IMAT Physics · Heat and Thermodynamics

Temperature, Heat and How Heat Moves

Temperature measures how hot a body is; heat is energy that flows because of a temperature difference, by conduction, convection or radiation.

All Heat and Thermodynamics notes

Why this matters

No past question has asked about temperature scales, expansion or heat transfer on their own. Every gas and calorimetry question in the chapter needs kelvin, though, and a calorimetry question in 2012 used thermal conductivity as a distractor.

Concept 1 of 3: Temperature, heat and the Kelvin scale

The particles of every body jiggle about. Temperature tells you how energetic that jiggling is on average. Put a hot body against a cold one and energy flows from hot to cold until both reach the same temperature; that flowing energy is heat. The Kelvin scale starts at absolute zero, where the jiggling would stop, so a doubled kelvin temperature really means double the average energy.

Definition

Temperature measures the average kinetic energy of the particles. It is not an amount of energy.
Heat $Q$ is energy transferred because of a temperature difference, always from hotter to colder. It is measured in joules.
Internal energy is the total kinetic and potential energy of all the particles in a body. A bath at 40 °C holds more internal energy than a cup at 80 °C.
Two bodies in contact are in thermal equilibrium when they are at the same temperature and no net heat flows. If A and B are each in equilibrium with C, they are in equilibrium with each other (the zeroth law), which is what lets a thermometer work.
Absolute zero is $0\ \text{K} = -273.15\ ^\circ\text{C}$ . IMAT usually rounds to 273.
One kelvin and one degree Celsius are the same size, so a temperature change has the same number in both scales.

Celsius to kelvin

T\,(\text{K}) = \theta\,(^\circ\text{C}) + 273

$T$ absolute temperature, in K
$\theta$ temperature in degrees Celsius

Worked example

Normal body temperature is 37 °C and liquid nitrogen boils at 77 K. Write each in the other scale. A patient's temperature then rises from 37 °C to 39 °C: what is the rise in kelvin?

Practice this conceptself-check · 4 quick reps

A temperature change is not converted by adding 273

Adding 273 converts a temperature reading. A difference of 50 °C is a difference of 50 K, because the two scales have the same step size. Options that add 273 to a temperature rise are wrong.

Heat and temperature are different quantities

Temperature is an average per particle; heat is energy that moves. A large cool lake holds far more internal energy than a small hot spark. Statements treating a body as containing heat, or temperature as an amount of energy, are wrong.

Concept 2 of 3: Heat transfer: conduction, convection and radiation

Energy can get from hot to cold in three ways. Particles can pass it hand to hand to their neighbours, warm fluid can carry it bodily by flowing, or it can travel as electromagnetic waves with no matter at all. Knowing which needs a medium answers most questions on this topic.

Definition

Conduction: energy passes from particle to particle by collisions. In metals free electrons carry it fast, so metals are good conductors; still air, wool and plastics are poor ones (insulators).
The rate of conduction through a slab grows with its area, its thermal conductivity and the temperature difference, and falls with its thickness.
Convection: a heated fluid expands, becomes less dense and rises, while cooler, denser fluid sinks to take its place. It cannot happen in a solid.
Radiation: all bodies emit infrared radiation, more strongly the hotter they are. It needs no medium. Matt black surfaces absorb and emit it best; shiny, light surfaces reflect it.

Mechanism	How the energy moves	Needs a medium?	Everyday example
Conduction	Vibrating particles and free electrons pass energy to neighbours	Yes; works best in solids, especially metals	The handle of a metal pan getting hot
Convection	Warm, less dense fluid rises and cooler fluid sinks, forming a current	Yes; only liquids and gases	Warm air rising above a radiator
Radiation	Electromagnetic waves, mainly infrared	No; it crosses a vacuum	Sunlight warming the Earth through space

Practice this conceptself-check · 4 quick reps

Feeling colder does not mean a lower temperature

Objects left in the same room reach the same temperature. Metal feels colder than wood because it conducts energy out of your skin faster, not because it is cooler.

Concept 3 of 3: Thermal expansion of solids and liquids

Warmer particles vibrate with larger swings, so on average they sit a little further apart. Every length of a solid grows by a small fixed fraction for each kelvin. That is why bridges have expansion joints and why a thermometer liquid climbs its tube.

Definition

Linear expansion: a rod of length $L_0$ heated by $\Delta T$ grows by $\Delta L = \alpha L_0 \Delta T$ , where $\alpha$ is the coefficient of linear expansion (unit $\text{K}^{-1}$ ).
Volume expansion: $\Delta V = \beta V_0 \Delta T$ . For a solid, $\beta \approx 3\alpha$ . Liquids expand more than solids.
As a body expands its mass is unchanged, so its density falls.
Water is an exception: from 0 °C to 4 °C it contracts when heated, so it is densest at about 4 °C. Ice floats and lakes freeze from the top down.

Linear expansion

\Delta L = \alpha L_0 \Delta T

$\Delta L$ increase in length, in m
$\alpha$ coefficient of linear expansion, in K⁻¹
$L_0$ original length, in m
$\Delta T$ temperature rise, in K (or °C)

Worked example

A steel rail is 25 m long at 10 °C. Steel has

\alpha = 1.2 \times 10^{-5}\ \text{K}^{-1}

. How much longer is the rail on a day at 40 °C?

Practice this conceptself-check · 4 quick reps

Water does not always expand when heated

Between 0 °C and 4 °C water contracts as it warms, and it is densest at about 4 °C. Options claiming every liquid expands on heating at every temperature, or that water is densest at 0 °C, are wrong.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Temperature, heat and the Kelvin scale
Celsius to kelvin
$T\,(\text{K}) = \theta\,(^\circ\text{C}) + 273$
Thermal expansion of solids and liquids
Linear expansion
$\Delta L = \alpha L_0 \Delta T$

Reference tables (1)

Heat transfer: conduction, convection and radiation3 rows

Mechanism	How the energy moves	Needs a medium?	Everyday example
Conduction	Vibrating particles and free electrons pass energy to neighbours	Yes; works best in solids, especially metals	The handle of a metal pan getting hot
Convection	Warm, less dense fluid rises and cooler fluid sinks, forming a current	Yes; only liquids and gases	Warm air rising above a radiator
Radiation	Electromagnetic waves, mainly infrared	No; it crosses a vacuum	Sunlight warming the Earth through space

Watch out for (4)

A temperature change is not converted by adding 273
→ Temperature, heat and the Kelvin scale
Heat and temperature are different quantities
→ Temperature, heat and the Kelvin scale
Feeling colder does not mean a lower temperature
→ Heat transfer: conduction, convection and radiation
Water does not always expand when heated
→ Thermal expansion of solids and liquids

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