Ask a Physicist: Cold Light and Negative Work

It’s been a while since we got around to opening up the “Ask a Physicist” inbox, but we’ve had some great questions recently, and you can look forward to Ask a Physicist being a more regular feature on the Buzz Blog. Let’s get to it!

Grunka, from Scotland, asks:
If light slows down at extremely cold temperatures, would the light in space travel faster if it had a pathway which was at an average temperature of 3º C?”

While it’s true that scientists have slowed and even stopped light in its tracks at low temperatures in special materials, this can’t really be generalized to “colder light is slower”. In fact, almost the opposite is true! Since light moves fastest in a vacuum, and since temperature is a measure of the kinetic energy of particles in a medium, light will move slower through any medium with a measurable temperature than it would through a vacuum; the fewer particles you have in a given volume, the lower their temperature tends to be.

But your question becomes really interesting when you realize that we’re NOT in a perfect vacuum—the space near the earth, with innumerable solar wind particles and photons streaming through it, is relatively hot! Light traveling through the plasma that makes up the sun can take ten thousand years to get from the core to the surface, because it’s constantly being bounced and redirected by the hydrogen and helium atoms.

Perhaps somewhere, in the deep and frozen vacuum of the Great Void, you WOULD find light moving faster than it does in our neck of the woods!

Michele, from the US, asks:
In an isobaric [ed: constant pressure] ideal gas process, compressing a gas will result in a lower temperature. It makes sense that less kinetic energy would be required to create the same pressure in a smaller volume. However, to compress the gas, you must do work on that gas. Where do the Joules of work go, if the temperature is decreasing? A decrease in temperature would seem to indicate a smaller internal energy, so why is the work done on the gas considered to be positive? And how would you actually do the work – by cooling the gas? So removing heat is positive work? Adding heat to a system is a positive input of joules to a system in other problems involving thermodynamics. What am I missing here?

Excellent question! You’ll be pleased to know that your intuition is very much correct; most of what you’re missing is a minus sign. Compressors are, in fact, “work-consuming devices”, meaning they do “negative work” on the gas, or the gas is actually doing work on them. When air blows past a wind turbine, the air does work on the blades. The blades, meanwhile, do negative work on the air,

I think the main confusion arises because your question started with the assumption that the process is isobaric, meaning that the gas stays at the same pressure the whole time. If the pressure and the number of gas molecules in your sample are fixed, the only free variables in the ideal gas equation (P*V=n*R*T) are V and T, so your assertion that a denser sample would have a lower temperature is correct. Unfortunately, if you want the situation to stay isobaric, you can’t just compress the gas; it’ll stay at the same temperature and go to a higher pressure. But if you cool the gas, taking energy out of the system (and again doing negative work), it will stay at the same pressure, but contract to occupy a smaller volume.

The fact that we can decrease temperature to decrease volume while maintaining that isobaric state—but NOT vice versa—has to do with the so-called “Arrow of Time“, the principle that entropy always increases.

You may also read these articles