MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Radiation Page 1

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1.

 The different modes of transfer of thermal energy are: (i) conduction (ii) convection (iii) radiation

Radiation is the mode of transfer of thermal energy in the form of electromagnetic waves. Energy, thus, transferred is referred to as radiant energy or radiation.

• Transfer of energy by electromagnetic waves
• No material medium needed
• Possesses properties of light like reflection, refraction, interference, rectilinear propagation and polarisation
• Velocity of radiation in air c = 3 × 108 m/s
• Wavelength greater than that of red colour; lies in the infrared region of the electromagnetic spectrum. Wavelength ~ 10-6 m to 10-3 m

Coefficient of Absorption: The ratio of the quantity of radiant energy absorbed by a body per unit area per unit time to the total quantity of radiant energy incident upon it per unit area per unit time is called the coefficient of absorption.

Q = quantity of incident radiant energy per unit area per unit time.
Qa = quantity of energy absorbed by body per unit area per unit time.

 Coefficient of absorption a = Qa Q

or absorptive power or absorptivity

Coefficient of Reflection: The ratio of the quantity of radiant energy reflected by a body per unit area per unit time to the total quantity of radiant energy incident upon it per unit area per unit time is called the coefficient of reflection.

Q = quantity of incident radiant energy per unit area per unit time.
Qr = quantity of energy reflected by the body per unit area per unit time.

 Coefficient of reflection r = Qr Q

(or reflective power or reflectivity)

Coefficient of Transmission: The ratio of the quantity of radiant energy transmitted by a body per unit area per unit time to the total quantity of radiant energy incident upon it per unit area per unit time is called the coefficient of transmission.

Q = quantity of incident radiant energy per unit area per unit time.
Qt = quantity of energy transmitted by the body per unit area per unit time.

 Coefficient of transmission t = Qt Q

(or transmissive power or transmissivity)

Relation between 'a', 'r' and 't'

Let Q be the total quantity of radiant energy incident on a body.
Qa, Qr, Qt are the quantities of energy absorbed, reflected and transmitted by the body, respectively.
Then
Qa + Qr + Qt = Q

 \ Qa + Qr + Qt = Q Q Q Q Q

\ a + r + t = 1

Diathermanous Body
is a body through which heat radiation can pass (diathermic or diathermal bodies). Example: Quartz, iodine, hydrogen, oxygen, etc.

Athermanous Body is a body through which heat radiation cannot pass through.
Example: Moist air, water, wood, etc.

The coefficient of transmission of these bodies is zero (t = 0).

2

Black Body, Emissivity

Emissive Power (E): The quantity of radiant energy emitted per unit time per unit area of a body at a given temperature is called the emissive power (E) of the body at that temperature.

The emissive power of a body depends on:
(i) nature of the surface of the body
(ii) temperature of the body

 E = 1 dQ SI unit: Joule or Watt A dt m2 - sec m2

Black Body
A body which absorbs all the radiant energy incident upon it and reflects or transmits none is called a perfectly black body.

• It absorbs all incident energy. \ a = 1
• It does not reflect or transmit heat. \ t = 0, r = 0
• At a given temperature, emissive power (Eb) of a black body is greater than the emissive power (E) of any other body. (Eb > E)
• No perfectly black body exists.
• Practical black body - Lamp black or platinum black
- (absorbs 95% - 98% of the incident radiant energy).

Coefficient of Emission or Emissivity: The ratio of the quantity of radiant energy emitted per unit time per unit area of a body at a given temperature to the quantity of radiant energy emitted per unit time per unit area of a perfectly black body at the same temperature is called the coefficient of emission or emissivity of the body.

E = Emissive power of a body
Eb = Emissive power of a black body

 Emissivity e = E Eb

\ for a perfectly black body e = 1

3

Prevost's Theory of Heat Exchanges

Every material body, at any temperature above absolute zero, radiates heat to the surroundings and at the same time absorbs heat from the surroundings.

• The rate of emission of heat by a body depends upon its absolute temperature.
• The rate of emission of heat by a body does not depend upon the temperature of its surroundings.
• A body at a higher temperature than the surroundings radiates heat at a faster rate than it absorbs.
\ It loses heat and its temperature falls.
• A body which is at a lower temperature than the surroundings absorbs heat at a faster rate than it radiates.
\ It gains heat. Its temperature rises.
• In the case of thermal equilibrium, the process of radiation and absorption continue to take place. The rate of heat radiated in unit time by the body equals the rate of heat absorbed in unit time. Hence, there is no net loss or gain of heat. Its temperature is unchanged.

4

At a given temperature, the ratio of the emissive power of a body to its absorptive power is constant and is equal to the emissive power of a black body at the same temperature.

 E = Eb a

 But E = e    \ a = e Eb

\ Alternative statement of Kirchhoff's law: At any given temperature, the emissivity of a body is equal to its coefficient of absorption.

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