Swans on Tea

We got a new toy in the lab recently — a thermal sensor, aka an IR thermometer, which uses the incoming radiation profile to sense the temperature of a remote object. It’s useful because it does not require physical contact. (I wasn’t there the day it arrived, and rumour has it that it “saw” some things that cannot be unseen as it was “tested” using quasi-calibrated biological standards of temperature at 37ºC )

So how does it work?

All objects will emit electromagnetic radiation; the ideal is a blackbody which emits according to

$latex P = A\epsilon{\sigma}T^4$

A is the area, sigma is a constant, T is temperature, and epsilon is the emissivity, which is 1 for a blackbody

If we look at an object about the size of a 2L soda bottle (roughly 4 cm radius, 33 cm tall), we find that at 300K, it emits about 7.5 Watts of power. Because the blackbody spectrum is a continuum, this represents a wide spectrum of wavelengths, which will have a peak in the infrared, somewhere around 10 microns. In thermal equilibrium its temperature will not be changing, which means it’s also absorbing 7.5 Watts from its surroundings (ignoring conduction and convection losses, which should be small) If the object is not in thermal equilibrium, it wither radiates more power and cools down, or absorbs extra radiative energy and heats up.

But that’s if it’s a perfect blackbody. If it isn’t — the emissivity is less than 1 — some of the incoming radiation is reflected. If less radiative power is absorbed, it has to have a lower temperature to be in equilibrium (or, at the same temperature, it radiates a lower power). So at a given emissivity, one could measure the radiation profile, and values at a few wavelengths will indicate the shape of the blackbody curve and will tell you the temperature.

I did this, though with a 12 oz (355 ml) can instead of a 2L bottle. You can see the dot of the built-in laser pointer showing that the sensor is pointed at the can.

Whoa! This is a can right out of my fridge, and is obviously not at 61ºF. What’s going on? Well, the emissivity did it. An aluminum can, even with some coloring, is nowhere near a blackbody. Depending on the particulars of how much oxidation and level of polishing, the emissivity of aluminum can range from about 0.2 to below 0.1. The thermometer’s spec sheet says it assumes a value of 0.95, so there’s quite a discrepancy. This means the sensor is getting a mix of radiation from the can (below 40ºF) and from the surrounding room-temperature items (and a little from me, sitting less than a meter away), and this skews the results.

What if we cut down on the reflections? I encased the can in a single sheet of paper.

OK, that’s significantly better. The paper is in good contact with the can and the can might be slightly warmer than in the first shot, as it’s been sitting at room temperature or been handled by a warm-blooded creature, so the surface temperature may have gone up a little. Cooling the paper down to the can’s surface temperature probably had a negligible effect.

What about a black surface?

That’s lower, though not dramatically (and probably not significant in terms of instrument sensitivity), though the same caveats apply — the can can only have warmed between shots. I didn’t return it to the fridge, and I was handling it.

There’s a cautionary tale here — you want to trust your instruments, but you have to know what is actually being measured to ensure you don’t let systematic errors into your results.

Label Puzzler: Original Recipe AND New Flavor?

[W]hile the box is closed, the ice cream inside exists in a quantum superposition of states in which it is both “original recipe” and “new flavor,” and only when the box is opened and the ice cream observed does the wave function collapse into either an “original” or “new” state. Alternatively, the two states would decohere and two new universes would form, in one of which you are eating original-recipe ice cream and in the other a parallel You is enjoying the new flavor. (I don’t think there’s any scenario in which a cat spontaneously forms. Please!)
…
Please let me know if you are interested in serving as an expert witness for a possible quantum-physics defense to consumer-law claims involving allegedly self-contradictory labels.

I’ll do this one pro bono. A new flavor has to be the original recipe. No quantum mechanics involved. People think of original recipe as meaning a throwback (especially since the New Coke debacle), but it doesn’t have to be that way. It’s only a contradiction if you know it’s not redundant. No label superposition. It would be neat to have entangled flavors, though, like one half-gallon of chocolate and one of vanilla, but you don’t know which is which until you open one of the containers.