energy - wordpress.com2. a model rocket is fired straight up with an initial speed of 8 ms-1. the...
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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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