Leave a hot object and a cold object in contact for long enough, and something predictable always happens — they meet in the middle. That meeting point is thermal equilibrium.
📘 What you need to know
Thermal energy always flows from a hotter region to a cooler region, never the other way
Thermal equilibrium is reached when two substances in contact stop exchanging any net thermal energy and reach the same temperature
This can only happen if the two substances are in thermal contact with one another
The hotter region cools while the cooler region warms, until both reach the same final temperature
Once at equilibrium, energy is still exchanged at the particle level — it’s just that the net transfer becomes zero
The Direction of Thermal Energy Flow
Whenever two regions at different temperatures are in contact, thermal energy always moves from the hotter one to the cooler one. This continues until the temperature difference disappears entirely — at which point there’s nothing left to drive any further net transfer.
Two regions in thermal contact always end up at the same temperature — the hotter one cools, the cooler one warms
What Is Thermal Equilibrium?
Thermal equilibrium is defined as the state reached when two substances in contact no longer exchange any net heat energy, both having settled at an equal temperature. From this point on, there’s simply no temperature difference left to drive further net transfer between them.
Reaching Equilibrium Over Time
The two regions don’t jump straight to their final shared temperature — the hotter one cools gradually while the cooler one warms gradually, both curves levelling off as they converge on the same value.
Both temperatures converge on the same final value, but the actual equilibrium temperature depends on the initial temperature difference and other factors
Quick recap: Thermal energy always flows hot to cold. Two substances in thermal contact eventually reach the same temperature, at which point net energy transfer stops.
WE 1
Two identical metal blocks, one at 80 °C and one at 20 °C, are pushed together and insulated from their surroundings. Describe how their temperatures change over time, and state the eventual outcome.
Reasoning
Thermal energy flows from the hotter block to the cooler block, so the 80 °C block gradually cools while the 20 °C block gradually warms.
Outcome
Since the surroundings are insulated and the blocks are identical, both temperatures converge on the same final value and then stop changing.
The blocks reach thermal equilibrium at a shared intermediate temperature
WE 2
A thermometer, initially at room temperature (22 °C), is placed into a cup of tea at 85 °C. Explain why the thermometer’s reading takes time to settle, and state what its final reading depends on.
Reasoning
The thermometer and the tea are not initially at the same temperature, so thermal energy must flow between them via conduction until they reach thermal equilibrium.
What the final reading depends on
The reading stabilises once no more net thermal energy is being exchanged; since the tea has a far greater mass than the thermometer, the final reading ends up very close to the tea’s own temperature.
The reading settles once the thermometer and tea reach thermal equilibrium
💡 Top tips
Thermal equilibrium means equal temperature, not necessarily equal internal energy or equal mass
“No net transfer” doesn’t mean nothing is happening at the particle level — individual exchanges still occur, they just balance out
Two substances can only reach thermal equilibrium with each other if they are in thermal contact, whether directly or through a conducting medium
Don’t assume the final equilibrium temperature is always the simple average of the two starting temperatures — that depends on other factors like mass and specific heat capacity
⚠ Common mistakes
Assuming thermal equilibrium is reached instantly, rather than gradually over time
Forgetting to account for energy exchanged with the surroundings if a system isn’t actually insulated
Confusing thermal equilibrium (equal temperature) with a substance simply stopping being heated
Assuming the equilibrium temperature must be exactly midway between the two starting temperatures, regardless of mass or material
Up next: Changes of State — where we look at what happens as a substance shifts between solid, liquid and gas.
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