Radiation & Heat: Questions Answered

[Niles]

Homework Statement

Hi all. This is not a homework-question, but something I've thought about.

1) When I put a frying-pan on the hotplate (let's say that the hotplate has a temperature of 400 K), then no matter how long the frying-pan is on the plate, the maximum temperature the pan will gain is 400 K?

2) When you touch a piece of steel when it is summer-time (e.g. a hand-rail), the steel sometimes feels extremely hot. This is of course because the steel conducts heat very well. But what is the maximum temperature this steel can acquire?

Thanks in advance.

 

[mgb_phys]

1) When I put a frying-pan on the hotplate (let's say that the hotplate has a temperature of 400 K), then no matter how long the frying-pan is on the plate, the maximum temperature the pan will gain is 400 K?

Yes,

2) When you touch a piece of steel when it is summer-time (e.g. a hand-rail), the steel sometimes feels extremely hot. This is of course because the steel conducts heat very well. But what is the maximum temperature this steel can acquire?

In theory the temperature of the surface of the sun!
In practice it depends on:
The reflectivity of the surface - a perfect black will absorb more energy.
The fraction of the area of the surface facing the sun.
Most importantly the rate of cooling to the surroundings.

If you put a perfectly black material inside a perfectly insulated box the part of it facing directly toward the sun would reach the same temperature as the sun.

The same thing applies to the earth,
Imagine drawing a sphere around the Earth with the radius of the Earth's orbit.
The sun's disc would fill a very small fraction of the surface of that sphere, the rest would be cold dark space.
The Earth receives energy from that fraction of the area that is the sun's disc and relects some of it.
The Earth then heats up and emits it's own heat to the rest of that area.
By knowing the temperature of the sun and the fraction of the surface covered by the sun you can work out what temperature the Earth should be.

 

[Niles]

Thanks; it is very kind of you to answer.

 

[Niles]

Hmm, wouldn't it only gain the same temperature as the Sun if all the Sun's radiation hit the hand-rail?

E.g. if only 1% of the Sun's radiation hits the hand-rail, then how can one explain that it will eventually get the same temperature as the Sun?

 

[mgb_phys]

There's an important difference between heat and temperature.
Temperature is more like a pressure or voltage, and heat is more like volume or amount.

Imagine a flood barrier with a very tiny leak, eventually the leak will fill up the land to the same level as the sea, the leak can be a fraction of 1% of the barrier - this just controls how long it takes to fill up, not the eventual level.
Now if water can also drain away somewhere else then the level of flooding will be a balance between the rate that water is flowing in and flowing out.
It's the same with temperature, heat will flow from the hot to cold until the coldis the same temperature, but at the same time it will also flow from the colderobject away to anything colder. If you wait long enough it will reach an equilibrium which just depends on the rate of heat flowing in and out.

 

[Niles]

I know this thread is old, but I thought about this again, and then I remembered this thread.

I have a question to my post #1 (and the subsequent answer). I guess the answer to this question lies in conservation of energy.

Let's say that in order for the hotplate to have a temperature of 400 K for 1 hour, it must use X Joules. Then the frying pan will acquire X Joules, assuming none is lost to the surroundings. Then how do we know that X Joules will make the frying pan 400 K hot? Doesn't this depend on the size and material of the frying pan?

 

[mgb_phys]

You normally assume the hot plate is connected to an energy supply and so can maintain it's temperature.

 

[Niles]

My problem is that I can't see why it is (otherwise than just intuitively) that when we have an object of temperature 400 K (it is maintained at this temperatuer), then other objects in contact with it will also be max. 400 K. Why is this?