Wallace Hall Academy Physics Department. Energy. Pupil Notes Name:

Transcription

1 Wallace Hall Academy Physics Department Energy Pupil Notes Name:

2 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 P 1T 1/V 1 = P 2T 2/V 2 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 2

3 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. 3

4 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. 4

5 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 o C -1. Calculate the final temperature of the brakes once the car comes to rest if their initial temperature was 19 o C. 5

6 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 m 2. 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. 6

7 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 m 2. The area of the heel in contact with the ground is m 2. Calculate the pressure on the ground. 7

8 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 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 N on one wall of a cubic container. One edge of the cube measures 2 m. Calculate the pressure of the hydrogen. 8

9 Pressure variation with temperature at constant volume experiment Aim: To determine the relationship between pressure and temperature at constant volume. In a group of 2 or 3 discuss what you think will happen to the pressure of the gas as the temperature is increased. Diagram: Method: Results: Pressure (Pa) Temperature ( o C) 9

10 As you will see the graph does not go through the origin. This is because we plotted temperature in o C rather than in Kelvin. 10

11 Kelvin scale of temperature We use the Celsius scale of temperature as it is convenient for everyday use with water freezing at 0 o C and boiling at 100 o C 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 C = K 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 o C is equal in size to 1 K. This means a temperature increase of 34 o C 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 o C 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 ( o C) Temperature (K) 11

12 Conclusion: Evaluation: 12

13 Volume variation with temperature at constant pressure experiment Aim: To determine the relationship between volume and temperature at constant pressure. In a group of 2 or 3 discuss what you think will happen to the volume of the gas as the temperature is increased. Diagram: Method: Results: Volume (cm) Temperature ( o C) Temperature (K) 13

14 Conclusion: Evaluation: 14

15 Pressure variation with volume at constant temperature experiment Aim: To determine the relationship between pressure and volume at constant temperature. In a group of 2 or 3 discuss what you think will happen to the pressure of the gas as the volume is increased. Diagram: Method: Results: Volume (cm 3 ) Pressure (Pa) 15

16 The graph above looks like an inverse relationship so complete the table below and try to plot pressure versus the inverse volume. Volume (cm 3 ) Pressure (Pa) 1/Volume (cm -3 ) 16

17 Conclusion: Evaluation: 17

18 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. P 1 = V 1 = T 1 = P 2 = V 2 = T 2 = Examples cm 3 of air is contained in a syringe at atmospheric pressure ( Pa). If the volume is reduced to 20 cm 3, without a change in temperature, calculate the new pressure. 18

19 2. A cylinder of oxygen at 27 o C has a pressure of Pa. Calculate the new pressure if the gas is cooled to 4 o C? litres of a fixed mass of air is at a temperature of 10 o C. 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 Pa to Pa. At the same time, the container is compressed from 125 cm 3 to 100 cm 3. If the initial temperature of the gas was 30 o C, calculate the final temperature of the gas. 19

20 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. 20

21 2. Explain using kinetic theory how a decrease in the temperature of a gas leads to a decrease in volume at constant pressure. 3. Explain using kinetic theory how an increase in the volume of a gas leads to a decrease in pressure at constant temperature. 21