Did you think you could crack it?
Earlier, I presented a puzzle about keeping your home from turning into an oven during a heatwave. The scenario is simple. The physics, however, gets a bit tricky. Here is the solution.
Imagine a room with just one layer: curtains. When the sun beats down, that energy hits the window. The curtains absorb it. They get hot. Eventually, they reach an equilibrium. They radiate heat at the same rate they absorb it. Half that heat goes back out the window. The other half sneaks into the room.
So, a single layer blocks 50% of the sun’s energy. Simple enough.
Now, add a second layer. Put roller blinds on the glass, and hang curtains over them. You now have two distinct layers of protection. How much sun energy actually gets inside the room this time?
We’re ignoring the glass, the material’s color, and the room’s shape. Assume homogeneous materials and thermal equilibrium.
What’s the number?
33 percent.
That is the answer.
Breaking Down the Math
Let’s look at why the number drops so dramatically.
We need to track the heat flow once everything settles down. The curtain radiates energy both inward and outward. Let’s call that amount h.
If the curtain is radiating h in both directions, it is putting out 2h total. This energy comes from the blind sitting right behind it. So, the blind must be radiating 2h toward the curtain and 2h back toward the window.
But the blind isn’t working alone. It’s also receiving that h radiating from the curtain.
So, what is the blind radiating total? It’s radiating 4h. Two parts go toward the curtain. Two parts go out the window. But only three of those parts (3h ) actually come from the original sun. The fourth part is just recycled heat from the curtain itself.
If the sun provides 3h, and only h makes it all the way into the room, the math is straightforward.
h divided by 3h equals roughly 33 percent.
Two layers work better than one. Not 50-50, which you might expect. 33.
The lesson? Double glazing the window treatment works. It’s not magic. It’s just thermodynamics.
Thanks to Alan Williams-Key for setting the puzzle. I’ll return in two weeks with the next challenge.
