Thermodynamics – Why It Takes Long for a Gas to Reach Thermal Equilibrium

kinetic-theorystatistical mechanicsthermodynamics

Imagine a 1m cube of air in an insulated container, where you have heated the air in one half but not in the other. Intuitively, given molecules are moving so fast, you would expect the energetic particles from the hot side to distribute themselves throughout the box within milliseconds, equalising the temperature. Why does this instead take much longer?

I thought of this question while waiting for a warm room to cool down after opening a window. Clearly my mental model of temperature is wrong because it seems to me that heat should move through a gas way faster than it actually does.

Best Answer

The mean-free path of a nitrogen molecule in air at STP is about 60 nm, so the molecules may travel quite quickly, but they do not go very far before the run into another molecule and get stopped.

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