Flashcards in Thermal Expansion Deck (22)
Thermal Expansion of Solids
When a solid is heated it expands in all 3 dimensions, and increases in length, breadth and thickness.
Within normal temp ranges, a homogeneous (properties are the same in all directions) such as in iron bar, expands uniformly, therefore its expansion in any direction is proportional to the rise in temperature.
The expansion is also proportional to the length of the bar but varies depending on what the substance is made of.
Coefficient of Linear Expansion
Amount by which length of a substance expands when temp is raised by 1 degrees is called the coefficient of linear expansion of the substance.
Temp scale must be stated.
To calculate the increase in length of a body:
original length x coefficient of linear expansion x temp rise.
To find total new length, the original length must be added.
Nickel-Iron Alloy (Invar)
Invar is an alloy of iron and nickel.
Coefficient of Linear expansion of invar is 1% that of steel.
Used to make measuring rods and tapes and things that must stay the same over a range of temps.
This only applies to the particular alloy that contains 36% nickel.
Allowing for expansion in large metal structures e.g. Bridges
Allowances must be made for expansion due to large changes in temps.
Even a bridge with a span of 20m could change by 14mm between hottest and coldest temps (original length x coefficient of linear expansion x temp rise).
Allowances made by fixing one end of a bridge and putting other end on rollers or a sliding bearing so expansion and contraction can occur without exerting a side load on a fixing.
Railway lines can be laid in 45 or 60 ft with gaps in between to allow for expansion and contraction .
Modern railway lines are able to take up suspension as tension or compression in the rail, with expansion joints at distances of 800m.
Allowing for expansion in large metal structures e.g. Buildings
In buildings the change in temp is not normally so big due to internal heating.
But some expansion must be accounted for in the steel framework as to not distort the brickwork.
In a fire situation, rise in temp is great and situation could arise in which a long beam could exert sufficient side load on the top of a wall and cause a collapse.
Problems with expansion
Problems encountered with materials that are poor thermal conductors.
In a fire situation, heating the inner face of a tall brick wall will cause expansion on that face, while the outer face remains cool. This will cause leaning outwards at the top and can cause the structure to collapse.
If 2 strips of different metals of same length with different coefficients of linear expansions, placed next to each other both would heat and expand differently.
If they were strapped together throughout their length, it would create a curve. They would straighten when cooled. This is called a bimetallic strip.
If one end of a bimetallic strip is fixed, a change in temp would cause the free end to move. This movement can be used to open or close an electrical circuit to cause an alarm to actuate, or to switch off a heater.
When a bimetallic strip is used in this way it is called a thermostat.
Coefficients of Superficial and Cubical expansion of Solids.
Coefficient of superficial (area) expansion is twice the linear coefficient and that of cubical expansion is three times the linear coefficient.
Expansion depends on external dimensions of the solid and is not affected by any voids.
Cubical expansion of a hollow metal box is the same of that of a solid block of the same metal and same external volume as the box.
Thermal Expansion of Liquids-
Liquid has to be contained in a vessel, so the expansion is affected by the expansion of the vessel, therefore the apparent expansion is always less than the actual expansion.
The coefficient of cubical expansion of liquids is much greater than that of solids (with the exception of water) so the expansion of a liquid is always greater than the expansion of its vessel.
Cubical expansion of liquids example
Considering the cubical expansion coefficients of glass, mercury and alcohol.
Thermal expansion of mercury is about 8 times that of glass, and alcohol is nearly 50 times that of glass.
The coefficient of cubical expansion of steel is about 30 times less than many liquids. Due to this, a sealed container e.g. a storage tank completely full of a liquid may be a hazard in a fire situation because of the internal pressure created by expansion. Pressure relief valve will help this.
Massively helps if a vessel is not completely full.
Used in glass sprinkler heads - Sealed glass bulbs full of liquid .
These break to operate and release water from the head when they are heated to a pre determined temp.
The effect of expansion on density
Density of a substance is the ratio of its mass to its volume, an increase in temp results in a decrease in density
The volume of a given mass of a substance increases as its temp rises.
The expansion of gases-
Temperature, Pressure, Volume
The volume of a gas can be changed by altering the volume of the container as it will expand to fill all available space. If the volume is decreased, the pressure is increased.
Increased pressure is due to more collisions of the molecules of the gas, both with each other and the container walls. These collisions create more pressure.
Molecules in a liquid are closer together than in a gas, so they cannot be compressed further like gases can.
Heating a gas increases kinetic energy of the molecules, and they collide more often. Therefore the pressure increases (providing the volume is unchanged). By increasing the volume as it is heated, the pressure can be kept constant.
Temp, pressure and volume and 3 variables which change with each other when dealing with a gas.
The Gas Law
The Law of Pressures
Solid or liquids will expand with a rise in temp by an extent determined by the coefficient of cubical expansion.
But gases all expand by the same amount for the same temp rise.
Changes in volume of gas depends on changes in temp and pressure.
To study interaction between temp, pressure and volume, one of them must be kept constant to see how the other two react.
This method forms the basis of the gas laws by which the behaviour can be determined.
(Change in Pressure)
For a gas at a constant temp, the volume of a gas is inversely proportional to the pressure upon it.
If pressure is doubled, the volume is halved (provided the temperature is constant).
When a gas is compressed e.g. being pumped into a tyre, heat is generated and the valve gets warm. If the pressure of the gas is measured before the it returns to its original level, Boyle's Law doesn't hold, since the temp is not the same as it was before it was pumped in.
If V1 and P1 are initial volume and pressure, and V2 and P2 are the final volumes and pressure, then:
(Change in Temp)
The volume of a given mass of a gas at a constant pressure increases by 1/273 of its volume at 0 Degrees Celsius for every 1 degrees Celsius rise in temp.
All gases expand by 1/273 of their volume for every 1 degrees Celsius rise from 0 degrees provided the pressure remains constant.
It is essential to take the initial volume at 0 degrees Celsius.
As gases expand their density decreases. This is why hot air rises e.g. a balloon or hot fire gases.
Where V1 and T1 are the initial volume and absolute temp and V2 and T2 are final volume and final absolute temp (Kelvin Temp):
V1/T1 = V2/T2.
Volume of a given mass of gas is directly proportional to its absolute temp providing the pressure is kept constant. Volume increases as temp increases.
The Law of Pressures
(Volume kept constant)
The pressure of a given mass of a gas is directly proportional to its absolute temperature, provided that its volume is kept constant.
Concerning when volume is kept constant i.e. when a cylinder of gas has its valve closed and is heated.
P1/T1 = P2/T2
The General Gas Law
The three gas laws can be combined into a single mathematical equation:
P1V1 / T1 = P2V2 / T2
This general expression can be used for a given mass of gas when pressure, temp and volume all change.
This allows you to remember all 3 laws, just remove the quantity which is being kept constant from both sides of the equation. e.g. remove V1 and V2 from both sides (They are equal so they cancel out each other), then insert the values that you know.
This is only applicable to gases as long as they remain as gases over the temp and pressure changes. If temp and pressure is reached where there is a change of state then the laws are no longer applicable.
The Liquefication of Gases
An increase in pressure increases the boiling point of a liquid.
Many substances that are gases at normal temps and atmospheric pressure can be compressed so much that their boiling point is raised above atmospheric temperature and liquifies (e.g. propane and ammonia).
Other gases cannot be liquified at atmospheric temperature no matter how much pressure is applied. These are called permeant gases.
But if temp is lowered sufficiently it becomes possible to liquefy them by compression (e.g. methane, oxygen).
Critical Temperature and Pressure
Perfect conditions to liquefy it.
Critical pressure only works at the critical temp.
Above critical temp, no possible pressure can do it.
Critical temp-Won't liquify at this temp due to pressure alone and can turn into a vapour ?!
Go above critical temp, no amount of pressure can make it liquify. When at critical temp the pressure needed to liquify is called the critical pressure.
For a gas there is a critical temp above which it cannot be liquified by increasing pressure alone.
E.g. CO2 can be compressed to a liquid at 20 Degrees Celsius, but at 40 degrees Celsius it will remain a gas.
Its critical temp is 31.1 degrees Celsius. Below this it can be liquefied by increased pressure and it should be described as a vapour. Above this temp it cannot be liquefied and is properly described as a gas or a true gas as it is above the critical temp.
The pressure required to liquefy a vapour as its critical temp is called the critical pressure.
Liquefied Gases in Cylinders
Liquefied gases in cylinders do not obey the gas laws since below critical temp any change in pressure, temp or volume will result in liquefication of gas or evaporation of liquid.
Therefore, pressure in a cylinder of liquified gas will remain constant even as the gas is drawn off (providing temp remains the same) since more liquid will evaporate to make up for the gas drawn off.
Therefore cylinder pressure is not an indication of amount of gas in a cylinder.
A true gas will obey the gas laws and the pressure will fall as the gas is drawn off, therefore pressure in the cylinder is an indication of amount of gas it contains.
When liquefied gas is stored in cylinders, allowance must be made for expansion of liquid in case cylinder is heated beyond critical temp and liquid turns into a vapour.
This can lead to huge increase in pressure with a risk of explosion. To minimise the risk, cylinders are never completely full with liquid.
Amount of gas that can be liquefied into a cylinder is determined by its filling ratio, different from gas to gas and depends on density of the gas
Filling ratio= weight of liquified gas which may be charged / Weight of cylinder completely full of water.
Filling ratio of ammonia is 0.5, so a cylinder capable of holding 10kg of water may only be charged with 5kg of ammonia. A cylinder of same size could be charged with 12.5kg of sulphur dioxide a the filling ratio is 1.25.