Conduction, convection and radiation
Conduction
Heat can travel in three ways: conduction, convection and radiation. Let us start with conduction.
Leave a steel spoon in a pot of hot dal. Soon the handle gets hot too. Heat has travelled along the spoon, although the spoon itself has not moved.
In conduction, energy passes from particle to particle through a body, from its hot part to its cold part. In metals, free electrons carry most of it, which is why metals conduct heat so well.
Take a rod of length L and cross-section A, with its ends held at temperatures T C and T D. Wrap its sides in insulation, so heat can only flow along it.
Once things settle into a steady state, the temperature falls evenly along the rod, and a steady heat current H flows from the hot end to the cold end.
H is proportional to the area and to the temperature difference, and inversely proportional to the length. H equals K A, times T C minus T D, over L.
K is the thermal conductivity of the material, in watts per metre per kelvin. Silver has 406 and copper 385, but glass has only about 0.8, and wood about 0.12.
That is why cooking pots are made of metal, often with a copper base, while their handles are wood or plastic. And still air, trapped in a woollen sweater, is a very poor conductor that keeps you warm.
Now join a steel rod and a copper rod end to end. In the steady state the same heat current must flow through both, so the poorer conductor needs a steeper temperature drop.
An NCERT example: steel, 15 centimetres long, with twice the area of a 10 centimetre copper rod. The steel end is at 300 degrees and the copper end at 0. Setting the two heat currents equal gives a junction temperature of about 44 degrees.
Try it: heat through a rod
- This is the NCERT steel–copper example: the junction settles at about 44 °C.
- The graph is lined up with the rods. Its slope is steeper where K A is smaller.
- Untick “Join a second rod” to test H = KA(T_C − T_D)/L for one rod.
- Try glass or wood to see how small H becomes.
Convection
In liquids and gases, heat has a faster way to travel: the fluid itself moves, carrying the heat with it. This is convection.
Heat a pan of water from below, and drop in a few crystals of potassium permanganate. Watch the purple streaks rise in the middle and sink at the sides.
The water at the bottom warms, expands and becomes less dense. The denser, colder water sinks under gravity and pushes the warm water up. A loop of moving water forms: a convection current.
When the flow happens on its own, because of differences in density, it is natural convection. Gravity plays an essential part; without it, there would be no natural convection.
When a pump or a fan pushes the fluid along, it is forced convection. A fan heater, the cooling system of a car engine, and the blood pumped round our body are examples.
Natural convection drives sea breezes. By day the land heats up faster than the sea. Warm air rises above the land, and cooler air from the sea flows in to take its place.
At night the land cools faster. Now the air over the sea is warmer, so the flow reverses, and a land breeze blows out to sea.
On a much larger scale, convection drives the trade winds. Hot air rises near the equator, and cooler air flows in from the north and the south to replace it.
Radiation and blackbodies
Between the Sun and the Earth is almost empty space, so neither conduction nor convection can carry heat across. Yet sunlight warms us. This third way is radiation.
Every body emits energy as electromagnetic waves, which travel at the speed of light and need no medium. Very hot bodies glow; cooler ones emit mostly invisible infrared.
A body that absorbs all the radiation falling on it is called a blackbody. It is also the best possible emitter. Dark surfaces come close, which is why we wear light-coloured clothes in summer.
Watch an iron rod heated in a flame. First it glows dull red, then orange, then yellowish white. As it gets hotter, more of its radiation shifts to shorter wavelengths.
Plot the energy a blackbody radiates against wavelength. The curve rises to a peak and falls away. As the temperature goes up, the peak moves to shorter wavelengths.
Wien’s displacement law says λ m times T is a constant, b, equal to 2.9 × 10⁻³ metre kelvin. The Sun’s spectrum peaks near 480 nanometres, so its surface is at about 6000 kelvin.
The total power radiated climbs very steeply with temperature. Stefan’s law: H equals e σ A T to the fourth, where σ is 5.67 × 10⁻⁸ watts per square metre per kelvin to the fourth.
Here e is the emissivity: 1 for a perfect blackbody, and less for real surfaces. Double the kelvin temperature, and the power radiated goes up sixteen times.
A body also absorbs radiation from surroundings at temperature T s. So its net rate of loss is e σ A, times T to the fourth minus T s to the fourth.
The Earth’s surface, warmed by the Sun, radiates infrared. Gases like carbon dioxide, methane and water vapour absorb part of it and send some back down, keeping the Earth warmer. This is the greenhouse effect.
Without it, the Earth’s average surface temperature would be about minus 18 degrees Celsius. But burning fossil fuels keeps adding these gases, trapping more heat and causing global warming.
Try it: blackbody spectrum
- Raise T and watch the peak slide to shorter wavelengths: λₘT = 2.9 × 10⁻³ m K.
- Tick “Show a reference curve” to compare two temperatures.
- Doubling T multiplies the power σT⁴ by 16.
Red star, blue star
Through a telescope, one star looks reddish and another looks bluish white. Treating both as blackbodies, which statement is correct?
- The red star is hotter, because red means hot
- The bluish-white star is hotter, because its radiation peaks at a shorter wavelength
- They are at the same temperature; colour depends only on size
- The red star is hotter, because red light has a longer wavelength
Answer
B. Wien’s law, λₘT = b, says the hotter the body, the shorter its peak wavelength. A bluish-white star peaks towards the blue end, so it is hotter than a red star, whose peak is towards the red or infrared. A heated iron rod also goes red → orange → white as it gets hotter.
Iron and brass bars
An iron bar (K = 79 W m⁻¹ K⁻¹) and a brass bar (K = 109 W m⁻¹ K⁻¹), each 0.1 m long with area 0.02 m², are joined end to end and lagged. The free iron end is at 373 K and the free brass end at 273 K. What is the temperature of the junction in the steady state?
- 315 K
- 323 K
- 331 K
- 300 K
Answer
A. In the steady state the same H flows through both bars. With equal L and A: 79(373 − T) = 109(T − 273). So 29 467 + 29 757 = 188T, giving T ≈ 315 K. The junction is closer to the cold end because brass, the better conductor, needs a smaller temperature drop. (H = 79 × 0.02 × 58 / 0.1 ≈ 916 W.)
Summary
- Conduction (steady state):
H = K A (T_C − T_D)/L - Wien’s displacement law:
λₘ T = b = 2.9 × 10⁻³ m K - Stefan’s law:
H = e σ A T⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ - Net loss to surroundings:
H = e σ A (T⁴ − Tₛ⁴)
- Conduction: particle to particle, no bulk motion. Metals conduct well; air, wood and glass are poor conductors.
- Convection: the fluid moves and carries heat. Natural convection needs gravity; forced convection uses a pump or fan.
- Radiation needs no medium. A blackbody is the perfect absorber and emitter; hotter bodies peak at shorter wavelengths and radiate as T⁴.
- Greenhouse gases absorb the Earth’s infrared and send part of it back, keeping the Earth warm; adding more of them causes global warming.