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O-Level Physics · Secondary 3 and 4

Thermal Physics

Thermal physics explains heating and temperature using the kinetic particle model of matter. You learn how particles in solids, liquids and gases are arranged and move, why a gas exerts pressure, how energy is transferred by conduction, convection and radiation, and how to calculate the energy needed to heat a substance or change its state. These ideas explain cooking, insulation, sea breezes and why sweating cools you, and they build on the energy work from mechanics.

What the syllabus expects

  • Describe the arrangement and motion of particles in solids, liquids and gases using the kinetic particle model
  • Explain gas pressure in terms of particle collisions and use pV = constant for a fixed mass of gas at constant temperature
  • Describe conduction, convection and radiation and explain everyday applications of each
  • Distinguish between heat capacity and specific heat capacity and use Q = mcΔθ
  • Describe melting, boiling and evaporation and use Q = ml for latent heat
  • Explain why the temperature stays constant during a change of state

The kinetic particle model

All matter is made of tiny particles in constant motion. In a solid, the particles are closely packed in a regular arrangement and vibrate about fixed positions, held by strong attractive forces. In a liquid, the particles are still close together but in a disordered arrangement, and they can slide past one another. In a gas, the particles are far apart and move randomly at high speed, with negligible forces between them except during collisions. A higher temperature means a higher average kinetic energy of the particles. Brownian motion, the random jiggling of smoke particles seen under a microscope, is evidence for this model. The smoke particles are being bombarded unevenly by fast-moving air molecules too small to see. The internal energy of a substance is the total kinetic and potential energy of its particles.

Gas pressure

Gas particles collide with the walls of their container. Each collision exerts a small force, and the total force per unit area is the gas pressure. If a fixed mass of gas is squashed into a smaller volume at constant temperature, the particles hit each unit area of wall more frequently, so the pressure rises. For a fixed mass of gas at constant temperature, pV = constant, so p₁V₁ = p₂V₂. For example, 120 cm³ of gas at 1.0 × 10⁵ Pa compressed to 40 cm³ reaches 1.0 × 10⁵ × 120 ÷ 40 = 3.0 × 10⁵ Pa. If instead the gas is heated at constant volume, the particles move faster on average, hitting the walls more often and with greater force, so the pressure increases.

Conduction, convection and radiation

Conduction is the transfer of thermal energy through a material by vibrating particles passing energy to their neighbours. In metals, free electrons also carry energy quickly, so metals are good conductors. Non-metals, liquids and especially gases are poor conductors, which is why trapped air makes a good insulator. Convection happens only in fluids. A heated region of fluid expands, becomes less dense and rises, while cooler, denser fluid sinks to take its place, setting up a convection current. This is why heaters are placed low in a room and air conditioners high up. Radiation is the transfer of energy by infrared electromagnetic waves and needs no medium, so it can cross a vacuum. Dull black surfaces are good emitters and absorbers of infrared, while shiny silver surfaces are poor emitters and good reflectors. A vacuum flask reduces all three processes.

Heat capacity and specific heat capacity

The heat capacity C of an object is the energy needed to raise its temperature by 1 K (or 1 °C), measured in J/K. The specific heat capacity c of a substance is the energy needed to raise the temperature of 1 kg of it by 1 K, measured in J/(kg K). The energy needed for a temperature change Δθ is Q = mcΔθ. A temperature change of 1 °C is the same as a change of 1 K, so either unit works for Δθ. Water has a high specific heat capacity of about 4200 J/(kg K). Heating 2.0 kg of water from 25 °C to 75 °C needs 2.0 × 4200 × 50 = 420 000 J. Because water stores so much energy for each degree, the sea warms and cools more slowly than the land.

Changes of state and latent heat

A pure substance melts and boils at fixed temperatures. During a change of state, the energy supplied is used to overcome the attractive forces between particles and increase their potential energy, not their average kinetic energy, so the temperature stays constant. This energy is latent heat. The specific latent heat l is the energy needed to change the state of 1 kg of a substance without a change in temperature, so Q = ml. For water, the specific latent heat of fusion is about 3.3 × 10⁵ J/kg and of vaporisation about 2.3 × 10⁶ J/kg. Evaporation is different from boiling. It happens at any temperature, only at the surface, when the most energetic particles escape. The particles left behind have a lower average kinetic energy, so the liquid cools. Evaporation is faster at higher temperature, with a larger surface area, in moving air and in lower humidity.

Worked example

A 2000 W kettle contains 0.50 kg of water at 30 °C. Take the specific heat capacity of water as 4200 J/(kg °C) and its specific latent heat of vaporisation as 2.3 × 10⁶ J/kg. Assume no energy is lost to the surroundings. (a) Calculate the energy needed to bring the water to 100 °C. (b) How long does this take? (c) The kettle keeps boiling for a further 115 s. What mass of water boils away?

  1. Temperature rise: Δθ = 100 − 30 = 70 °C.
  2. Energy to heat the water: Q = mcΔθ = 0.50 × 4200 × 70 = 147 000 J.
  3. Time: t = E ÷ P = 147 000 ÷ 2000 = 73.5 s.
  4. Energy supplied while boiling: E = Pt = 2000 × 115 = 230 000 J.
  5. The temperature stays at 100 °C during boiling, so use Q = ml: m = Q ÷ l = 230 000 ÷ 2 300 000 = 0.10 kg.

Answer: (a) 147 000 J (1.47 × 10⁵ J) (b) 73.5 s (about 74 s) (c) 0.10 kg

Common mistakes

  • Saying particles in a solid do not move. They vibrate about fixed positions, and they vibrate more as the temperature rises.
  • Saying the particles themselves expand when a substance is heated. The particles stay the same size, the spaces between them increase.
  • Writing heat rises in a convection answer. Explain that the heated fluid expands, becomes less dense and rises, while cooler denser fluid sinks.
  • Using Q = mcΔθ during melting or boiling. The temperature is not changing then, so use Q = ml.
  • Explaining the flat part of a heating curve by saying no energy is being absorbed. Energy is still being supplied, but it goes into overcoming the attractive forces between particles rather than raising their kinetic energy.
  • Mixing up evaporation and boiling. Evaporation happens at any temperature and only at the surface, boiling happens at a fixed temperature throughout the liquid.

Exam tips

  • On a heating or cooling curve, label each flat section as a change of state and use Q = ml there, and use Q = mcΔθ only on the sloping sections.
  • In gas pressure explanations, mention the frequency of collisions per unit area of wall, and when temperature changes, also mention the average speed of the particles.
  • For heat transfer questions, name the process and then explain it with particles or waves. For convection always include the change in density.

Practice questions

1. Easy: How much energy is needed to raise the temperature of a 3.0 kg aluminium block from 20 °C to 60 °C? The specific heat capacity of aluminium is 900 J/(kg °C).

Show answer

Q = mcΔθ = 3.0 × 900 × (60 − 20) = 3.0 × 900 × 40 = 108 000 J (1.08 × 10⁵ J).

2. Medium: A fixed mass of gas has a volume of 300 cm³ at a pressure of 1.2 × 10⁵ Pa. It is compressed slowly at constant temperature to 90 cm³. Find the new pressure.

Show answer

4.0 × 10⁵ Pa. Using p₁V₁ = p₂V₂: p₂ = 1.2 × 10⁵ × 300 ÷ 90 = 4.0 × 10⁵ Pa. The volume is divided by 10/3, so the pressure is multiplied by 10/3.

3. Harder: Calculate the energy needed to turn 0.20 kg of ice at 0 °C into water at 20 °C. Use 3.4 × 10⁵ J/kg for the specific latent heat of fusion of ice and 4200 J/(kg °C) for the specific heat capacity of water.

Show answer

About 8.5 × 10⁴ J. Melting at 0 °C: Q = ml = 0.20 × 3.4 × 10⁵ = 68 000 J. Heating the water from 0 °C to 20 °C: Q = mcΔθ = 0.20 × 4200 × 20 = 16 800 J. Total = 68 000 + 16 800 = 84 800 J.

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