School Science Lessons
2023-11-25
(UNPh23a)
Thermal expansion, liquids, solids
Contents
23.2.0 Liquid expansion caused by heat
23.3.0 Solid expansion caused by heat
23.2.0 Liquid expansion caused by heat
23.3.02 Fluid expansion
Experiments
23.2.8 Coefficient of expansion of oil
23.2.9 Coefficient of expansion of liquid in flask and U-tube
23.108 Expansion and contraction of liquids
23.113 Expansion of liquid in a thermometer
23.2.4 Expansion of water and kerosene
23.48 Freezing water expands
23.4.6 Heat water in a sealed flask
23.2.1 Liquid expansion
23.3.0 Solid expansion caused by heat
See: Expansion (Commercial).
23.3.01 Solid expansion caused by heat
23.0.0 Coefficient of thermal expansion, negative thermal expansion (NTE)
23.3.16 Compensated balance wheel of a watch
23.3.15 Motor vehicle flashing lights
23.3.031 Thermal shock, borosilicate glass
23.3.10 Trevelyan rocker
Experiments
23.105 Ball and ring, ring and plug
23.3.8 Bar breaker, the force of contraction
23.3.9 Bend glass by expansion
23.107 Bimetallic strip, compound bar, invar, thermostat
23.106 Expansion of solids when heated apparatus
23.3.12 Expansion tube
23.3.13 Expanding wire, sagging wire
23.3.11 Expanding quartz and glass
23.3.1 Expanding solids when heated
23.3.3 Expansion gauge
23.3.7 Shrink fit
23.113 Expansion of liquid in a thermometer
Experiment
Fill a flask with coloured water.
Insert a one hole stopper carrying a 30 cm length of glass tubing until the water rises 5 cm in the tubing.
Put the flask in a beaker of water.
Heat the beaker and observe the water level in the tubing.
The water rises in the tubing.
However, if you carefully observe the water level in the tubing when the heating begins, you will see that it falls slightly and then begins to rise!
It falls, because the glass in the flask starts to expand before the water inside.
When the heat energy reaches the water it expands.
So the expansion of liquid you see in a thermometer is really the expansion of liquid less the expansion of the glass tube.
23.48 Freezing water expands
Experiment
You can do this experiment at home.
Fill an ice cube tray exactly with water to make separate ice cubes.
Put the ice cube tray in the freezer.
The next day the level of the ice cubes is higher than the former level of the water.
So water expands when it freezes to form ice.
Take out some of the ice cubes and put them in water.
The ice cubes can float in water.
So when water changes to ice, it expands.
23.0.0 Coefficient of thermal expansion, negative thermal expansion (NTE)
See diagram 23.107: Bimetallic strip, compound bar, invar.
Thermal expansion
Most substance expand when heated as distances between atoms increase.
The coefficient of thermal expansion characterizes the expansion of various bodies as the degree of expansion divided by the change in temperature.
The coefficient of linear thermal expansion is the ratio of the change in length per degree K to the length at 273 K.
The coefficient of volume expansion is about three times the linear coefficient.
Negative thermal expansion
Negative thermal expansion (NTE) (not called "thermal contraction"), occurs in some substances, e.g. zirconium tungstate (ZrW2O8), zirconium, vanadate (ZrV2O7), scandium trifluoride (ScF3), forms of silicon between 18 and 120 Kelvin, and rubber bands.
Glass-ceramic cooktops are non-porous mixtures of MgO, Al2O3, SiO2 glass with positive coefficient of thermal expansion and crystals with negative coefficient of thermal expansion, a material that experiences no thermal shock.
Water
The coefficient of thermal expansion of water drops to zero as it is cooled to 4oC (3.983oC), then becomes negative.
Water has a maximum density at this temperature.
In sub-zero temperatures, the ice on the surface of a pond may have a lower temperature than the water underneath it, so fish can survive below the ice.
Tooth fillings
If tooth fillings had the same coefficient of thermal expansion as tooth they would not expand to cause toothache when drinking a very hot cup of tea.
Bimetallic strips
Materials with compensating coefficients of thermal expansion are used in bimetallic strips and invar.
23.2.1 Expansion and contraction of liquids, thermal expansion of different liquids
See diagram 23.4.2: Heated liquids expand.
Experiments
1. Use two identical small flasks with one hole stoppers and tubes passing though into the liquid.
Fill the bottles with different liquids.
Put the bottles in a container of hot water.
The different rise of liquids inside the tubes shows the difference in expansion of the liquids.
2. Put some coloured water in a small bottle or flask fitted with a one hole stopper and glass tube that extends into the bottle.
Heat the bottle.
The water level initially falls as the bottle expands then rises as the liquid is warmed and expands.
Cool the bottle.
Depending on the rate of cooling the liquid will initially rise as the bottle contracts and then drop as the liquid cools and contracts.
This experiment shows the principle of the liquid in glass thermometer.
Note that the water level drops at first when you begin the heating and then it rises, because the glass starts to expand before the water inside.
If a long tube filled with red water is immersed in a boiling water bath, the level of the red water will drop before rising.
3. Use two identical small plastic bottles.
Insert a thin long glass tube into the stopper of each bottle.
Fill each bottle with different liquids, e.g. water and alcohol, or vinegar and machine oil.
Place the two bottles simultaneously into a beaker of hot water.
Observe the difference between the heights increased of liquids in the two glass tubes.
At the same temperature, the expansion of different liquids is different, the increases of their volumes are different.
4. Fill a conical flask full of coloured water and plug its mouth with a stopper with a glass tube inserted in it.
Dip the glass tube into the water so that the height of the water in the glass tube is 30 mm.
Place the flask in a large beaker.
Pour hot water on the surface of the flask.
Observe the change in height of the water column at the glass tube. Pour cold water on the surface of the flask.
Observe the change in height of the water column in the glass tube again.
23.2.4 Expansion of water and kerosene
Experiments
1. Note the level of water in a vertical tube at room temperature.
Heat the water in the beaker until it is a constant 20oC above the previous room temperature and note the level water in the tube again.
2. Repeat the experiment using kerosene instead of water.
Be careful! Kerosene is inflammable!.
So heat the beaker with an electric hot plate.
Compare the expansion of kerosene with the expansion of water.
23.2.8 Coefficient of expansion of oil
Experiment
Use a hydrometer to measure the density of olive oil as it cools.
23.2.9 Coefficient of expansion of liquid in flask and U-tube
Experiments
1. Flask
A flask is filled with a liquid such that the upper level of liquid is in the neck of the flask and can be marked.
When the flask is heated, the liquid expands and the new level of liquid in the neck of the flask can be marked.
However, this difference of levels does not represent the true expansion of the liquid, because the glass in the flask has also expanded.
The apparent increase in volume of the liquid is the difference between the true increase in volume and the increase in volume of the flask.
Observe the exact position of the mercury meniscus in a mercury-in-glass thermometer.
Plunge the bulb of the thermometer into boiling water and observe the immediate drop in level of the mercury meniscus cause by the expansion of the glass.
Later, the level of the meniscus rise as heat is conducted into the mercury.
2. U-tube
Find the true coefficient of expansion of a liquid, by using the method balancing columns in a U-tube.
Put into a U-tube mercury or any other liquid that does not dissolve in the liquid to be tested.
Pour the liquid to be tested into both arms of the U-tube so that the level of mercury is the same in both arms.
Immerse both arms of the U-tube in a liquid at temperature t1 and not the height h1 of the columns above the mercury.
Immerse both arms of the U-tube in a liquid at temperature 1, higher than t1, and not the height h2 of the columns above the mercury.
23.3.01 Solid expansion
See: Linear expansion (Commercial).
See diagram 23.4.7: Expansion of a solid.
Expansion due to heat, thermal expansion, expansivity, coefficient of expansion
Most bodies increase their volume upon heating under normal pressure.
Solids retain their shape during temperature variations,.so distinguish between linear expansion, area expansion and volume expansion (cubic expansion).
Applications of solid expansion include shrink fitting, riveting, expansion gap, expansion roller, bimetallic strip, fire alarm, thermostat.
Put the cover on the pot before heating the pot, because the pot will expand on heating and then you cannot put the top on the pot.
Linear expansion
The length of a solid changes with temperature.
The coefficient of linear expansion, α, is the fraction by which the length at 0oC changes per oC change in temperature.
For example, for Aluminium, α = 23 × 10-6, but most tables just show Aluminium = 23, Copper 16.7, Iron 11.8, Glass 8.5.
If a solid at temperature t1, width length L1, expands at temperature t2 to length L2, then L2 =L1 [1 + α (t2 - t1)], OR
L = Lo (1 + α T), where α = the coefficient of linear expansion, L = final length, Lo = original length, T = change in temperature,
Surface expansion (superficial expansion, area expansion)
Similarly A2 = A1 [1 + 2 α (t2 -t1)], OR
A = Ao (1+2 α T)
α A = 1 / A × dA / dT, where A = area and dA / dT is the rate of change of that area per unit change in temperature.
Surface expansion has been likened to expansion of a photographic print.
Cubic expansion
V2 = V1 [1 + 3 α ([t2 - t1)]
The coefficient of cubic expansion for a solid, is about three times the coefficient of linear expansion.
A cube of edge 1 cm at 0oC and volume 1 cc would become a cube of edge (1+ α ) cm at 1oC,
so its volume would become (1 + α )3 = (1 + 3x +3x2 + α3 ) cc.
However, for solids, α is very small, so x2 and x3 are negligible, hence the formula V2 = V1 [1 + 3 α ([t2 - t1)].
23.3.03 Thermal shock, borosilicate glass
Thermal shock is differential expansion where at places on a material stress expansion causes a crack to form and the structure to fail.
Thermal shock can often be avoided by changing temperature more slowly, i.e. reducing the thermal gradient, and during manufacture, reducing the coefficient of thermal expansion, and reducing the Young's modulus.
Borosilicate glass has a coefficient of thermal expansion less than any other glass, so is used in test-tubes.
Experiment
Be careful! Turn on the electricity to a light bulb.
Turn off the electric power then immediately spray water on the hot light bulb.
23.3.02 Fluid expansion, coefficient of volume change, thermal expansion of water
All of the above formula are applicable only if α has a small value and do not apply to substances where α changes with temperature.
When a volume change with temperature occurs, the fraction by which he volume at 0oC changes per oC is the coefficient of volume change, e.g. mercury = 180 × 10-6, air = 3400 × 10-6.
Liquids generally increase in volume as the temperature increases and have coefficients of cubic expansion about 10 times that of solids.
Water is an exception, because as you heat water from 0oC, it contracts rather than expands.
At 4oC, water occupies its smallest volume, i.e. it has the highest density.
So water obeys the general laws of thermal expansion, except in the temperature interval from 0oC to 4oC.
The cubic expansion formula does not apply to expansion of gases, because all gases expand by 1/273 of their volume at 0oC as in Charles's law.
For expansion of gases, you must use Charles's law (The law of volumes):
The volume of an ideal gas at constant pressure is directly proportional to the absolute temperature.
Air, and most other gases at atmospheric pressure, have a coefficient of cubic expansion of 0.0034 (oC)-1.
23.3.1 Expanding solids when heated
See diagram 23.106: Expansion of solid A = copper tubing, B = clamp, C = bicycle spoke roller, D = straw.
Experiments
1. To show and compare thermal expansion of different metals.
The expansion apparatus consists of a cast iron base with two vertical supports that hold the metal expansion rod.
The pointer is zeroed by the adjusting screw illustrated and the burners lighted beneath the rod.
Use aluminium, brass, copper and mild steel expansion rods.
Expansion of the rod causes deflection of the pointer and this deflection may be compared for the different metals for the same time interval.
2. Use a 2 metre piece of stout copper tubing.
Put it on a table and fix one end by a clamp.
Underneath the other end put a bicycle spoke to act as a roller.
A drinking straw fixed to the roller by wax will show any movement of the rod resting on it.
Blow steadily down the tube between the fixed end and the middle.
This arrangement detects the expansion of the tube caused by the hot breath.
Pass steam through the tube, and note the motion of the pointer.
Repeat the experiment with different types of tubing.
3. Heat a 60 cm copper rod for five minutes with a Bunsen burner.
Note the movement of the pointer.
The rod rests on a knitting needle so when the rod moves it rolls the needle.
If the expanding rod caused the needle to do one complete turn of 360 degrees, the hot copper rod has expanded a distance equal to the circumference of the knitting needle.
23.3.3 Expansion gauge
See: Bar and gauge.
See diagram 23.4.10: Expansion gauge
Engineers use expansion gauges to check whether metal parts are no larger than a certain size.
23.3.7 Shrink fit
Experiments
Heat a brass ring and slip it onto a slightly tapered steel bar.
23.3.8 Bar breaker, the force of contraction
See: Bar and Gauge (Commercial).
Experiments
1. Heat an iron bar then tighten it in a yoke so it breaks a cast iron bar when the bar cools.
2. Bar breaker
Construct a strong iron bar so that it rests in two yokes on a cast iron base.
Pin the bar on one end by a thin cast iron pin, and thread it on the other end so that it can be tightened.
Heat the bar with the gas jets located directly beneath the bar.
Tighten the bar as it is heated.
After the bar is fully tightened, dowse it with water.
As the bar contracts the forces present are large enough to snap the cast iron pin.
There is a delay between initial cooling and fracture of up to 30 seconds.
23.3.9 Bend glass by expansion
Experiments
Heat one edge of a strip of plate glass with a Bunsen burner to cause the glass to bend towards the cooler side.
23.3.10 Trevelyan rocker
See diagram: Trevelyan rocker.
The Trevelyan rocker is a brass or copper bar and an extension.
The brass bar has an S-shaped cross-section so that the bottom surface has two parallel knife edges.
Experiments
Heat the Trevelyan rocker and place the brass bar on a cold lead block with the end of the extension resting on the bench.
The rocker starts to vibrate due to the rapid expansion of the lead causing the rocker to tip from edge to edge and emit a musical note.
Press on the rocker with a pencil point to change the pitch of the note.
The action is related to other rockers, e.g. the "celt" or rattle back.
23.3.11 Expanding quartz and glass
Experiments
Heat both quartz and glass tubes with a high temperature torch and plunge into water.
Heat a piece of quartz tube and quench it in water. Try the same thing with Pyrex and soft glass.
23.3.12 Expansion tube
See diagram 23.4.7: Expansion of a solid.
Experiments
Pass steam through an aluminium tube with a dial indicator to show the change in length.
One end of a tube rests on a needle attached to a pointer that moves as the tube is heated.
23.3.13 Expanding wire, sagging wire
Experiments
Heat electrically a long iron wire or nichrome wire with a small weight hanging at the midpoint and see it sag.
Pass one end of a heated wire is passed over a pulley to a weight.
The pulley has a pointer attached.
23.3.15 Motor vehicle flashing lights
32.5.9.2 Flashing lamp direction indicators
Flashing lamp direction indicators current heats the hot wire, so it elongates and allows the armature assisted by its spring to move towards the
iron core and close the contacts.
Blinking lights on cars use a small unit containing is a bimetallic strip that heats up as current flows through it.
The strip bends and opens the circuit.
On cooling, the strip straightens and closes the circuit.
You can adjust the timing of the cycle with a screwdriver.
23.3.16 Compensated balance wheel of a watch
See diagram 23.107: Compensated balance wheel of a watch.
Examine the compensated balance wheel in a watch.
As the temperature rises, the radius arm of the balance wheel expands to increase the moment of inertia about the axis and increase the period.
The increasing temperature also reduces the elasticity of the hair spring to also increases the period.
To compensate for these effects, the balance wheel is made of two strips of dissimilar metals fastened together, bimetallic strips, so that the metal with the smaller coefficient of expansion is on the inner side of the bimetallic strip.
When the temperature increases, the radius of curvature of the bimetallic strip decreases, because of the lesser increase in length of the inside strip and P and Q are fixed, so R and S move in towards the axis, the moment of inertia of the balance wheel is lessened and the corresponding decrease in period compensates exactly for the increase in period caused by the change in elasticity.
23.4.6 Heat water in a sealed flask
See diagram 23.4.6: Heat water in a sealed flask
1. Fill the flask of some cold water of height 1-2 cm.
Seal the mouth of the flask with a one hole rubber stopper.
Insert a straight capillary through the stopper so that the lower end of the capillary enters the water and is about 1-2 mm from the bottom of the flask.
The upper end of the capillary remains outside the flask.
Heat the coloured water in the beaker to the temperature of 80oC more.
Place the flask into the hot water in the beaker to heat the water in the flask to 70oC.
During heating, tightly press the mouth of the flask with your hand to seal the air in the flask.
After 2 minutes, suddenly take your hand off the mouth of the flask and observe a stream of water spurting out of the upper end of the capillary tube.
2. Place a wet coin on the upper end of the capillary tube.
It will move up and down gently to produce some vibration sound.
When you heated the air in the flask, its volume did not increase, because you sealed the flask with your hand.
So the air pressure increased and a stream of water current spurted out of the upper end of the capillary tube when you take your hand off the mouth of the flask.
23.105 Ball and ring, ring and plug
Ball and ring, (Commercial).
See diagram 23.105: Ring and plug.
See diagram 23.105A: Ball and ring.
Experiments
1. The experiment demonstrates the diameter expansion of metal caused by heat.
At room temperature a ball that is slightly larger than the ring will not pass through it.
Heat the ring over the Bunsen burner.
The ball can now pass through the ring.
2. The apparatus consists of a ball and ring constructed so that at room temperature the ball just passes through the ring.
On heating the ball in the bunsen flame, expansion is demonstrated by the ball being unable to pass through the ring.
3. The apparatus consists of a heavy metal ball that at room temperature just passes through a hole in the base plate of the support.
Expansion is demonstrated by heating the ball in the bunsen flame, whereupon the ball is unable to pass through the hole.
4. Use a large metal screw and a screw-eye through which the head of the screw just passes.
Alternatively, use a metal ball that just passes through a metal ring, or a bar that will just pass through a gauge.
Attach the screw and screw eye into the ends of a stick.
Hold the stick to heat the head of the screw in a burner flame.
Try to pass the screw through the screw eye.
The screw cannot pass, because of expansion caused by heating.
Keep the screw hot and heat the screw eye in the flame simultaneously.
Now the screw head can pass through the screw eye.
Keep the screw head in the flame and cool the screw eye in cold water.
The screw head cannot pass through the screw eye.
5. If you cannot open a glass jar with a metal screw top, hold the jar upside down so that the metal screw top is touching hot water.
The metal screw top expands more than the glass and you can open the glass jar.
23.106 Expansion of solids when heated apparatus
See diagram 23.106: Expansion of a solid when heated
Experiments
Use a 2 m piece of stout copper tubing, A.
Put it on a table and fix one end with a clamp, B.
Underneath the other end put a bicycle spoke to act as a roller, C.
Fix a drinking straw to the roller by wax to show any movement of the rod resting on it, D.
Blow steadily down the tube between the fixed end and the middle.
This arrangement detects the expansion of the tube caused by the hot breath.
Pass steam through the tube and note the motion of the pointer.
Repeat the experiment with different types of tubing.
23.107 Bimetallic strip, compound bar, invar, thermostat
See: Compound bar, (Commercial).
See diagram 23.107: Bimetallic strip 1, compound bar, invar
See diagram 23.107a: Bimetallic strip 2.
Coefficient of liner expansion of brass = 19 × 10-6 K-1 at 20oC.
Coefficient of liner expansion of invar steel = 1.2 × 10-6 K-1 at 20oC.
"Invar" is trade name for an alloy composed of iron 63.8%, nickel 36%, carbon 0.2%.
"Invar" is abbreviation of "invariable".
It is used in surveyors' measuring tapes, pendulums, and tuning forks.
Bimetallic strips are used to switch thermostats and fire alarms on or off when a small bimetallic strip acts as a switch by bending away from an electrical contact when heated.
Experiments
1. The experiment demonstrates the unequal expansion of different metals.
Strips of dissimilar metals bonded together bend when heated.
Use a bimetallic strip with brass on one side and steel on the other side.
When this strip heated over a Bunsen burner, the strip curves toward the steel side.
When cooled in liquid nitrogen, the strip curves toward the brass side.
The bimetallic strip suffers appreciable curvature within a few seconds of being placed in the flame of the bunsen burner.
Leave the bimetallic strip in a container of liquid nitrogen.
The bimetallic strip curves towards the brass side, because the brass contracts more.
2. A pair of iron and brass strips riveted together bends when heated, because of the difference of expansion of the two metals.
The strip curves towards the steel side, because the brass expands more.
Mount a pointer on the end of a bimetallic strip.
3. Use two 25 cm strips of brass and invar steel welded together as a bimetallic strip.
Make holes in the metal strips with a nail and fix small tacks as rivets.
Fasten the strips together by cutting them with projections at equal intervals and bend the projections over to interlock.
The strip curves towards the steel side, because the brass expands more.
23.108 Expansion and contraction of liquids
See diagram 23.108: Expansion and contraction of liquids.
See diagram 4.6: Expansion and contraction of liquids 1.
See diagram 4.7: Expansion and contraction of liquids 2.
Experiments
1. Fit a flask with a one-hole stopper and a 30 cm length of glass tubing that extends into the flask.
Add coloured water to the flask so that it extends 5 cm up the glass tubing.
Slowly heat the flask while carefully watching the level of coloured water in the glass tubing.
When you heat the flask, the water level initially falls as the glass in the flask expands then rises as the water expands.
Cool the flask under the tap.
The level of coloured water in the glass tubing first rises as the glass in the flask contracts then drops as the coloured water cools and contracts.
So the expansion of liquid you see in a thermometer is really the expansion of liquid less the expansion of the glass tube.
2. Use two identical small bottles fitted with one-hole stoppers and glass tubing passing though into the bottles.
Fill the bottles with different liquids.
Put the bottles in a container of hot water.
The different rise of liquids inside the glass tubing shows the difference in expansion of the different liquids.
3. Place some coloured water in a flask.
Insert a one-hole stopper and glass tube so that it extends downward into the fluid and upward.
Pour warm water over the flask and the coloured water rises in the tube.
Pour cold water and the coloured water drops inside the tube.