2012

How long the Universe takes to cool by a tenth of a kelvin

Round: Theory
Points: 10
Level: Silver
Taught in: Section 13.5

Adapted from IOAA 2012 (Rio de Janeiro), theory problem 10. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

Assume that the Universe is flat with $Ω_{0} = 1$ and no dark energy, that the present temperature of the background radiation is 2.73 K, and that the temperature is inversely proportional to the scale factor. Take $H_{0} = 72$ km/s/Mpc. How long, from now, will the Universe take to cool by 0.1 K?

I solved it without the solution

AnswerThe Universe takes about 520 million years to cool by 0.1 K.

This problem also appears among the olympiad problems of Section 13.5, The age and history of the Universe, which teaches the ideas it uses. Equation and figure numbers refer to the course.