature of 10 oC. Calculate what the temperature will

be if the volume is increased to 140 litres if its pressure remains constant.

4. The pressure of a fixed mass of nitrogen is increased from 1.3×105 Pa to 2.5×105 Pa. At the

same time, the container is compressed from 125 cm3 to 100 cm3. If the initial temperature of

the gas was 30 oC, calculate the final temperature of the gas.

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Gas law explanations

An increase in temperature causes an increase in pressure at constant volume.

An increase in temperature causes an increase in volume at constant pressure.

An increase in volume causes a decrease in pressure at constant temperature.

We are able to perform calculations on the above statements but it is also important to be able to

explain why the changes occur using kinetic theory.

The temperature of a gas is directly related to the

kinetic energy of the individual gas particles.

The force exerted by a gas on the inside of container

walls is directly related to the force exerted by

individual gas particles on the container walls.

The volume of a container is directly related to the

area of its internal walls.

The pressure of a gas is related to the force exerted

by individual gas particles and the area of the

internal container walls.

Examples

1. Explain using kinetic theory how an increase in the temperature of a gas leads to an increase

in pressure at constant volume.

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2. Explain using kinetic theory how a decrease in the temperature of a gas leads to a decrease in

volume at constant pressure.

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3. Explain using kinetic theory how an increase in the volume of a gas leads to a decrease in

pressure at constant temperature.

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