This was a scene in the Jean Claude Van Dam movie TimeCop in the 1980’s. Spray the baddie’s arm with liquid nitrogen for 5 seconds, and a good swift kick shatters it.
Now consider that you can toss a moderately thick steak on a roaring flame and the center (half an inch in) will still be raw a minute or several later. Burning at the stake (not steak) was a drawn-out torture, especially as it started with the feet before the torso. Why would cold conduct through flesh any faster than heat? Plus, there’s fluid (blood) conveying warmth from the torso. Even at extreme temperatures, it takes a while.
Isn’t vacuum a remarkably good insulator, in that heat transfer would only occur through radiation, not conduction/convection? The reason the radiators on manned spacecraft are often so large, and objects are often rotated to help with thermal equilibrium. I’d think it would take awhile.
Was the limb tourniqueted or was blood still able to circulate? EDIT: I see Chronos, among others, already got to the TQ and blood part.
Might break, but it won’t shatter. I think the scene in the OP is like when Mr. Wizard immerses a rose in liquid nitrogen for a few seconds then taps it and it shatters into dust. That won’t happen with your arm.
I think that’s actually a very good analogy. A steak is going to start say 70 degrees Fahrenheit, and the grill is probably 500F or so, a difference of 430F. A living arm is close to 100F, and liquid nitrogen is -330F, a difference of 430F. The heat transfer to the outer surface is going to be different, grill to steak vs arm to LN2, but the conduction through the meat is going to be about the same rate (again, that’s assuming there’s no blood flowing in the arm).
When I took a course on computer modelling of thermal processes, they described it like this - imagine the item divided into tiny cubes, say 1mm on a side. Each is at a specific temperature. you apply a known temperature change to on surface, and assume as each cube changes temperature, as the clock ticks, it conduct X% of that thermal change to its neighbour(s) if they are at a different temperature - how fast does it travel through the item, from cube to cube? By experiment, you can get an estimate of the factor of thermal conductivity rate. As I mention with the steak example above, the thermal conductivity rate of flesh (which is solid, no convection currents, so strictly conduction) is not that high. It could take a long time for an arm to freeze solid, just as it takes half an a hour or more for the center of a roast to reach cooking temperature. (Not being that domestic, I have no idea how long it takes to make a 5-inch-diameter roast un-raw, but I’m going to guess 375F for at least 20 minutes to get the center appreciably warm. Also remember the state change for water - liquid to solid - is 80 calories per cc (? It’s been a long time…) so there’s additional cooling required above and beyond going from 20°C to 0°C and you need to be significantly below freezing for the shatter effect, and water has the higher specific heat compared to most media.
You might get nitrogen bubbles and the bends (depending on air mixture being breathed), and extreme bends could cause strokes and death, but any vapour embolism, one assumes, would turn back to liquid once it proceeded toward an area with more pressure.