Assume that the distance d between the sun and the earth decreases. Then the Earth's average temperature will go up. The fraction of the power radiated by the Sun that is received on Earth is proportional to 1 d 2 , the power radiated by the earth is proportional to T 4 . Deduce the dependence of the temperature T of the earth is proportional to the distance between the sun and the earth.

The power radiated by earth is proportional to the power received from the sun, and since the power received from the sun is inversely proportional to d 2 , so will be the power radiated by the earth. Now, the power radiated is described as ( σ A T 4 ) ,hence we can write the following, σ A T 4 ∝ 1 d 2 since σ , A are constants, then T 4 ∝ 1 d 2 T ∝ 1 d

Assume that the distance d between the sun and the earth decreases. Then the Earth's average temperature will go up. The fraction of the power radiated by the Sun that is received on Earth is proportional to 1 d 2 , the power radiated by the earth is proportional to T 4 .The expected rise in temperature if the distance decreases by 1 . 0 % .Take the average temperature of the earth to be 288 K .

We can deduce that T ∝ 1 d T is the temperature of the earth, d is the distance between the sun and the earth. Using the error propagation rule in case of powers we can write, ∆ T T = 1 2 ∆ d d Given T = 288 K , ∆ d d = 1 . 0 % ∆ T = 1 2 0 . 01 × 288 K = 1 . 44 K

Estimate the intensity of radiation emitted by a naked human body of the surface area 1 . 60 m 2 , temperature 37 ∘ C , emissivity 0 . 90 at a distance of 5 . 0 m from the body. Given σ = 5 . 67 × 10 - 8 W / m 2 . K 4

The power of the radiation emitted by a body is given by the formula : P = ε σ A T 4 Given surface area 1 . 60 m 2 , temperature 37 ∘ C , emissivity 0 . 90 distance 5 . 0 m and σ = 5 . 67 × 10 - 8 W / m 2 . K 4 Putting values, P = 5 . 67 × 10 - 8 × 0 . 9 × 1 . 6 × ( 37 + 273 ) 4 = 754 W . Considering a sphere of radius d = 5 . 0 m , with the human body at the centre, so the intensity of radiation at the surface of the sphere will be: I = P A The area of a sphere is 4 πd 2 I = 754 4 × π × 5 2 = 2 . 4 W m - 2

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Diploma

IMPORTANT

Earn 100

By what factor does the rate of radiation from a body increase when the temperature is increased from $50^{\circ} C t o 100^{\circ} C$ .

Important Questions on Energy Production

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 30

The graph shows variation with wavelength of the intensity of radiation emitted by two bodies of identical shapes.

Question Image

Explain why the temperature of the two bodies is the same?

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 30

The graph shows variation with wavelength of the intensity of radiation emitted by two bodies of identical shapes.

Question Image

If the upper line corresponds to a black body.Calculate the emissivity of the other body.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 31

The total power radiated by a body of area

5.00 k m^{2}

and emissivity

0.800

1.35 \times 10^{9} W

. Assume that the body radiates into a vacuum at temperature

0 K

.Calculate the temperature (in Kelvin) of the body.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 32

Assume that the distance

d

between the sun and the earth decreases. Then the Earth's average temperature will go up. The fraction of the power radiated by the Sun that is received on Earth is proportional to

\frac{1}{d^{2}}

, the power radiated by the earth is proportional to

T^{4}

. Deduce the dependence of the temperature

T

of the earth is proportional to the distance between the sun and the earth.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 32

Assume that the distance

d

between the sun and the earth decreases. Then the Earth's average temperature will go up. The fraction of the power radiated by the Sun that is received on Earth is proportional to

\frac{1}{d^{2}}

, the power radiated by the earth is proportional to

T^{4}

.The expected rise in temperature if the distance decreases by

1.0 %

.Take the average temperature of the earth to be

288 K

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 33

Determine the term intensity in the context of radiation.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 33

Estimate the intensity of radiation emitted by a naked human body of the surface area $1.60 m^{2}$ , temperature $37^{\circ} C$ , emissivity $0.90$ at a distance of $5.0 m$ from the body.

Given $σ = 5.67 \times 10^{- 8} W / m^{2 .} K^{4}$

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 34

A body radiates energy at a rate

P

. Deduce that the intensity of radiation at a distance

d

from the body is given by

I = \frac{P}{4 \times π \times d^{2}}

By what factor does the rate of radiation from a body increase when the temperature is increased from 50∘C to 100∘ C.

Important Questions on Energy Production

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By what factor does the rate of radiation from a body increase when the temperature is increased from $50^{\circ} C t o 100^{\circ} C$ .