Note on Heat Radiation and Surface Temperature of the Sun

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Prevost's Theory of Heat Exchange

According to this theory, every body radiates heat radiation continuously at all temperatures. Suppose a body K is at the higher temperature than the surroundings and it will radiate more quantity of heat to the surroundings. It will absorb less heat from the surroundings. When the temperature of the body falls and makes thermal equilibrium with surrounding then the amount of heat radiated by body K is equal to heat absorbed from the surrounding. So, the quantity of heat radiated per unit area of the surface in unit time depends the temperature of the body and not on the surroundings.

Applications of Heat Radiation

  1. White coloured are preferred in summer and dark coloured clothes in summer. As white clothes reflect back heat radiation and black cloth absorb heat radiation.
  2. Polish reflectors are used in electric heaters to reflect maximum heat in the room.
  3. Hot pipes and radiators used in rooms are painted black because they can radiate the maximum amount of heat to the room.
Detection and Measurement of Heat Radiation

Various instruments are used to detect and measure the thermal radiation. Some of them are bolometer and thermopile

Bolometer

(a) Platinum strip (b) wheat stone bridge
(a) Platinum strip (b) wheat stone bridge

It is based on the principle of Wheatstone bridge. It consists of a thin foil platinum strips which are made a grid-type structure as shown in the figure. Four grids are joined to form the arms of the Wheatstone bridge as shown in the figure.

The radiation falls on the bolometer, all the grids have same resistance, so

$$R_1 = R_2 = R_3 = R_4$$

$$\frac {R_1}{R_2} = \frac {R_3}{R_4}$$

The bridge is balanced and galvanometer shows null deflection. When radiation falls on grid 1 and 4, their resistances increases along with their product.but the product of R2R3 remains unchanged, we have

$$R_1R_2 >R_3 R_4$$

$$\frac {R_1}{R_2} >\frac {R_3}{R_4}$$

Then, the bridge becomes unbalanced and the galvanometer shows a deflection which indicates the presence of radiation. The magnitude of deflection is proportional to the radiation falling upon the bolometer. The bolometer is usually enclosed in a glass in a glass bulb evacuated to a low pressure which increases the sensitivity of the instrument.

Thermopile

A Thermopile
A Thermopile

Thermopile is based on the principle of Seebeck's effect which states that when two junctions of the thermocouple are kept at a different temperature, emf is generated.

A number of thermocouples are joined in series which are made of antimony and bismuth in thermopile. The free ends of the thermocouple are joined to a galvanometer as shown in the figure. In the series combination of thermocouples, the emf generated is multiplied so that sensitivity of the system increases. The radiation falls on a series of junctions while other series of junctions are protected from the radiation that is covered with felt.

The face of hot junctions is blackened to absorb most of the radiation falling on it. There is the difference in temperature between them and the current flows in the circuit which is shown by the galvanometer. The radiation is detected by observing the deflection in the galvanometer.

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Heat radiated by the sun.

Determination of Temperature of the Sun

Stefan's law of black body radiation can be used to determine the temperature of the sun. We know that the sun is radiating heat radiation in all direction.

The measurement of heat received by perfectly black body placed on the earth's surface per unit area per second, the area being perpendicular to the direction of sun's ray is known as solar constant.

Let us consider the sun as a perfectly black body. If 'T' is the absolute temperature of the sun, then the total energy emitted per second by the sun is given by emitted per second by the sun is given by

$$E = 4\sigma T^4 \times A $$

$$E = \sigma T^4 \times 4\pi r^2\dots (i)$$

where, 'r' is the radius of the sun. the energy emitted by the sun is spread all around the sun and is received by a sphere of radius 'R'. Hence, energy falling in the sphere of radius 'R' is given by

$$E' = S \times Area$$

$$E' = S \times4 \pi R^2 \dots (ii)$$

So, we must have,

$$E = E'$$

$$\sigma T^4 \times 4\pi r^2 = S \times 4 \pi R^2$$

$$T^4 = \frac {S \times R^2}{\sigma r^2}$$

$$T = \left ( \frac{SR^2}{r^2\sigma }\right)^{1/4}$$

where,

Solar Constant (S) = 1400 watt/m^2

Radius of the sun (r) \(= 7\times 10^8\)

Distance of the sun from the earth (R) \(= 1.5 \times 10^{11} m\)

Stefan's Constant \(\sigma = 5.67 \times 10^{-8} watt m^2 k^{-4} \)

on solving

$$\therefore T = 5800 K$$

According to the theory of heat exchange, every body radiates heat radiation continuously at all temperatures. 

Bolometer is based on the principle of Wheatstone bridge.

Thermopile is based on the principle of Seebeck's effect which states that when two junctions of thermocouple are kept at different temperature, emf is generated.

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