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When most materials are heated they expand and this increase their volume. One example of expansion is the fitting of the starter ring gear to the flywheel. The gear is heated until it expands sufficiently to pass over the rim of the flywheel, and when it is cool the gear tries to return to its original size, this gripping the flywheel with considerable force.
All metals do not expand equally when heated through the same range of temperature, e.g. aluminium alloy expands more than cast iron; copper and brass expand more than mild steel. Gudgeon pins (hardened steel) are removed and replaced y dipping aluminium-alloy pistons in boiling or very hot water' the difference in expansion -- the piston expands more than the gudgeon pin -- makes the pin an easy push fit.
Coefficient of Expansion
A number which denotes the degree of expansion of a substance is called the coefficient of expansion of the material. There are three types of expansion namely, linear, superficial and cubical, and each has its own coefficient of expansion:
1. The coefficient of linear expansion is the increase in unit length of a material when its temperature is raised by 1 degree C. The coefficient fo linear expansion for various metals have been found by experiment and they are given in the list below.
2. The coefficient of superficial expansion is the increase in unit area of a material when its temperature id raised by 1 degree C. Its value is double that of the coefficient of linear expansion for the same material.
3. The coefficient of cubical expansion is the increase in unit volume of a material when its temperature is raised by 1 degree C. Its value in three times that of the coefficient of linear expansion for the same material.
Coefficient of Linear Expansion
Materials Per 1 deg C
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Mercury 0.000 059 9Aluminium 0.000 022 1Brass 0.000 018 9Copper 0.000 017 1Iron 0.000 011 7Cast Iron 0.000 011 2Steel 0.000 0119Invar 0.000 001 0
Taking aluminium as an example: one mm of aluminium expands 0.000 022 1 mm for 1 deg C rise in temperature. One metre of aluminium expands 0.000 022 1 metre for 1 deg C rise in temperature. If the temperature rise is doubled the expansion (increase in length) will be doubled also, e.g. one mm of aluminium will expand 0.000 022 1 multiplied by 2, equals 0.000 044 2 mm for a 2 deg C rise n temperature, and a two mm length of aluminium will also expand 0.000 022 1 multiplied by 2 for 1 deg C rise in temperature.
We are now able to calculate the increase in length (linear expansion) of a material and the following examples show the methods used. One example of cubical expansion is also given.
Example. Calculate the gap required in a piston ring to allow for expansion, under working conditions, given the following data:
Cylinder bore diameter, 60 mm
Normal temperature, 18 deg C
Working temperature, 162 deg C
Coefficient of expansion, cast iron, 0.000 011 2 per degree C
Ring circumference = 60 x mm (linear measurement)
Ring expansion = Circumference x coefficient of expansion x temperature rise
= 60 x x 0.000 011 2 x (162 --18) mm
= 0.3041 mm
Therefore the gap necessary to allow for expansion should be at least 0.3 mm. In practice, however, the cylinder expands also and the ring gap would be rather less than this figure.
Liquid and gases have no definite form, and when heated cubical expansion only takes place. The cubical coefficient of expansion (each given as per degree C) of three common fluids are:
Water, 0.000 45
Petrol, 0.002 17
Air, 0.003 65
Example. The cooling system of an engine contains exactly 9 litres of water. Before starting the engine, the temperature of the water is 15 deg C; after a run the temperature of the water is found to be 85 deg C. Calculate the volume of water lost by expansion through the overflow pipe (cubical expansion of water is 0.000 45 per 1 degree C).
Expansion of water = Volume of water x coefficient of expansion x temperature rise
= 9 x 0.000 45 x (85 -- 15) litres
= 0.2834 litres
1. By how much is the diameter of an aluminium piston increased when its temperature is raised from 4 deg C to 204 deg C? The diameter at 4 deg C is 75 mm. Coefficient of expansion for aluminium is 0.000 022 1 per degree C.
2. By how much is the length of a steel rod, 3048 mm, increased when its temperature is raised from 4 deg C to 38 deg C? The coefficient of linear expansion is 0.000 011 9.
3. a) A steel rod 2500 mm long lengthens 1.75 mm when its temperature is raised by 55 deg C. What is the coefficient of expansion of steel?
b) By how much will a steel rod shortens when its temperature falls from 120 deg
C to 10 deg C? Its original length is 3048 mm.
4. The coefficient of linear expansion of iron is 0.000 012 and that of aluminium
0.000 023. A rod of iron and a rod of aluminium are both 305 mm long at 100 deg C. What will be the difference in their length at 20 deg C?
5. A brass rod measures 900 mm at 0 deg C and increases in length by 1.65 mm
when heated to 100 deg C. What is the coefficient of linear expansion of brass per
6. A copper pipe in a heating system is 9145 mm long at the normal temperature of
15 deg C; find its length when water at a temperature of 85 deg C flows through it. Coefficient of expansion of copper per degree C = 0.000 017.
7. An iron tyre of diameter 50 cm at 15 deg C is to be shrunk on to a wheel of diameter 50.35 cm. To what temperature mist the tyre be heated so that if will slip over the wheel with a radial gap of 0.5 mm.(Coefficient of linear expansion of iron = 0.000 012/deg C)
8. A metal rod has a length of 100 cm at 200 deg C. At what temperature will its length be 99.4 cm if the coefficient of linear expansion of the material of the rod is 0.000 02/deg C.
9. A square metal plate, each side 100 cm long at 0 deg C, has a circular hole of diameter 40 cm in the middle of it. At what temperature will the sides be 101 cm long, and what will then be the diameter of the hole? (Coefficient of linear expansion of the metal = 0.000 012 5/deg C.)
10. A compound strip of brass and iron 10 cm long at 20 deg is held horizontally with the iron upper most. When heated from below with a Bunsen, the temperature of the brass is 820 deg C and of the iron 770 deg C. Calculate the difference in lengths of the iron and the brass. (Coefficient of linear expansion of brass = 0.000 019/deg C; of iron = 0.000 012/deg C.)