Did you solve it? Do you think like a physicist?

Earlier today I set you a puzzle about keeping homes cool in a heatwave. Here it is again with the solution.

Imagine a room with a set of curtains. When the Sun is shining, its energy comes through the windows where it is absorbed by the curtains. The curtains get hotter and hotter until they reach a temperature at which they are radiating as much heat as they absorb. The curtains radiate 50 per cent of this heat back towards the window, and 50 per cent of the heat into the room.

In other words, curtains stop 50 per cent of the energy from the Sun.

Imagine a room with roller blinds and curtains. The blinds line the windows, and the curtains cover the blinds. There are thus two layers of protection from the Sun.

Now what percentage of the Sun’s energy gets into the room?

(Assume the blinds and curtains are made out of homogeneous material, and that the system has reached equilibrium. Also, this is a simplified model, so ignore the glass windows, the colour of the materials and the shape of the room.)

Solution 33 per cent.

Workings

Below is a diagram that shows the heat flow when the system reaches equilibrium, i.e. when both curtains and blinds reach their individual stable temperatures.

The curtain is radiating the same amount inwards and outwards. Let the energy radiated in either direction be h.

If the curtain has absorbed a total of 2h, it must have got this energy from the blind. We deduce that the blind is radiating 2h forwards and backwards.

The blind, however, is also receiving h form the curtain. So, of the 4h that it is radiating, only 3h comes from the Sun.

If 3h is coming in, and h enters the room, the percentage of the Sun’s energy is 33 per cent.

I hope you enjoyed this puzzle. I’ll be back in two weeks.

Thanks to Alan Williams-Key for today’s puzzle.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.