Convection and radiation · Physics Class 11–12 | StemPy Lab
Course 10.3·Lesson 2 of 3
Convection and radiation
In convection, a warmed fluid rises and carries heat with it, as in sea breezes and boiling pans. Radiation is heat carried by electromagnetic waves, even through a vacuum. A body at T radiates P=eσAT4 (Stefan's law), most strongly at λm=Tb
about 25 min1 simulation2 practice questions1 Python program4 questions to check yourself
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Convection
Warm the bottom of a pan of water. The warmed water expands, becomes less dense, and rises; cooler water sinks to take its place. The moving fluid carries the heat: this is convection.
Two drawings of convection. On the left, a beaker of water that is heated at the middle of the bottom. A red arrow shows the warm water that rises in the middle. Blue arrows show the cooler water that goes down at the two sides and comes back to the bottom. On the right, a sea breeze. The land is warm in the daytime, and the air above it rises. Cooler air from the sea moves in near the ground to take its place, and the air high up moves toward the sea.
Natural convection is driven by differences of density: sea breezes by day, land breezes by night, the wind systems of the Earth.
Forced convection uses a fan or a pump: a car's radiator, a room heater with a fan, blood carrying heat round the body.
Radiation
The Sun warms us across empty space. Every body gives out thermal radiation, electromagnetic waves, and it needs no material to travel.
Stefan's law: a body of area A and emissivity e (between 0 and 1; 1 for a perfect black body) at a kelvin temperature T radiates
P=eσAT4,σ=5.67×10−8W m−2K−4
It also absorbs radiation from its surroundings at T0, so its net loss is eσA(T4−T04).
Wien's law: the radiation is strongest at a wavelength
λm=Tb,b=2.90×10−3m K
A graph of the power that a black body emits at each wavelength, from 0 to 3.5 micrometres, for four temperatures, 3000, 4000, 5000 and 6000 kelvin. Each curve rises to a peak and then falls. A hotter body has a much higher peak, and the peak is at a shorter wavelength. A dashed line joins the peaks, and it follows Wien's law, lambda max times T equal to 2.9 times 10 to the power minus 3 metre kelvin. The visible range, 0.4 to 0.7 micrometre, is shaded.
You should find that twice the temperature gives sixteen times the power, and that the strongest wavelength reaches visible light only above about 4000K.
Kirchhoff's law: a surface that absorbs a wavelength well also emits it well. A dull black surface is the best absorber and emitter; a shiny one the poorest.
Watch out. Stefan's and Wien's laws use kelvin. A body at 27∘C is at 300K.
A worked example
A radiator panel of 1.2m2, emissivity 0.90, is at 60∘C in a room whose walls are at 20∘C. How much heat does it lose by radiation?
Kelvin.T=333K, T0=293K.
Net loss.0.90×5.67×10−8W m−2K−4×1.2m2×((333K)4−(293K)4)=302W.
Strongest wavelength.333K2.90×10−3m K=8.7μm, in the infrared.
Practise with new numbers
Try it in Python
The program works out the radiator panel of the example.
Remember these
Convection: a moving fluid carries the heat.
Stefan: P=eσAT4; net eσA(T4−T04).
Wien: λmT=2.90×10−3m K.
Good absorbers are good emitters.
Check yourself
Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.
A body radiates most strongly at 10μm. What is its temperature?
Why does a room heater warm the whole room though it is in one corner?
The kelvin temperature of a star's surface is tripled. By how many times does each square metre radiate more?
Why are houses in hot countries often painted white?
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