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 . 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

A body radiates energy at a rate P . The intensity of radiation at a distance d from the body is given by I = P 4 × π × d 2 .State the assumption made to derive this result.

To attain the expression for intensity of radiation emitted by a point source , we have to consider a sphere around the source and then calculate the expression of intensity on that surface. In this process we have to assume the radiation is emitted uniformly in all directions around the source.

E M B I B E

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

EASY

Diploma

IMPORTANT

Earn 100

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.

Important Questions on Energy Production

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}}

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

. The intensity of radiation at a distance

d

from the body is given by

I = \frac{P}{4 \times π \times d^{2}}

.State the assumption made to derive this result.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 35

The graph shows the variation of the intensity of the radiation emitted with wavelength by the black body.

Question Image

Determine the temperature (in kelvin) of the black body.

MEDIUM

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 35

The graph shows the variation with wavelength of the intensity of the radiation emitted by the black body.

Question Image

Copy the diagram, and on the same axes, draw a graph to show the variation with wavelength of the intensity of radiation emitted by a black body of temperature $600 K$

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 8 - Energy Production>Test yourself>Q 36

Define the term albedo.