When will it cool?

Classical Mechanics Level 2

I have a cup of warm coffee and it has a temperature of 9 0 ∘ C 90^{\circ}C . It takes 5 minutes to cool down from 9 0 ∘ C 90^{\circ}C to 8 0 ∘ C 80^{\circ}C . Theoretically, when will it cool down to exactly the room temperature after reaching 8 0 ∘ C 80^{\circ}C ? ?

Assume the room temperature is 2 0 ∘ C 20^{\circ}C .

After less than 30 minutes Never After 30 minutes After more than 30 minutes

Abha Vishwakarma by Abha Vishwakarma , 20, India

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1 solution

Steven Chase
Oct 8, 2018

Cooling is an exponential process, so the temperature will asymptotically approach room temperature, without ever truly getting there. It's interesting to contemplate how quantum mechanics comes into this in reality. For example, what happens when the theoretical delta between actual and room temperature is smaller than the smallest allowable quantum?

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