gcse science a unit 3 physics p1.1-p1.2

31
AQA GCSE Science A Unit 3 Physics Summary Notes Part 1 (P1-P3) Prepared and compiled by Steve Bishop March 2013

Upload: steve-bishop

Post on 12-Apr-2015

1.068 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: GCSE Science A Unit 3 Physics P1.1-P1.2

AQA GCSE Science A

Unit 3

Physics Summary Notes Part 1

(P1-P3) Prepared and compiled by

Steve Bishop

March 2013

Page 2: GCSE Science A Unit 3 Physics P1.1-P1.2

2

Contents  P1.1 The transfer of energy by heating processes and the factors that affect the rate at which that energy is transferred .............................................................................................. 3  

P1.1.1 Infrared radiation ...................................................................................................... 4  

P1.1.2 Kinetic theory ............................................................................................................ 4  

P1.1.3 Energy transfer by heating ....................................................................................... 5  

P1.1.4 Heating and insulating buildings ............................................................................... 7  

P1.2 Energy and efficiency ...................................................................................................... 9  

P1.2.1 Energy transfers and efficiency .............................................................................. 10  

P1.3 The usefulness of electrical appliances ........................................................................ 11  

P1.3.1 Transferring electrical energy ................................................................................. 12  

GCSE questions .................................................................................................................... 14  

Page 3: GCSE Science A Unit 3 Physics P1.1-P1.2

3

P1.1 The transfer of energy by heating processes and the factors that affect the rate at which that energy is transferred

Energy can be transferred from one place to another by work or by heating processes. We need to know how this energy is transferred and which heating processes are most important in a particular situation.

I can:

✓ � compare ways in which energy is transferred in and out of objects by heating and ways in whichthe rates of these transfers can be varied

� evaluate the design of everyday appliances that transfer energy by heating, including economicconsiderations

� evaluate the effectiveness of different types of material used for insulation, including U-valuesand economic factors including payback time

� evaluate different materials according to their specific heat capacities.

Key words

Conduction Convection Radiation Emit Absorb Conductor Insulator Kinetic theory Evaporation Condensation Energy Work Transfer U-values Payback time Specific heat capacity

Page 4: GCSE Science A Unit 3 Physics P1.1-P1.2

4

P1.1.1 Infrared radiation

a) All objects emit (give out) and absorb (take in) infrared radiation.If an object is a good emitter, it will also be a good absorber.

b) The hotter an object is the more infrared radiation it radiates (gives out) in a given time.If the object is cooler than its surroundings it will absorb more heat than it emits, so it will warm up.

c) Dark, matt surfaces are good absorbers and good emitters of infrared radiation.

d) Light, shiny surfaces are poor absorbers and poor emitters of infrared radiation.

e) Light, shiny surfaces are good reflectors of infrared radiation.

P1.1.2 Kinetic theory

a) The use of kinetic theory to explain the different states of matter.

The diagram above shows the difference between a solid, liquid and a gas.

As a substance is heated the particles will vibrate more and move about more.

In a solid the particles are arranged in a tight pattern, they don’t have much energy and so only vibrate a little

In a liquid the particles are close together, but can move past each other.

In a gas the particles have much more energy than in liquids or solids, they are free to move in any direction.

Heating gives the particles more energy; this will cause solids to melt and liquids to boil.

b) The particles of solids, liquids and gases havedifferent amounts of energy.

Page 5: GCSE Science A Unit 3 Physics P1.1-P1.2

5

P1.1.3 Energy transfer by heating a) The transfer of energy by conduction, convection, evaporation and condensation involves particles,and how this transfer takes place.

b) The factors that affect the rate of evaporation and condensation.

Evaporation is when a liquid turns to a gas Condensation is when a gas turns to a liquid.

c) The rate at which an object transfers energy by heating depends on:

� surface area and volume � the material from which the object is made � the nature of the surface with which the object is in contact.

d) The bigger the temperature difference between an object and its surroundings, the faster the rate atwhich energy is transferred by heating.

Page 6: GCSE Science A Unit 3 Physics P1.1-P1.2

6

Conductors and insulators Conduction occurs when particles vibrate and pass on their energy to a neighbouring particle. Materials with particles close together conduct heat much faster then materials with large spaces between particles. Metals are good conductors because of their free electrons. The electrons are free to move around inside the metal so they transfer the energy very quickly to other particles.

Convection As air warms up, it expands and so is less dense. It will then rise. As it cools it becomes more dense and so will sink. Sea breezes are also caused by convection currents:

Page 7: GCSE Science A Unit 3 Physics P1.1-P1.2

7

P1.1.4 Heating and insulating buildings One way to reduce the amount of heat that escapes from a house is to insulate it so that the heat energy escaping is reduced.

Important ways of reducing heat loss in a home are:

• Loft insulation – this is a thick layer of fibre glass laid across the loft space. It reduces conduction and convection.

• Cavity wall insulation – this is foam squirted between the gaps between bricks. It reduces conduction and convection.

• A jacket for the hot water tank this reduces conduction and radiation. Payback time – the time taken to recoup the initial payment - for these is calculated by:

Initial cost ÷ annual saving Example It costs £250 to install and fit loft insulation in a house. It saves £50 a year. How long is the payback time? Solution using: Payback time = Initial cost ÷ annual saving

Then £250 ÷ £50 = 5 years. U-values a) U-values measure how effective a material is as an insulator. The U-value shows how fast heat can transfer through a material. The higher the U-value the faster the heat transfer. b) The lower the U-value, the better the material is as an insulator. Good insulators have a low U-value.

Page 8: GCSE Science A Unit 3 Physics P1.1-P1.2

8

c) Solar panels may contain water that is heated by radiation from the Sun. This water may then be used to heat buildings or provide domestic hot water.

d) The specific heat capacity of a substance is the amount of energy required to change the temperature of one kilogram of the substance by one degree Celsius. It indicates how much energy a substance can store.

E = m x c x 𝛳 E is energy transferred in joules, J m is mass in kilograms, kg 𝛳 is temperature change in degrees Celsius, °C c is specific heat capacity in J / kg °C

Example How much energy is required to heat 3 kg of water from 20 °C to 100 °C. The specific heat capacity of water is 4200 J/ kg°C. Solution

Using E = m x c x 𝛳 Substituting m = 3 kg c = 4200 J/ kg°C T = 100-20 = 80 °C Gives E = 3 x 4200 x 80 =

Other ways of reducing energy loss include: � replacing filament bulbs with low energy light bulbs and LED lighting

� replacing old appliances with energy efficient ones Newer appliances have an energy label. More efficient appliances are rated A. � ways in which ‘waste’ energy can be useful, eg heat exchangers.

Page 9: GCSE Science A Unit 3 Physics P1.1-P1.2

9

P1.2 Energy and efficiency Appliances transfer energy but they rarely transfer all of the energy to the place we want. We need to know the efficiency of appliances so that we can choose between them, including how cost effective they are, and try to improve them.

I can:

✓ � compare the efficiency and cost effectiveness of methods used to reduce ‘energy consumption’

� describe the energy transfers and the main energy wastages that occur with a range of appliances

� interpret and draw a Sankey diagram.

Key words Appliance Efficiency Cost effectiveness Sankey diagram

Page 10: GCSE Science A Unit 3 Physics P1.1-P1.2

10

P1.2.1 Energy transfers and efficiency

a) Energy can be transferred usefully, stored, or dissipated, but cannot be created or destroyed.

b) When energy is transferred, only part of it may be usefully transferred; the rest is ‘wasted’.

c) Wasted energy is eventually transferred to the surroundings, which become warmer. The wastedenergy becomes increasingly spread out and so becomes less useful.

d) To calculate the efficiency of a device using:

efficiency = useful energy out (x100%) total energy in

efficiency = useful power out (x100%) total power in

Sankey diagrams can be used to show efficiencies:

Page 11: GCSE Science A Unit 3 Physics P1.1-P1.2

11

P1.3 The usefulness of electrical appliances We often use electrical appliances because they transfer energy at the flick of a switch. We can calculate how much energy is transferred by an appliance and how much the appliance costs to run.

I can:

✓ � compare the advantages and disadvantages of using different electrical appliances for a particularapplication

� consider the implications of instances when electricity is not available.

Key words Appliance Transducer Dynamo Power Kilowatt-hours

Page 12: GCSE Science A Unit 3 Physics P1.1-P1.2

12

P1.3.1 Transferring electrical energy a) Examples of energy transfers that everyday electrical appliances are designed to bring about.

Name one transducer (device) that changes:

A. Sound energy to electrical energy …………………………………………….

B. Chemical energy to electrical energy …………………………………………….

C. Electrical energy to light energy …………………………………………….

D. Potential energy to kinetic energy …………………………………………….

Page 13: GCSE Science A Unit 3 Physics P1.1-P1.2

13

Draw a chain diagram to show the energy changes that occur when:

A. An electric drill is switched on

B. A Bunsen burner is ignited

C. A mass is lifted 1 metre

D. A bullet is fired from a rifle

E. A rubber ball is bounced on the floor.

b) The amount of energy an appliance transfers depends on how long the appliance is switched onand its power.

c) To calculate the amount of energy transferred from the mains using:E = P x t

E is energy transferred in kilowatt-hours, kWh P is power in kilowatts, kW t is time in hours, h

Example How much energy is transferred if a 1 kW fire is left on for 2 hours?

Solution Using E = P x t Substituting in P = 1 kW and t = 2 h gives

E = 1 x 2 = 2 kWh

d) To calculate the cost of mains electricity given the cost kilowatt-hour.If 1 kWh cost 14p.

How much does it cost to run a 1 KW fire for 2 hours?

We have already calculated the kWh above

So the cost will be 14 x 2 = 28p

This equation may also be used when: E is energy transferred in joules, J P is power in watts, W t is time in seconds, s

Page 14: GCSE Science A Unit 3 Physics P1.1-P1.2

14

GCSE questions

Q1. Marbles inside a box can be used as a model for the particles in a solid, a liquid or a

gas.

Use words from the box to complete the following sentences. Each word can be used once, more

than once or not at all.

gas liquid solid

(a) The particles in a ........................................ vibrate about fixed positions.

(b) The particles in a ............................. move at high speed in any direction.

(c) The particles in a ........................................ are arranged in a pattern.

Q2. Many people use a sleeping bag when they sleep in a tent. Sleeping bags, designed to

keep a person warm, have a fibre filling.

(i) Complete the sentence by choosing the correct words from the box.

conduction convection radiation

The fibre is designed to reduce heat transfer by ..................................... and

.......................................

(ii) Explain why the fibre is good at reducing heat loss from a person sleeping in the bag.

............................................................................................................................

............................................................................................................................

............................................................................................................................

...........................................................................................................................

Page 15: GCSE Science A Unit 3 Physics P1.1-P1.2

15

Q3. The diagram below shows a vacuum flask.

(a) Give two features of the flask which reduce heat loss by conduction.

1. ........................................................................................................

2. ........................................................................................................

(b) Give one feature of the flask which reduces heat loss by radiation.

............................................................................................................

Q4.

(a) The drawing shows water being heated

in a metal saucepan.

(i) Some energy is transferred from the hotplate to the air by infrared radiation.

What is meant by infrared radiation?

………………………........................................................................................................................

………………………........................................................................................................................

(ii) Explain, in terms of the particles in the metal, how energy is transferred through the base of

the saucepan.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

(b) Energy is transferred through the water by convection currents.

Explain what happens to cause a convection current in the water.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Page 16: GCSE Science A Unit 3 Physics P1.1-P1.2

16

Q5. (a) The diagram shows a hot water system.

(i) Explain why the boiler is below the hot water tank.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

(ii) Why is heat energy transferred from hot water in the tank to the surrounding air?

………………………........................................................................................................................

………………………........................................................................................................................

(iii) Name the process by which energy is transferred through the sides of the tank.

………………………........................................................................................................................

(iv) How may heat loss from the hot water tank be reduced?

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Page 17: GCSE Science A Unit 3 Physics P1.1-P1.2

17

(b) One way of reducing heat loss from a house is by cavity wall insulation. Foam is pumped

between the inner and outer brick walls as shown in the diagram.

How is heat loss from a house reduced by:

(i) having a cavity wall?

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

(ii) filling the cavity with foam?

………………………........................................................................................................................

………………………........................................................................................................................

Q6. The diagram shows a side view of a double-glazed window.

(a) Use each of the terms in bold to explain how heat is lost from

inside a house through the window.

conduction convection radiation

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Page 18: GCSE Science A Unit 3 Physics P1.1-P1.2

18

(b) Besides heat, state one other form of energy that passes through double-glazed windows.

………………………........................................................................................................................

(c) Explain why plastic foam cavity wall insulation cuts down energy transfer between warm

inner walls and cooler outer walls.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

(d) When it rains the walls and windows of a house get wet.

Explain how the drying process can increase the cooling of the house.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Q7. Energy consultants tell their customers how to

save money. They explain how people can reduce

energy loss from their homes.

This picture shows the percentage energy loss from

different parts of a house.

(a) Heat can be transferred through materials in

different ways.

(i) What is the main way heat is transferred around a room in a house?

………………………........................................................................................................................

(ii) What is the main way heat is transferred through the walls of a house?

………………………........................................................................................................................

Page 19: GCSE Science A Unit 3 Physics P1.1-P1.2

19

(b) Calculate the percentage energy loss through the walls of the house.

………………………........................................................................................................................

………………………........................................................................................................................

(c) Suggest the two most effective methods of reducing heat loss for this house.

1 ...................................................................................................................

2 ...................................................................................................................

Q8. An energy minister said that people could do more to conserve energy.

He advised home owners to fit insulating jackets to their hot water tanks.

(a) A home owner paid £10 to fit a hot water tank jacket. By doing this, he saved £15 a year on

his fuel bill.

How many months would it take to pay back the cost of fitting a hot water tank jacket?

......................................................................................................................

......................................................................................................................

.................................... months

(b) Modern hot water tank jackets are made of a silvered plastic bag containing glass fibre

packing.

Explain how this type of jacket reduces heat loss from the hot water tank.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Page 20: GCSE Science A Unit 3 Physics P1.1-P1.2

20

Q9. The diagrams show the cross-section of three double glazed windows.

The gap between the two sheets of glass can be filled with either air or a mixture of air and

argon.

The U-values for different types of double glazed windows, using different types of glass

X and Y, are given in the table.

(a) Which type of window, 1, 2, 3 or 4 is the least energy efficient?

........................................................................................................................

(b) Which two windows should be compared to decide if adding argon to the gap improves the

energy efficiency of the window?

........................................................................................................................

(c) A householder is going to buy new windows. The sales assistant recommends that the

householder buys windows with a 20 mm gap. These windows are much more expensive than

those with a 16 mm gap.

It is not worth the householder paying the extra cost to buy 20 mm windows rather than 16 mm

windows.

Page 21: GCSE Science A Unit 3 Physics P1.1-P1.2

21

Explain this in terms of energy efficiency.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Q10. (a) The diagram shows the average energy transferred each second by a television.

(i) Calculate the average efficiency of the television.

Show clearly how you work out your answer.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Efficiency = .................................................

(ii) Suggest one environmental reason why the average efficiency of the television should be as

high as possible.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

(iii) Suggest why the energy transferred by a television set changes while you are watching it.

………………………........................................................................................................................

………………………........................................................................................................................

Page 22: GCSE Science A Unit 3 Physics P1.1-P1.2

22

(b) The diagrams show the energy transferred each second for three different types of lamp.

For each lamp the electrical energy input each second is 100 joules.

The street lamp is the most efficient.

Explain why.

………………………........................................................................................................................

………………………........................................................................................................................

Which lamp is the least efficient?

………………………........................................................................................................................

Q11. Having more efficient electrical

appliances in our homes saves money and

can be better for the environment.

(a) We can use Sankey diagrams to

show how efficient electrical appliances

are.

This is a Sankey diagram for a small electric motor.

(i) How much of the energy supplied to the electric motor is wasted?

............................................. J/s

Page 23: GCSE Science A Unit 3 Physics P1.1-P1.2

23

(ii) Work out the percentage efficiency of the electric motor.

Show clearly how you work out your answer.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Percentage efficiency = .................................... %

(iii) Suggest an environmental reason why the percentage efficiency of the motor should be as

high as possible.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

(b) A microwave oven has a power rating of 850 W.

If the microwave oven is turned on for 6 minutes, how much energy will it use?

Show clearly how you work out your answer.

State the units in your answer.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Q12. The diagram shows what happens to each 100 joules of energy from crude oil when it is

used as petrol in a car.

The widths of the arrows show exactly how much energy is transferred in each particular way.

(a) Complete the diagram by adding the correct energy value alongside each arrow.

Page 24: GCSE Science A Unit 3 Physics P1.1-P1.2

24

(b) Calculate how efficient the car engine is at transferring the energy from petrol into useful

movement.

Show clearly how you work out your answer.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Q13. (a) The diagrams in List A show three electrical appliances. Each appliance is designed

to transfer electrical energy.

Draw one straight line from each appliance in List A to the useful output energy produced by that

appliance in List B.

Draw only three lines.

List A List B

Appliance Useful energy output

Page 25: GCSE Science A Unit 3 Physics P1.1-P1.2

25

(b) The diagram shows the energy transformations produced by a TV.

(i) Which are the useful energy outputs?

………………………........................................................................................................................

………………………........................................................................................................................

(ii) Use the information in the diagram to calculate the efficiency of the TV.

Write down the equation you use, and then show clearly how you work out your answer.

………………………........................................................................................................................

………………………........................................................................................................................

Efficiency = ................................

(iii) What eventually happens to the useful energy transferred by the TV?

………………………........................................................................................................................

………………………........................................................................................................................

Q14. 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.

(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.

Page 26: GCSE Science A Unit 3 Physics P1.1-P1.2

26

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

(b) Explain what happens to the waste energy.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Q15. The diagram shows the label from a new freezer.

(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 = £ ..............................

Page 27: GCSE Science A Unit 3 Physics P1.1-P1.2

27

(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 = £ ........................................

(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.

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

………………………........................................................................................................................

Q16. The pictures show six different household appliances.

(a) Four of the appliances, including the fan heater, are designed to transform electrical energy into

heat.

Name the other three appliances designed to transform electrical energy into heat.

1 .................................................................................................................................

2 .................................................................................................................................

3 .................................................................................................................................

Page 28: GCSE Science A Unit 3 Physics P1.1-P1.2

28

(b) Complete the following sentence using one of the words in bold.

chemical heat kinetic sound

Energy that is not usefully transformed by the fan heater is wasted as

................................................. energy.

(c) The table gives information about two different fan heaters.

Complete the following sentence by drawing a ring around the line in the box that is correct.

Fan heater L fan heater M.

Q19. The instruction booklet for a washing machine contains the following information.

(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.

....................................................................................................................................................

....................................................................................................................................................

....................................................................................................................................................

....................................................................................................................................................

Cost = ................................... pence

(b) Why does it cost more to use the washing machine on the HOT cycle than

on the COOL or the FAST cycle?

........................................................................................................................

........................................................................................................................

Page 29: GCSE Science A Unit 3 Physics P1.1-P1.2

29

Q17. (a) Each letter A, B, C, D and E represents an energy transformation.

A electrical to gravitational potential

B electrical to heat

C electrical to kinetic

D electrical to light

E electrical to sound

Match each of the following devices to the useful energy transformation that it is designed to

make.

Write the correct letter, A, B, C, D or E, in the box below the device. Use each letter once or not

at all.

(b) The bar chart shows the power of three electric kettles.

(i) What is the power of kettle Y?

...........................................................................................................................

(ii) In one week each kettle is used for a total of 30 minutes.

Which kettle costs the most to use?

...........................................................................................................................

(iii) A new ‘express boil’ kettle boils water faster than any other kettle.

Draw a fourth bar on the chart to show the possible power of an ‘express boil’ kettle.

Page 30: GCSE Science A Unit 3 Physics P1.1-P1.2

30

(c) Some friends are going on holiday. They want to be able to boil water to make their own hot

drinks. They cannot decide which to take, a travel kettle or a small portable immersion heater that can

be placed in a mug.

(i) Give one advantage of taking the travel kettle.

....................................................................................................................................................

....................................................................................................................................................

(ii) Give one advantage of taking the immersion heater.

....................................................................................................................................................

....................................................................................................................................................

Page 31: GCSE Science A Unit 3 Physics P1.1-P1.2

31

Q20. The pictures show three different types of electric heater.

(a) The ceramic heater is run on full power for 5 hours.

Use the following equation to calculate, in kilowatt-hours, the amount of energy transferred from

the mains to the heater.

energy transferred = power × time

Show clearly how you work out your answer.

....................................................................................................................................................

....................................................................................................................................................

Energy transferred = .............................. kilowatt-hours

(b) Which heater will be the most expensive to run on its highest heat setting?

....................................................................................................................................................

(c) A heater is needed for a small office. Comparing each type of heater with the other two, give

one advantage of using each type of heater in the office.

oil-filled panel heater .................................................................................................

.....................................................................................................................................

fan heater ....................................................................................................................

.....................................................................................................................................

ceramic heater .............................................................................................................

.....................................................................................................................................