Matter and the particle model · Model
Temperature, particle motion and internal energy
A spark from a grinder is at a thousand degrees and it bounces off your arm without a mark. A bath at forty, barely more than body temperature, already feels properly hot. Both facts are about energy, and neither is about temperature alone.
Start here
A spark at 1000 °C and a bath at 40 °C.
A grinding wheel throws a shower of white-hot sparks against your forearm and you feel a faint tick, nothing more. A bath at 40 °C, barely more than body temperature, already feels properly hot.
Which one holds more energy?
The bath, easily — by something like a hundred million times. The spark is at about 1000 °C and the bath at 40 °C, so the spark wins on temperature by a wide margin and loses on everything else. Temperature says how much kinetic energy each particle has, on average. Internal energy is that added up over every particle there is, and a bath has an enormous number of particles while a spark has almost none. That is why the spark bounces off your arm and does nothing, while the bath, far cooler on the thermometer, holds enough to keep a whole body warm for an hour.
Every particle in every object is moving — vibrating in a solid, sliding past its neighbours in a liquid, flying about in a gas. Temperature is a measure of how much kinetic energy one particle has, on average. It says nothing whatever about how many particles there are.
Internal energy is the total: the kinetic energy of every particle in the object, plus the energy stored in the forces holding them together. It is measured in joules, and it depends on the temperature and on how much stuff there is. Two objects at the same temperature can hold wildly different internal energies.
Heating moves internal energy from the hotter object to the colder one, and it keeps going until both are at the same temperature. Which way it goes is decided by temperature; how much there is to move is decided by internal energy. Confusing the two is the commonest mistake in this part of physics, and the spark is the cleanest place to see the difference.
At the bench · four amounts of the same substance, one thermometer
Same temperature, wildly different energies.
Change a control to begin
Every one of these is water, and the slider sets all four to the same temperature. The bars are the energy each one holds — and they are nothing like each other.
Commit first. A mug and a bath are both at 60 °C. Which holds more internal energy?
How much water
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Thermometer reads
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Mass of water
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Internal energy above 0 °C
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A bathful holds
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Key fact
Temperature measures the average kinetic energy of one particle, in degrees Celsius. Internal energy is the total energy of all the particles added together, in joules. Temperature decides which way heating goes; internal energy decides how much there is to move.
Think again
“Temperature and heat are two words for the same thing.”
They are not even the same kind of quantity. Temperature is a state an object is in, measured in degrees; heating is a process — energy on the move from a hotter object to a colder one — measured in joules. An object does not contain heat. It contains internal energy, and heating is one of the ways that energy gets in or out. The everyday sentence “the heat in this room” is really about internal energy, and the confusion it creates is worth undoing carefully.
“Adding energy to something always makes it hotter.”
Not while it is changing state. Put a beaker of ice and water on a hotplate and the thermometer sits at 0 °C, minute after minute, while the energy pours in — because that energy is going into breaking the forces holding the solid together rather than into speeding the particles up. Only when the last of the ice has gone does the temperature start to climb again. The internal energy rose the whole time; the temperature did not.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Read the model
Two beakers of water are at 50 °C. One holds 100 g, the other 400 g. Which statement is right?
Rung 2 · The one that catches people
A spark from an angle grinder lands on your arm at about 1000 °C and does no harm. Why not?
Rung 3 · Explain
Explain the difference between temperature and internal energy, using a mug of tea and a swimming pool.
Rung 4 · Take it somewhere new
A storage heater holds bricks that are warmed overnight and give the energy out through the day. Explain why bricks are used rather than the same volume of air, in terms of particles and internal energy.
Key note
Temperature measures the average kinetic energy per particle, and is read in degrees Celsius. Internal energy is the total energy of every particle in an object, measured in joules, and depends on the temperature and on how much matter there is. A spark at 1000 °C holds almost no internal energy because it has almost no mass; a bath at 40 °C holds an enormous amount. Heating is energy transferred from a hotter object to a colder one, and it stops when their temperatures are equal.
Going further
Water is unusually expensive to warm up. It takes about 4200 J to raise one kilogram of it by one degree, against roughly 900 J for aluminium and 130 J for lead. That number is the specific heat capacity, and water has one of the highest of any ordinary substance — which is why it is used in radiators and cooling systems, why coastal towns have milder winters than inland ones, and why a hot water bottle stays useful for hours.
There is a floor to all this. Cool an object and its particles move less; at −273.15 °C they carry the least energy the laws of physics permit, and no further cooling is possible. That point is absolute zero, and it is why scientists usually measure temperature in kelvin, which starts there. Nothing has ever reached it, though laboratories have got within a few billionths of a degree.
Before this lesson
Connects to
- Heating and thermal equilibrium
Which way energy travels when two things at different temperatures touch — this lesson is about how much there is to travel.
- Changes of state
Where the energy goes while the temperature is not moving.
- Solids, liquids and gases
What the particles are doing in each state, before a temperature is put on it.
At GCSE this becomes
- Specific heat capacity and its required practical, specific latent heat, and internal energy as the sum of kinetic and potential stores in the particle model.
Where to next
Ask Mr Badmus AI
Muddled about when to say temperature and when to say energy?
The bench is a teaching model. Energies are calculated as mass × 4200 J/kg°C × temperature above 0 °C, using a single specific heat capacity for water and ignoring its small variation with temperature. Masses are nominal: a teaspoon 5 g, a mug 250 g, a kettleful 1.7 kg and a bathful 80 kg. The bars use a logarithmic scale so that four quantities spanning five orders of magnitude can be shown together, and 0 °C is the reference the energies are measured above rather than a reading the bench takes.
Lesson content © MrBadmusAI.