Heat

“Don't let yourself get attached to anything you are not willing to walk out on in 30 seconds flat if you feel the heat around the corner.”
    Robert DeNiro as Neil McCauly, Heat (1995)

This quote has nothing to do with this blog post. I just like Heat.

Heat makes things expand. This occasionally gets used as a plot device in inflation stories. So today we’ll be taking a look at thermal expansion.

So the question is, how much bigger can heat make things? Short answer: not that much.

Dealing with gasses is simple thanks to the beauty of the Ideal Gas Law.

PV = nRT

therefore

V = nRT/P

where

P = pressure
V = volume
n = number of gas molecules, in moles
R = the universal gas constant
T = temperature, in Kelvin

It has a number of implications, but the important one for our purposes is this: all gasses respond to heating/cooling the same way. Assuming pressure remains constant, an absolute increase in temperature by 10% will cause an increase in volume by 10% whether you’re dealing with oxygen, hydrogen, helium, or methane.

To demonstrate, let’s use our hapless victim from the post Water. She’s currently filled with two thousand liters of hydrogen and oxygen, making her slightly over five feet in diameter (and dangerously explosive, but that’s an issue for a different post).

Let’s assume that water she consumed, and resulting converted gas, was at 60℉ and that gas is slowly heating up to body temperature, 98.6℉. When you convert to Kelvin and run the numbers, and assuming pressure stays constant, she goes from 2000 liters to 2,149 liters. Volume increases by 7.5%, resulting in an increase in diameter of about an inch and a half.

I’m sure that our test subject would find that to be quite significant, but the casual observer wouldn’t notice.

We can push this a bit farther, but there are limits. We have to keep the temperature within a range that will neither freeze nor cook a person. If we start at 32℉ and heat to 105℉, we get a 15% increase in volume and a three inch increase in diameter.

So heat doesn’t provide a significant amount of expansion over any reasonable temperature range. But you shouldn’t feel obligated to be reasonable. Exaggerations of various sorts are central to inflation fiction, so please carry on.