Thermal energy transfers

Physics · The particulate nature of matter. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Matter is made of particles. In a solid they vibrate about fixed positions, in a liquid they move past each other, and in a gas they are far apart, which is why gases have low densities. The kelvin temperature is proportional to the mean kinetic energy of the particles. Internal energy is the total of the random kinetic energy and the potential energy of all the particles.

Heating either raises the temperature (specific heat capacity) or changes the state at a constant temperature (specific latent heat). It never does both at once.

Energy moves by conduction, convection and radiation. A hot black body radiates a power that depends on its area and on T4, and its peak wavelength becomes shorter as it gets hotter.

Rules to remember

Common mistake

Students put Celsius temperatures into formulas that need kelvin. Use kelvin for mean kinetic energy, Stefan–Boltzmann and Wien's law; a temperature change ΔT is the same in both scales.

Worked example

A 2.0 kW heater is placed in 1.5 kg of water at 20 °C. The specific heat capacity of water is 4200 J kg−1 K−1 and no energy is lost. How long does the water take to reach 100 °C?

  1. Temperature change ΔT = 100 − 20 = 80 K.
  2. Energy needed: Q = mcΔT = 1.5 × 4200 × 80 = 504 000 J.
  3. time = energy ÷ power = 504 000 ÷ 2000 = 252 s.

Answer: About 250 s (a little over 4 minutes).

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