Anonymous asked: Why can a table feel hot and cold at the same time if you have one hand in cold water and the other in hot and then you touch the table with both hands? It really doens't make sense to me and it would be embarrassing to ask my teacher.
We usually find it intuitive to think of hot and cold as properties inherent in some object. We usually think that ice (solid water) is cold. And that’s a useful thing to know. It’s a pragmatic simplification— it’s not entirely correct, but it gives us an easy way to remember something useful (that’s the pragmatic part) about the world.
The downside of these simplifications is that they remove some of the subtleties and cause certain types of results to be unexpected. For example, what do you think would happen if you dropped (and by ‘dropped’ I do mean ‘using proper safety devices gently placed’) ice into a cup full of liquid nitrogen? The nitrogen would actually very quickly begin to boil. From the perspective of the liquid nitrogen, the ice is really pretty hot.
This gives us a suggestion: maybe it’s not just about one object, but instead should depend on both of the objects involved. Our ideas of ‘hot’ and ‘cold’ aren’t really absolute notions, but rather comparisons. Given any two objects, we can compare their relative kinetic energies and say that one is hotter and one is colder (or maybe they’re about the same).
So this feeling of ‘hot’ and ‘cold’ actually comes from what I would call a temperature gradient— the difference between the two temperatures gives rise to the idea that from our perspective, ‘hot’ things are ‘hotter’ than we are and ‘cold’ things are colder than we are.
So let’s walk through an extreme version of your example (which I recommend not trying because danger):
- Put your left hand in ice water; call it approx. 0°C
- Put your right hand in hot water; call it approx. 40°C
- Let your hands acclimate to these temperatures. The second law of thermodynamics tells us that the system for each hand will spontaneously move towards equilibrium— each hand will move toward the temperature of the surrounding water and each pool of water will move toward the temperature of the respective hand.
- So now your left hand is cold and your right hand is hot.
- You place them both on a table that is 20°C.
- Your left hand is colder than this, so the table is hotter than this hand. You perceive this as ‘hot’.
- Your right hand is hotter than this, so the table is colder than this hand. You perceive this as ‘cold’.
So even though the table is a constant temperature, each hand has it’s own temperature gradient that is the difference in temperature between that hand and the table.
If you want a little bit more, the direction of the temperature gradient also tells you which way energy will flow— spontaneously from high to low energy; ‘hot’ to ‘cold’ so both become the same kind of ‘warm’. So if you think of energy as heat, it goes away from the hotter thing and toward the colder thing.
Really, that’s what we technically mean by ‘hot’ and ‘cold’. We, as a species, tend to be egocentric (for reasonable reasons, more or less) so we just implicitly compare things to our own temperature.
Hopefully that makes some sort of sense. If not, feel totally free to ask any sort of clarifying question. Science! [: