# Do small objects heat up faster in sunlight?

Its often said, that something with a higher surface area to volume ratio loses heat faster, but what about the opposite?

Think of two black cubes left in direct mid-day sunlight. Which one do you think would be warmer inside, the bigger one or the smaller one?

Like, would a smaller person thats stuck in direct sunlight on a hot day actually get hotter than a much larger person?
Smaller people usually have a higher surface area to volume than larger people.

Yes … the opposite is true … the heat is absorbed at the surface, thus more surface means more heat is absorbed … also, the heat can conduct through the object quicker if the distance to the surface is smaller … losing heat is the exact opposite in every way all things being equal …

[del]Out in the sun, then the heat is only being applied to one side, whereas the cooling will be in all direction … so in this case the object should cool faster than the sun heats it …[/del]

Too many variables to consider to answer your questions about things left out in the sun … although only one side is heated by the sun, solar radiation is of a much higher energy content … a penny flat against the sun will heat quite quickly, whereas a penny on edge not so much … and a sphere of equal mass somewhere in between …

Same thing. Everything else being equal, the higher the surface-to-volume ratio, the faster it reaches an equilibrium with the environment. I.e. it heats up faster and cools down faster. Because the cooling/heating rate is roughly proportional to the surface area, and the amount of heat necessary to change the object’s temperature by a certain amount is proportional to the volume (if the material is the same).

People would work differently than static objects. We have mechanisms to maintain body temperature (both to cool us down or heat us up), and these would depend on the person. Size would be one variable, but other things would make a difference. For example, age. Very young children and very old people have the hardest time regulating body temperature and are most vulnerable in extreme heat or cold. Or percentage of body fat. Or genetic predispositions.

So, just knowing one person is smaller would have limited utility in determining whether or not they’d heat up faster. Note this isn’t limited to people. How well most mammals deals with heat is also not strictly determined by size for any given species.

Right. And more fundamentally, people generate their own heat, so they must get rid of heat at the same rate to maintain body temperature.

Also, what does it mean for a person to be “hotter”? Human bodies try to maintain a constant heat. Someone standing in the summer sun isn’t at a higher temperature than someone standing in snow. At least not at the core of the body.

Yes… all other factors being equal.

As scr4 says, the object eventually reaches an equilibrium in a steady-state environment. But then, it’s not linear. An object had the size does not necessarily heat up to twice or four times the temperature, etc. Each factor in acquiring and losing heat has its own parameters.

And people sweat if necessary to maintain (to lower) body heat. There is probably a point where all the sweating one can do is not enough… then eventually you pass out and die.

Except in this case, with heating being supplied by the sun one just one side, only the surface area of that side would count. The other sides would actually be a negative (as long as the objects temperature was above that of the surrounding air).

What would heat up the fastest is an item hammered flat. Big or small, an item shaped like a piece of paper laying flat in the sun is going to heat up in about the same time.

Well the sunlight on a hot day isn’t much more than the sunlight on a cold day, and so its the temperature of the air that is important. So the smaller person’s skin has an easier job of keeping them cool, because their skin area to weight ratio is higher.

We can also consider whether the object is wet in dry air … the solar radiation will also be absorbed by the water covering the object and some of this water will evaporate carrying away the latent heat … (no small amount btw) … in saturated air this will be less energy carried away and the object will heat up faster … the technical and sciency phrase for this is that on humid days, it “feels like” it’s warmer …

H[sub]I[/sub] = -42.379 + 2.04901523T + 10.14333127RH - .22475541TRH - .00683783TT - .05481717RHRH + .00122874TTRH + .00085282TRHRH - .00000199TTRHRH
Where H[sub]I[/sub] = the feels like temperature (in ºF), T = actual temperature (in ºF) and RH = relative humidity (in %)

Ha ha ha ha … them meteorologists can be such clowns …

this is a lot more complicated than i thought

Are there theoretically any higher order terms that are negligible, or is that really it?

In other words, you’re claiming that heat stroke and freezing to death are the same thing.

Only if you’ve a poor grasp of the english language - note the “try to maintain”

How did you infer that from what I posted? “Heat stroke” and “freezing to death” are what happen when the environment is so extreme that the body can no longer maintain its temperature. I didn’t say anything about those conditions one way or another.

Here are a couple of simplified plots. As you can see, the body core temperature is maintained over a wide range of environmental temperature. (And in that context, “environment” is what contacts the skin, so if you are properly dressed for the weather, your body core temperature remains constant for a much wider range of air temperature than this plot shows.)