Thermal equilibrium

Physics A2 · Temperature. 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

Thermal energy is transferred from a region of higher temperature to a region of lower temperature. The direction is decided by temperature only. It does not depend on mass, on material or on which object has more internal energy.

When two objects in thermal contact reach the same temperature, the net transfer stops. They are then in thermal equilibrium. Energy still passes both ways between them, but at equal rates, so the net transfer is zero.

This is how a thermometer works. It is left in a liquid until it reaches thermal equilibrium with the liquid, and then its own temperature is the temperature of the liquid.

Rules to remember

Net thermal energy transfer is from higher temperature to lower temperature
Thermal equilibrium: same temperature, so no net transfer of thermal energy
Objects in thermal equilibrium need not have the same internal energy, mass or heat capacity
If A is in equilibrium with B, and B with C, then A is in equilibrium with C
Mixing with no losses: energy lost by the hot object = energy gained by the cold object
A thermometer reads its own temperature, so it must first reach equilibrium with the object

Common mistake

Students say energy flows from the object with more internal energy. It flows from the hotter object, even if that object is small and has much less internal energy.

Worked example

A small steel ball at 300 °C is dropped into a large tank of water at 25 °C. The water has far more internal energy than the ball. Which way is the net transfer of thermal energy, and when does it stop?

Compare temperatures, not internal energies: the ball (300 °C) is hotter than the water (25 °C).
Net transfer is from higher to lower temperature, so it is from the ball to the water.
The ball cools and the water warms very slightly until both are at the same temperature.
At that point they are in thermal equilibrium and the net transfer is zero.

Answer: From the ball to the water, until both reach the same temperature (just above 25 °C).

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