StudyPacks STUDY. KS4 SCIENCE The Cost of Electricity Using Energy and Cost formulas This Study Pack aims to cover: 1. Electrical power 2. Using Electrical energy 3. Cost effectiveness matters SP6 Study Packs are prepared by Qualified Teachers and Specialists and are a complete range of comprehensive compiled resources based on the UK National Curriculum covering the Primary and Secondary Frameworks including SATs and GCSE examinations. Student Name
Contents The cost of Electricity Notes 1-7 Practice questions 8-17 Exam questions 18-25 Mark scheme 26-31 1
2
3
The cost of using electricity You should be able to calculate the cost of using an electrical appliance when given enough information about it. The unit The amount of electrical energy transferred to an appliance depends on its power and the length of time it is switched on. The amount of mains electrical energy transferred is measured in kilowatthours, kwh. One unit is 1kWh. The equation below shows the relationship between energy transferred, power and time: energy transferred (kwh) = power (kw) time (h) Note that power is measured in kilowatts here instead of the more usual watts. To convert from W to kw you must divide by 1000. For example, 2000W = 2000 1000 = 2kW. Also note that time is measured in hours here, instead of the more usual seconds. To convert from seconds to hours you must divide by 3600. For example, 1800s = 1800 3600 = 0.5 hours. The cost Electricity meters measure the number of units of electricity used in a home or other building. The more units used, the greater the cost. The cost of the electricity used is calculated using this equation: total cost = number of units cost per unit For example, if 5 units of electricity are used at a cost of 8p per unit, the total cost will be 5 8 = 40p Remember that the number of units used can be calculated using this equation: units (kwh) = power (kw) time (h) so total cost = power (kw) time (h) cost per unit Electrical Power. 4
5
6
7
Power to the kitchen worksheet Aims In this worksheet you will show your knowledge of the units of energy and power and also practise using energy terms. Questions Before you start, check these for yourself. Do you know: the definition of power? Yes / No / Not sure a unit of power? Yes / No / Not sure a unit of energy? Yes / No / Not sure what the prefix kilo (k) stands for? Yes / No / Not sure You should look up any term that you do not know in your Student Book before you start. Look at the pictures of four devices found in a kitchen. Toaster Microwave oven Electric kettle Electric cooker 1200 W, 5.0 A Do not insert metal objects. 1.1 kw, 240 V Use correct containers inside. Capacity 1.8 litres, 2.0 kw. Do not operate without water inside. 10 kw, 240 V, 50 Hz Installation only by a qualified electrician. a What is the power of the electric cooker?... b Which device has the largest power?... c Which device transfers the lowest number of joules in one second? How many joules of energy does the kettle transfer in one second?.... d When switched on for the same length of time, which device transfers just a little more energy than the microwave oven? 8
Describing energy transfers When someone lifts up the kettle, chemical energy in their muscles is transferred to gravitational potential energy in the kettle and water. In the description of this energy transfer, the type of energy is described as well as the object that has the energy. Now it is your turn. 2.In these examples, use some of the terms from the following list: Energy that heats things up, electrical energy, kinetic energy, gravitational potential energy, chemical energy, sound a.the electric cooker in the picture in question 1 contains a fan to help the food cook more quickly. Describe the energy transfers that occur in the cooker. b.someone drops toast on to the floor. Describe the energy transfers as the toast falls and hits the ground. c.write down something else that happens in a kitchen and describe the energy transfer. 3.Draw two lines from each box on the left to link the quantity on the left with two correct units on the right. energy W J power kw h J/s 9
Read-a-meter worksheet Aims In this worksheet you will practise using the equations in the box and work out the cost of using some electrical appliances. Energy transferred = power time (J) = (W) (s) (kwh) = (kilowatt, kw) (hours) Questions To check the cost of using electricity in his house, a student reads the mini electricity meter on his fridge on June 1st and on August 24th. The diagram shows what the student sees on the two dates. 0 4 4 5 6 kwh June 1 st 0 4 4 8 0 kwh August 24 th The student notices that the unit of energy used on the meter is the kw h. His electricity company charges 14 p for 1 kw h. How many kw h of energy are used between the two dates? How much does the electricity cost the student between these two dates? A lamp is marked as having a power of 100 W. On average the lamp is used for 6 hours every day. i What is the power of the lamp in kw?... How many kw h of electrical energy would be used in one day?.. How many kw h of electrical energy would be used in 30 days?.. Look at the pictures of some devices found in a kitchen. Toaster Microwave oven Electric kettle Electric cooker Power 1.1 kw Power 2.0 kw Power 1200 W Power 10 kw 10
a Fill in the table to show how much energy is used by the toaster in the time given. Give your answers in joules (J). time / s 1 60 100 energy used / J Fill in the table to show how much energy is used by the appliance and the cost (to the nearest pence). Time is measured in hours (h) and the answer is in kilowatt-hours. 1kW h costs 14p. appliance time / h energy used / kw h cost / p toaster 1 toaster 5 microwave 0.1 cooker 2 kettle 0.4 Why do you think the cooker is the most expensive appliance in this particular kitchen? A student reads that The cost of electricity has increased in the last few years. For some electricity providers the price has risen from 14p to 20p. This means the cost of a cup of tea has increased from 140p to 160p. The student decides to check the stated increased cost. She finds that boiling the water in a kettle for a cup of tea takes about 2 minutes. i Convert 2 minutes into hours. How many kw h of electrical energy are used by the kettle? The cost of 1 kw h is 14p. What is the cost of using the kettle for 2 minutes? 11
Do you think the stated increased cost is reasonable? Explain your answer... The best rates worksheet Aims In this worksheet you will practise making calculations of electrical energy usage and the costs involved. You may find the equation and units in the box useful. Remember that 1 kilowatt-hour (kw h) is the energy needed to run a 1 kw appliance for 1 hour. Energy = Power time (J) = (W) (seconds) (kw h) = (kilowatt, kw) (hours) Questions 1 Choosing the best supplier Different energy suppliers charge different amounts for electrical energy. The table shows two different rates from one supplier. The rates shown have been rounded to the nearest pence. In the standard rate the first 900 kw h used per year is charged at the higher rate. All electrical energy above 900 kw h in one year is then charged at the lower rate. The online saver rate has the same rate for all electrical consumption. Cost of first 900 kw h Cost of all other kw h Standard rate 19p/kW h 8p/kW h Online saver rate 10p/kW h 10p/kW h The average use of electrical energy in a house in one year is 3000 kw h. There are 365 days in one year. a Calculate the cost of using 3000 kw h in one year using the online saver rate... 10p = b Calculate the cost of using 3000 kw h in one year using the standard rate. ( 19p) + (. 8p) =.. 12
c Use the table to help you answer the following questions. i Suggest why paying for electricity is cheaper when using the online saver rate for customers who use less than the average amount of electrical energy in one year....... ii Suggest why paying for electricity is cheaper when using the standard rate for customers who use a large amount of electrical energy in one year....... 2 An electric kettle has an electrical power input of 2000 W (2 kw). It is used for 6 minutes. There are 60 seconds in one minute. 6 minutes is 0.1 hours. d Calculate the electrical energy supplied to the kettle in J. watts seconds = J e Calculate the electrical energy supplied to the kettle in kw h. kw hours = kw h f Using your answers to part a and b show how to convert from J to kw h....... g 1 kw h costs 10p. Use your answer to part b to calculate the cost of using the kettle for 6 minutes...kw h.pence per kw h =..p 3 To keep medicines cool in an isolated hospital in a hot country, solar cells are used to provide power to run the refrigerator. During the day they also provide energy to charge batteries for nighttime use, so for any calculations consider the amount of energy produced by a solar cell to be over a complete day. The table provides information about a single solar cell and a refrigerator, as used in the country. Single solar cell Maximum output power in bright light is 4.0 W (0.004 kw), for an average of 5 hours per day. Refrigerator Input power required 120 W. The refrigerator needs this power for only 25% of the time. 13
h Suggest two reasons why it is a less sensible idea to power a refrigerator in the UK using solar cells....... i How much energy in kw h is available when one solar cell is producing its maximum power output for a day? kw hours = kw h j Calculate the number of kw h of energy used by the refrigerator when switched on for a complete day. Remember that 120 W is 0.12 kw and the refrigerator needs power for only 25% of the time....... k Using your answers to part b and c, calculate the minimum number of single solar cells needed to run the refrigerator....... Electrical energy Worksheet 1 The pictures show six different household appliances. Fan heater Vacuum cleaner Washing machine Iron Kettle Blender Name the four appliances in which electrical energy is usefully transferred into kinetic energy.... 14
... (4) 2 An electric motor is used to lift a load. The useful power output of the motor is 30 W. The total input power to the motor is 75 W. Calculate the efficiency of the motor. Write down the equation you use. Show clearly how you work out your answer.......... (3) 3 Which two of the following units are units of energy? a b c d J J/s kwh W... (1) 4 The diagram shows the readings on a household electricity meter at the beginning and end of one week. 5 2 3 4 0 5 2 5 5 5 Beginning of the week End of the week a How many kwh of electricity were used during the week?... (1) b On one day 35 kwh of electricity were used. The total cost of this electricity was 5.25. Calculate how much the electricity cost per kwh? Write down the equation you use. Show clearly how you work out your answer and give the unit.......... [H] (3) 15
c During the week a 2.4 kw kettle was used for 2 hours. Calculate how much energy was transferred by the kettle. Write down the equation you use. Show clearly how you work out your answer and give the unit.......... (3) 5 A student uses some hair straighteners. a The hair straighteners have a power of 90 W. What is meant by a power of 90 W?...... (2) b Calculate how many kilowatt-hours of electricity are used when the straighteners are used for 15 minutes? Write down the equation you use. Show clearly how you work out your answer and give the unit....... (3) c The electricity supplier is charging 14p per kwh. Calculate how much will it cost to use the straighteners for 15 minutes a day for one year. Write down the equation you use. Show clearly how you work out your answer and give the unit.... 16
... (2) 6 Filament bulbs are being replaced by compact fluorescent bulbs. A compact fluorescent bulb costs 12, a filament bulb costs 50p. A 25 W compact fluorescent bulb gives out as much light as a 100 W filament bulb. A filament bulb lasts for about 1000 hours; a compact fluorescent bulb lasts for about 8000 hours, although this time is significantly shorter if the bulb is turned on and off very frequently. A compact fluorescent bulb contains a small amount of poisonous mercury vapour. a Explain how a 25 W compact fluorescent bulb provides the same amount of light as a 100 W filament bulb but use less electricity?...... (2) b In this question you will be assessed on using good English, organising information clearly and usingspecialist terms where appropriate. Compare the advantages and disadvantages of buying compact fluorescent bulbs rather than filament bulbs................ (6) 17
Exam questions Q1. (a) List A shows three electrical devices. List B gives different forms of useful energy. Draw a straight line from each of the devices in List A to the useful energy form it produces in List B.Draw only three lines. (3) (b) Device Toaster Fan The power of each device is given in the table. Power 1.2 kw 30 W Personal Stereo 10 W Which one of the devices will transfer the most energy in 10 minutes? (1) (c) The diagrams show the readings on a domestic electricity meter in April and July. (i) How many Units (kwh) of electricity were used between the two meter readings?...... 18
Number of Units =... (1) (ii) One Unit costs 6p. Use the following equation to calculate the cost of the electrical energy used between the two meter readings. Show clearly how you work out your answer. total cost = number of Units cost per Unit...... Cost =... (2) (d) A 3000 watt electric cooker is switched on for 2 hours. Use the following equation to calculate the number of Units of energy transferred by the cooker. Show clearly how you work out your answer. energy transferred = power time (kilowatt-hour, kwh) (kilowatt, kw) (hour, h) Energy transferred =...kwh (2) (Total 9 marks) Q2. The instruction booklet for a washing machine contains the following information. Wash cycle Average power during cycle Time taken to run cycle HOT 1.6 kw 2 hours COOL 1.1 kw 1 ¼ hours FAST 1.2 kw ¾ hour (a) Electricity costs 15 pence per kilowatt-hour. Calculate, in pence, the cost of using the washing machine for one HOT wash cycle. Write down the equation you use, and then show clearly how you work out your answer............. (b) Cost =... pence Why does it cost more to use the washing machine on the HOT cycle than on the COOL or the FAST cycle? (2) 19
......(1) (Total 3 marks) Q3. Electrical appliances that are left on standby still use energy. The bar chart compares the average amount of standby energy wasted each year in every home in five countries. (i) In which country are the homes that waste, on average, the smallest amount of standby energy? Draw a ring around your answer. Australia France Japan UK USA (1) (ii) Suggest a reason why an average value is used for the standby energy wasted in the homes....... (1) (b) (i) Australia has one of the lowest electricity prices in the world. How does this low price seem to affect the amount of standby energy wasted?...... (1) (ii) In Australia, most electricity is generated in coal-burning power stations. The Australian government wants less electricity to be wasted. Wasting less electricity would be good for the Australian environment. Explain why....... 20
...... (2) (c) Energy is not usually measured in kilowatt-hours. Which one of the following units is usually used to measure energy? Draw a ring around your answer. hertz joule watt (d) (i) Electricity in Japan costs the equivalent of 17 pence per kilowatt-hour. (1) Use the information in the bar chart and the equation in the box to calculate how much the standby energy used in an average Japanese home costs each year. total cost = number of kilowatt-hours cost per kilowatt-hour Show clearly how you work out your answer. Give your answer in pence....... Cost =... pence (3) (ii) In Japan, the largest proportion of electricity is generated using nuclear fuels. Which one of the following statements gives a good reason for using nuclear fuels to generate electricity? Put a tick ( ) in the box next to your answer. A nuclear power station is very expensive to build. A small amount of nuclear fuel generates a large amount of electricity. It is easy to store nuclear waste safely. (1) (Total 10 marks) Q4. The diagram shows the label from a new freezer. 21
(a) An old freezer has an energy consumption per year of 350 kwh. Use the equation in the box to calculate the extra cost of using the old freezer for one year compared with using a new A rated freezer. total cost = number of kilowatt-hours cost per kilowatt-hour Assume 1 kilowatt-hour (kwh) of energy costs 12 p. Show clearly how you work out your answer. Extra cost per year =... (2) (b) The price of the new freezer was reduced in a sale. Reducing the price reduces the payback time for replacing the old freezer from 12 years to 9 years. Calculate, in pounds, how much the new freezer was reduced in the sale. Show clearly how you work out your answer. Price reduced by =... (2) (c) An advertisement in a shop claims that: Replacing an old freezer with a new A rated freezer will benefit the environment. Do you agree that replacing the freezer will benefit the environment? Answer yes or no.... Explain the reasons for your answer....2)total 6 marks) 22
Q5. The picture shows a food processor, which is used to grate, shred, liquidise and mix food. The table gives some information about the food processor. Energy input Useful energy output Power rating Electrical Kinetic 1200 watts Efficiency 0.8 (a) The food processor is used for a total of 30 minutes a day. Calculate the cost of the energy wasted by the food processor each day. Electricity costs 15 p per kilowatt-hour. Write down the equations you use, and then show clearly how you work out your answer................ Cost of waste energy =... p (4) (b) Explain what happens to the waste energy................ (2) (Total 6 marks) 23
Q6. A householder was out shopping when her electricity meter reading should have been taken. The electricity company estimated the reading and sent the following bill. Unfortunately, the bill was damaged in the post. (a) Use the equation in the box to calculate the cost of the electricity used between 12 June and 13 September. total cost = number of kilowatt-hours cost per kilowatt-hour Show clearly how you work out your answer....... Total cost =... (2) (b) The estimated reading shown on the bill was not very accurate. The correct reading was 62920. How many kilowatt-hours of electricity had the householder actually used between 12 June and 13 September?...... (2) (Total 4 marks) Q7. The drawing shows someone ironing a shirt. The top of the ironing board is covered in a shiny silver-coloured material. 24
Explain why the shiny silver-coloured material helps to make ironing easier............. (Total 2 marks) 25
Mark scheme M1. (a) each correct line scores 1 mark if more than 3 lines are drawn mark incorrect ones first, to a maximum of 3 lines 3 (b) toaster accept 1.2 kw 1 (c) (i) 400 1 (ii) 24 or 2400p full credit for their (c)(i) 6p for full credit the correct numerical answer must have the correct unit an answer of 24 or 2400 with no unit or the incorrect unit scores 1 mark (c)(i) 6 incorrectly evaluated scores 1 mark 2 (d) 6 allow 6000 for 1 mark allow 3 2 for 1 mark 2 [9] M2. (a) 48 allow 1 mark for calculating energy as 3.2 kwh 2 (b) largest power and longest time to run 1 [3] M3. (a) (i) France (ii) any one from: 1 different homes have different appliances(*) different homes have different numbers of appliances(*) (*) accept all homes are different standby power not the same for all appliances 26
some people will switch appliances off accept named appliances accept people waste different amounts of energy homes have different numbers of residents can t measure every (individual) home accept any sensible suggestions (b) (i) increases amount of energy wasted do not accept answers in terms of accurate / precise etc accept (encourages) people to leave appliances on (standby) accept increases it 1 1 (ii) any two from: less electricity needed / generated fewer power stations needed less coal is burned do not accept coal is non-renewable / running out answers in terms of fuel stocks neutral less pollutant gases produced accept named gases accept harmful for pollutant accept greenhouse gases accept reduce / slow / stop global warming accept reduces acid rain 2 (c) joule 1 (d) (i) 6800 accept 68 for 3 marks an answer of 68 gains 2 marks allow 2 marks for correct substitution ie 400 17 allow 1 mark for obtaining 400 answers of 7480, 4760, 12920, 4080 gain 2 marks 3 (ii) a small...... electricity 1 [10] M4. (a) 15 (b) 45 allow 1 mark for use of 125 (kwh) allow 1 mark for an answer 1500 allow both marks for 1500 pence / p allow 1 mark for correct calculation of annual cost for either freezer ( 27 and 42) 2 or their (a) 3 allow 1 mark for correct use of 3 allow 1 mark for 12 9 = 3 2 (c) any two from: the marks are for the explanation yes plus explanation less electricity / energy needed / used accept less energy wasted 27
less (fossil) fuels burned accept a named fossil fuel do not accept conserving (fossil) fuels less polluting gases emitted accept a named polluting gas / greenhouse gases / carbon emissions / reduce global warming accept an answer in terms of nuclear fuel eg less nuclear fuel required (1) less nuclear waste (1) 2 or no plus explanation old freezer must be disposed of hazardous chemicals inside freezer accept CFC gases (lot of) energy used in producing new freezer [6] M5. (a) 1.8 (p) PLUS these 4 marks can be broken down as follows: 1 mark for correct transformation and substitution into efficiency equation ie 0.8 1200 useful power PLUS 1 mark for useful power = 960 W / 0.96 kw PLUS 1 mark for waste energy transferred = 0.24 0.5 or waste energy transferred = 0.12 (kwh) 1 mark for cost = 0.12 15 where a mathematical error has been made full credit should be given for subsequent correct method 4 (b) the waste energy is transferred as heat and sound 1 to the surroundings where it spreads out / is shared by surrounding particles accept air for surroundings 1 [6] M6. (a) 19.20 allow 1 mark for correct substitution ie 160 12 allow 1 mark for an answer ( )1920 an answer of 1920p gains both marks an answer of 40.80 gains both marks allow 1 mark for 340 12 2 (b) 340 allow 1 mark for correctly using the reading 62580 ie 62920 62580 accept 40.80 for both marks 2 [4] M7. silver is a (good) reflector of heat (radiation) or silver reflects the heat (radiation) fact heat = infra red 28
ignore references to light accept shiny for silver good radiator negates the mark ignore references to good conductor do not accept bounce back 1 less heat is lost through the board or more heat is retained by the shirt explanation accept both sides of shirt heated reflects heat back up gets 1 mark only ignore mention of friction 1 [2] Answers to Power to the kitchen worksheet 1. a b c d e 10 kw Electric cooker Microwave oven 2000 joules Electric kettle 2. a) Electrical energy transfers to energy that heats the element of the cooker and also kinetic energy of the moving air as well as some sound energy. b) Gravitational potential energy transfers to kinetic energy as the toast falls and increases in speed. Some energy heats the air due to friction. When the toast hits the floor the kinetic energy tranfers to energy heating the molecules in the toast and the floor which are caused to vibrate with a little more kinetic energy. Some sound might be created, possibly by the person who dropped the toast! c) Many possible changes may be described. 3. energy W J power kw h h Read-a-meter Answers to J/s questions 1. 24 kw h Ii 336p = 3.36 29
ii iii b I )0.1 kw h 0.6 kw h 18 kw h 2a b time / s energy used / J 1 1200 60 72 000 100 120 000 appliance time / h energy used / kw h cost / p toaster 1 1.2 17 toaster 5 6.0 84 microwave 0.1 0.11 1.5 2 cooker 2 20 280 kettle 0.4 0.8 11 c) The cooker has a higher power rating and is likely to be switched on for much longer than the other appliances. 2 d i) = 0.033 hours 60 ii) 0.033 x 2 = 0.067 kw h iii) 0.067 x 14 = 0.93p iv) No. The cost of heating the water is a small fraction of the cost of the cup of tea, so for instance doubling the cost of the electricity only costs another 0.9p. The best rates Answers to questions 1. a) 3000 10p = 300.00 b) (900 19) + (2100 8) = 17,100 + 16,800 = 33,900p = 339.00 2 i The 10p rate (rather than 19p rate) will apply to most of your consumption. ii The 8p rate will apply to most of your consumption, offsetting the higher 19p rate for the first 900 kw h. a) 2000 6 60 = 720,000 J b 2 60 6 = 0.20 kw h 3. c 1 kw h = d cost = 0.2 10 = 2p 720 000 = 3,600,000 = 3.6 10 6 J 0.2 a) Answers include: It is less sunny in the UK (fewer hours or the Sun is not so high and gives less energy per second). Mains electrical connections are more likely to be available for the refrigerator and thus the extra cost of the solar cell is not warranted. 4 b 5 1000 = 0.020 kw h c 0.12 24 0.25 = 0.72 kw h d 0.72 0.02 = 36 30
Answers to Electrical energy worksheet 1. 1. 1.Fan heater Washing machine Blender Vacuum cleaner 4 2.Efficiency = usefulpower out x 100% total power in 30W 75W Efficiency = x100% Efficiency = 40% 3 3 a (J) and c (kwh) 1 4 a 215 b Total cost = number of kwh used X cost per kwh cost per kwh = total cost/number of kwh used cost per kwh = 525p/35 cost per kwh = 15p c E = P X t E = 2.4 kw X 2 h E = 4.8 kw h 5a 90 joules of energy are transferred each second b E = P X t E = 0.09 kw X 0.25 h E = 0.0225 kw h (3 marks) c cost = number of kw h used X cost per kw h cost per day = 0.0225 kw h X 14p = 0.315p cost for the year = 0.315p X 365 = 115p or 1.15 6 b There is a clear, balanced and detailed description of the advantages and disadvantages of buying compact fluorescent bulbs rather than filament bulbs. The answer shows almost faultless spelling, punctuation and grammar. It is coherent and in an organised, logical sequence. It contains a range of appropriate or relevant specialist terms used accurately. There is a description of a range of the advantages and disadvantages of buying compact fluorescent bulbs rather than filament bulbs. There are some errors in spelling, punctuation and grammar. The answer has some structure and organisation. The use of specialist terms has been attempted, but not always accurately. There is a brief description of at least two advantages and disadvantages of buying compact fluorescent bulbs rather than filament bulbs, which has little clarity and detail. The spelling, punctuation and grammar are very weak. The answer is poorly organised with almost no specialist terms and/or their use demonstrating a general lack of understanding of their meaning. No relevant content. Examples of physics points made in the response: Advantages of compact fluorescent bulbs: more efficient/4 times more efficient cheaper to use lasts longer/lasts 8 times as long better for the environment. Disadvantages of compact fluorescent bulbs: more expensive to buy/cost 24 times as much to buy disposal a problem because of mercury vapour shortened lifespan if turned on and off very frequently. 1 3 3 2 3 2 5-6 3-4 1-2 0 31