K326 / K327 / 2027
Kinetic particle model of matter overview

Topic 2 of 3

Temperature and internal energy

A rise in temperature corresponds to an increase in the average kinetic energy associated with the particles' random motion.

Kinetic energy is associated with motion. The particle model concerns random motion within a substance, including vibration in a solid. It is different from the whole object travelling across a room.

Consider the same gas first at 20°C and then at 50°C. In the warmer sample, the particles have greater average random kinetic energy. Their sizes and number do not increase just because the temperature rises.

Same gas, different temperatures

The particle count, symbol size and gas state are unchanged. The warmer sample has greater average random kinetic energy.

Blue arrows show particle motion. Lengths give a qualitative indication of speed; they do not give a numerical speed or temperature ratio.

20 °C

Gas at 20 degrees CelsiusTwelve equal-size particles are spread through a container of unchanged volume. Their blue motion arrows have varied directions and lengths. The particles at 20 degrees Celsius are already moving. Arrow lengths are qualitative; these are model snapshots, not measurements or tracked particles.

50 °C

Gas at 50 degrees CelsiusTwelve equal-size particles are spread through a container of unchanged volume. Their blue motion arrows have varied directions and lengths. At 50 degrees Celsius, the typical motion arrows are longer, although some are shorter. The warmer gas has greater average random kinetic energy, not a requirement that every particle always moves faster. Arrow lengths are qualitative; these are model snapshots, not measurements or tracked particles.

Individual speeds vary. Higher temperature describes the average random kinetic energy of all the particles.

These models show the same gas at 20°C and 50°C. The same number of equally sized particle symbols is used. Motion arrows have varied directions and lengths in both panels; the warmer sample has greater typical speeds, not one identical speed for every particle.

Average does not mean every particle moves alike

Particles have a range of kinetic energies and continually exchange energy in collisions. A temperature rise concerns the average over all the particles, not a requirement that every individual particle speeds up at every instant.

For a solid, particles continue vibrating about their positions. Warming makes the average kinetic energy of that vibration greater; it does not require particles to stream freely through the solid.

The Celsius readings establish which temperature is higher, but their ratio is not an energy ratio. For example, 50°C is not evidence for 2.5 times the average kinetic energy at 20°C. A cooler sample at these temperatures still contains moving particles.

Internal energy includes motion and interactions

Internal energy is an energy store made up of two particle contributions:

  • The total kinetic energy associated with the random motion of the particles.
  • The total potential energy between the particles, associated with their arrangement and interactions.

These are totals for the whole system, not the energy of one selected particle. The potential-energy contribution matters as well as the motion: changing the particles' arrangement can change internal energy without raising temperature.

Temperature is related to an average; internal energy is a total

Worked comparison

100 g and 200 g of the same liquid at 30°C

The two samples have the same average random kinetic energy per particle because they are the same substance at the same temperature.

The 200 g sample contains about twice as many particles. Adding their kinetic energies therefore gives about twice the total random kinetic energy, although the temperature has not doubled.

Internal energy also includes the total potential energy between those particles. Matching temperatures alone does not establish matching internal energies, and the temperature reading does not give a numerical value for either sample's internal energy.

For a fixed amount of one substance that stays in the same state, warming increases average random kinetic energy and increases internal energy. When comparing different samples, also consider the amount of material, the substance and its state. Temperature alone is not a complete energy comparison.

Keep motion of the whole body separate

A trolley moving across a room has a kinetic store associated with that overall motion. Its particles also move randomly and interact with one another; those contributions form its internal store.

Making the whole trolley move faster does not automatically mean its temperature has risen. Conversely, a stationary block can gain internal energy while its centre remains at rest.

Include both internal-energy contributions. "Total energy of moving particles" leaves out the potential energy between particles. "Average kinetic energy" describes the temperature relationship, not the full internal-energy store.

Optional check Two samples of the same liquid, 100 g and 200 g, are both at 30 degrees C. Which statement follows from the particle model?
Two samples of the same liquid, 100 g and 200 g, are both at 30 degrees C. Which statement follows from the particle model?

Measure the sample's temperature

Temperature may be represented by θ (theta) or T. The symbol θ commonly denotes a Celsius temperature in °C, while T commonly denotes a temperature in kelvin (K). These letters name the quantity; °C and K name the units. Always retain the stated scale and unit with a reading.

A thermometer measures temperature through a property that changes as its sensing region responds to the sample. Place and read it so that it represents the sample you intend to measure.

  1. Choose a suitable range and resolution. A thermometer covering -10°C to 110°C can include the 20°C and 50°C readings above. With divisions every 1°C, the scale does not justify reporting many decimal places.
  2. Immerse the sensing region correctly. Follow the instrument's immersion marking or instructions. A liquid-in-glass thermometer needs its bulb in the sample; do not leave the bulb mainly in the air above it.
  3. Avoid contact with the vessel. Keep the sensing region clear of the base and sides, especially while the vessel is being heated. Gentle stirring, where suitable, can reduce temperature differences within a liquid.
  4. Allow time for the response. For a sample held at a steady temperature, wait until the reading settles. If the sample is continuously warming, a slow thermometer can lag behind its changing temperature.
  5. Read the scale properly. View the top of a liquid-in-glass thermometer's column at eye level to reduce parallax. Record the unit and the relevant time when following a change.

Measurement reasoning

Two readings of the same warming liquid

A thermometer touches the heated base of a beaker. That region may be hotter than the bulk liquid, so its reading can be too high for the intended liquid temperature. Moving the sensor into the liquid, away from the base, addresses the placement problem.

A second thermometer is correctly placed but responds slowly. While the liquid warms, its reading can be below the liquid's current temperature. Repeating the same timing does not remove this response lag; use a suitable sensor and account for its response time.

Repeated readings can reveal variation, but they do not correct a sensor touching the wrong object or an unsuitable response time. A finely divided display also does not guarantee that the measurement is accurate.

Next, changes of state show why internal energy can change while temperature remains constant.