Sunday, March 24, 2013

Gosh, it feels cold!

Lubos Motl posted this extraordinary video on his site - ultra-high-speed cameras show the sub-orbital speed of the detonation wave in "Prince Rupert's Drops". You can skip the ad after a few seconds and also the chat at the end.

It's very cold at the moment, even in a centrally-heated house. Touch the exterior-facing walls or the double-glazed windows. They have a c. 20°C thermal drop across them - naturally they're quite cold even with the insulation. Despite the warm air in the house, you still feel quite chilly.

OK, let's try again, why is that exactly? The second law of thermodynamics tells us that heat flows from hot objects to cold ones. More operationally, your body radiates in the infra-red to its surroundings and your surroundings radiate in the infra-red back at you. But if they're colder than you, there's a net imbalance: you're doing most of the radiating at the walls and windows, they're not returning the favour. So you feel the chill.

How does this work at the level of individual molecules, how does this infra-red radiation actually occur? Only quantum mechanics can tell us. In a typical house at c. 20°C (infra-red radiation) energy transitions correspond to random changes in the vibrations of molecular components: it's like the atoms are connected together by bouncy springs as they thermally bash into one another.

In quantum mechanics this reminds us of harmonic oscillators and their energy eigenstates spaced at the order of ℏω - which at infra-red values of ω are pretty finely spaced. Throw in some Doppler smearing and you've got a continuous black-body spectrum.

So that's why we feel just a tad uncomfortable this week.