doPhysics · Thermal Physics 1
Temperature and Thermal Expansion
What temperature is and how it is measured, from two fixed points to the gas thermometer. Why solids grow when heated, how liquids and water behave, and the thermostats, clocks and rails that depend on expansion.
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Why this chapter
Why this chapter exists
Mechanics followed bodies that move as a whole. Now we look inside them, at the jiggling of their atoms, and the first thing we meet is temperature. This chapter gives temperature a precise meaning and a number, and shows how thermometers of glass, gas, platinum and light measure it. Then it follows the most visible effect of a change in temperature: things grow when heated. One small coefficient explains the gaps between rails, the click of an iron and the slow running of a warm clock. Water's odd behaviour explains why fish survive under a frozen lake.
You will learn
By the end of this chapter you will
- Explain thermal equilibrium, state the zeroth law, and tell heat from temperature and internal energy.
- Build a temperature scale from two fixed points, and convert between Celsius, Fahrenheit, Kelvin and any arbitrary scale.
- Correct the reading of a faulty thermometer and find the one temperature at which it is right.
- Explain how the gas, platinum resistance, thermocouple, clinical and infrared thermometers work, and why the gas thermometer is the standard.
- Explain thermal expansion from the lopsided pull between atoms, and use \(\Delta L = L\alpha\,\Delta T\), \(\beta = 2\alpha\) and \(\gamma = 3\alpha\), including holes and cavities.
- Separate the real and apparent expansion of a liquid, and find how density and upthrust change with temperature.
- Explain the anomalous expansion of water and why a lake freezes from the top.
- Work out the bend of a bimetallic strip and the errors of a warm pendulum clock and a warm steel rule; recall thermal stress.
Before you begin
Before you begin
From Mechanics you should know energy and the work-energy theorem, and the shape of a potential energy well from the chapter on potential energy. From Fluids you should know density and Archimedes' principle. From Elasticity you should know stress, strain and Young's modulus. You should be able to use the approximation \((1 + x)^n \approx 1 + nx\) for small \(x\).
Lessons
1
Temperature and Thermal Equilibrium
Two bodies in contact exchange heat until one property of theirs becomes equal. That property is temperature, the zeroth law says it is well defined, and two fixed points turn any steady property into a scale.
Thermal equilibrium and temperatureHeat is energy in transitA scale from two fixed points
2
Scales, Conversions and Faulty Thermometers
Celsius, Fahrenheit and Kelvin describe one temperature with different numbers. A gas at constant volume points to an absolute zero, any scale with two fixed points converts to any other, and a faulty thermometer is honest at exactly one temperature.
Celsius fahrenheit and kelvinAbsolute zeroArbitrary scalesFaulty thermometers
3
How Thermometers Work
Any property that changes steadily and repeatably with temperature can make a thermometer. The constant-volume gas thermometer is the standard, fixed by the triple point of water; platinum wires, thermocouples, clinical thermometers and infrared guns each suit their own range.
Thermometric propertiesConstant volume gas thermometerResistance and other thermometers
4
Why Solids Expand
The pull between atoms is lopsided, so a hotter atom swings further outward and the solid grows. A rod lengthens by \(L\alpha\Delta T\), an area grows twice as fast and a volume three times, and a hole grows as if it were made of the metal around it.
Why solids expandLinear expansionArea and volume expansionHoles expand too
5
Liquids, Density and the Strange Case of Water
A liquid is always held in a vessel that expands too, so what we see is its apparent expansion. Warming lowers density and changes the upthrust on a body. Water is the exception, densest at 4 °C, and so a lake freezes from the top.
Real and apparent expansionDensity upthrust and temperatureAnomalous expansion of water
6
Expansion at Work
Two metals bonded together bend when heated, and the bend runs the thermostat of an electric iron. A warm pendulum clock runs slow, a warm steel rule reads short, and a rod that cannot expand develops thermal stress.
Bimetallic stripPendulum clocks and temperatureScale readings and temperatureWhen expansion is blocked
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%The Workbook
Questions to solve on paper, marked by you.
Glossary
The key words of this chapter, with the meaning this chapter gives them.
- absolute zero
- The lowest possible temperature, −273.15 °C or 0 K, where the pressure of a gas at constant volume would fall to zero. No body can be cooled below it.
- anomalous expansion of water
- The contraction of water as it warms from 0 °C to 4 °C, which makes water densest at 4 °C. It is why lakes freeze from the top.
- apparent expansion
- The increase in the volume of a liquid as seen against the marks of its vessel, which expands too: \(\gamma_{\text{app}} = \gamma_{\text{real}} - \gamma_{\text{vessel}}\).
- bimetallic strip
- Two strips of different metals bonded face to face. When heated it bends, with the metal that expands more on the outside of the curve.
- coefficient of area expansion
- The fractional increase in area per kelvin, \(\beta = \Delta A/(A\Delta T)\). For an isotropic solid \(\beta = 2\alpha\).
- coefficient of linear expansion
- The fractional increase in length per kelvin, \(\alpha = \Delta L/(L\Delta T)\). For steel it is \(1.2 \times 10^{-5}\,\text{K}^{-1}\).
- coefficient of volume expansion
- The fractional increase in volume per kelvin, \(\gamma = \Delta V/(V\Delta T)\). For an isotropic solid \(\gamma = 3\alpha\); for a liquid it is the only coefficient.
- constant-volume gas thermometer
- A thermometer that holds a gas at a fixed volume and measures its pressure, which is proportional to the absolute temperature. At low pressure all gases agree, so it is the standard.
- fixed point
- A state of a substance that always occurs at the same temperature, such as melting ice at one atmosphere, used to mark a temperature scale.
- heat
- Energy transferred from one body to another because of a difference in their temperatures. It is measured in joules, and it is always a transfer, never something a body holds.
- ice point
- The temperature of pure ice melting under a pressure of one atmosphere: 0 °C, 32 °F or 273.15 K.
- internal energy
- The total energy of the molecules of a body: the kinetic energy of their random motion and the potential energy of their bonds. Heat flowing in raises it.
- isotropic
- Having the same properties in every direction. An isotropic solid expands by the same fraction along every line.
- Kelvin scale
- The absolute scale of temperature. Its zero is absolute zero and its degree, the kelvin, equals the Celsius degree, so \(T = t + 273.15\).
- platinum resistance thermometer
- A thermometer that measures the resistance of a pure platinum wire, which rises almost linearly with temperature. It is accurate and works from about −200 °C to over 600 °C.
- real expansion
- The true increase in the volume of a liquid when it is heated, whatever vessel holds it.
- steam point
- The temperature of pure water boiling under a pressure of one atmosphere: 100 °C, 212 °F or 373.15 K.
- temperature
- The property that decides the direction of heat flow between two bodies in contact: heat flows from the higher temperature to the lower. Bodies at the same temperature are in thermal equilibrium.
- temperature coefficient of resistance
- The fractional change in the resistance of a wire per degree, the \(\alpha\) in \(R_t = R_0(1 + \alpha t)\). For platinum it is about 0.00385 per °C.
- thermal equilibrium
- The state of two bodies in contact when no net energy flows between them. Their temperatures are then equal.
- thermal stress
- The stress in a body whose thermal expansion is blocked. For a rod held between rigid supports it is \(Y\alpha\Delta T\), as found in Elasticity.
- thermocouple
- Two wires of different metals joined at two junctions. An emf appears in the loop when the junctions are at different temperatures, so it can read temperature, even in a furnace.
- thermometric property
- A property that changes steadily and repeatably with temperature, one value for one temperature. Examples are the length of a mercury column and the resistance of a wire.
- thermostat
- A device that switches a heater or a cooler off and on to keep a temperature near a set value. Many use the bending of a bimetallic strip.
- triple point of water
- The single state in which ice, liquid water and water vapour exist together, at 611 Pa. Its temperature is defined as exactly 273.16 K.
- zeroth law of thermodynamics
- If two bodies are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. It is what makes a thermometer's reading meaningful.