Heat Transfer Class 11 Notes

Mechanism Of Heat Transfer

·  Convection :
             Heat transfer in a gas or liquid by the circulation of currents from one region to another. A current in a fluid that results from convection, The Pacific Plate is floating, propelled by convection currents deep in the mantle.

Quantitative Explanation of Heat Flow
 let a metal of original length ‘x’ and uniform cross-sectional area ‘A’.The ends of the rod are maintained at temperatures ø₁ and ø₂, such that, ø₁ > ø₂. It has experimentally observed that in the steady-state, the rate of heat (Q/t) is ,
       a) directly proportional to the cross-section area ‘A’,
             i.e. (Q/t) 𝞪 A……………………..1
        b) directly proportional to the temperature difference of two rods,
             i.e. ( Q/t ) 𝞪 ( ø₁ – ø₂ )…………2
        c) inversely proportional to the distance ‘x’ between the rods,
              i.e. ( Q/t)  𝞪   ( 1/x) ……………3
combining Eqn (1),(2),(3),
         Q/t 𝞪  { A(ø₁ – ø₂ )} / x
         Q/t = {k A(ø₁ – ø₂ )} / x………………..4
               where, k is called coefficient of thermal conductivity


Concept of temperature Gradient
 The temperature gradient is defined as the rate of change of temperature with the distance between the surface.
   i.e. (dø/dx) = (ø₁ – ø₂₎ / ( x₁ – x₂ )

          

·  Convection:
   It is defined as that mode of transmission of heat by which heat travels from one part of a body to another by the actual motion of the heated particles of the body. Land breeze and see-breeze are formed due to convection.
·       Radiation:
     The process of heat transmission in the form of electromagnetic waves is called radiation. Radiation does not require any medium for propagation. It propagates without heating the intervening medium. The heat energy transferred by radiation is called energy. The heat from the sun reaches the earth by radiation.

 

 Distinguish between conduction, convection, and radiation:

Conduction	Convection	Radiation
Material medium is essential.	Material medium is also essential.	Material medium is not essential.
Transfer of heat can be in any direction.	Transfer of heat can be vertically upward.	Transfer of heat can be in any direction in straight line.
Molecules do not leave their mean positions.	Molecules move from one place to another place.	Electromagnetic waves move from one place to another place.

 

Perfect black body:

A perfect black body is one that absorbs heat radiation of all wavelengths that fall upon it. Such a body neither reflects nor transmits the incident heat radiation and hence the body appears black. But when heated, it emits radiation which is called black radiation. The wavelength range of emitted radiation is independent of the material of the body and depends on the temperature of the blackbody.

 In practice, no material has been found to absorb all incoming radiation, but carbon in its graphite form absorbs all but about 3%. It is also a perfect emitter of radiation. At a particular temperature, the black body would emit the maximum amount of energy possible for that temperature. This value is known as black body radiation. It would emit at every wavelength of light as it must be able to absorb every wavelength to be sure of absorbing all incoming radiation. The maximum wavelength emitted by a black body radiator is infinite. It also emits a definite amount of energy at each wavelength for a particular temperature, so standard black body radiation curves can be drawn for each temperature, showing the energy radiated at each wavelength. All objects emit radiation above absolute zero. 

 Stefan’s law of black body radiation(Stefan-Boltzman Law):

It states that the total amount of heat energy radiated per second per unit area of a perfectly black body is directly proportional to the fourth power of its absolute temperature.

If E be the heat energy radiated per second per unit area by a black body of absolute temperature T₁ Then,
T ∝ σT⁴ ….........1
 If the body is not perfectly black, then
E = e σ T⁴ ...............…..2

 Where,

E is the emissivity of the body.
The heat energy radiated per second or power radiated by a body is given by,

  P=E∗A
P = eσT⁴∗A……….3

When a black body of absolute temperature T₁ is placed inside an in the closer of absolute temperature T₀, Then black body radiates as well as absorbs heat energy.

The heat energy radiated per second per unit area by the black body is,

Eemit = σT1⁴………4

 

The heat energy absorbed per second per unit area by the black body is given by,

Eabs = σTo⁴………5

 Hence, Net heat energy radiated per second per unit area by the body is

                         Enet = Eemit − Eabs

                                =σT1⁴−σTo⁴

                              =σ(T1⁴−To⁴)…………6

 If the body is not perfectly black, then

Enet = σe (T1⁴−To⁴)…………7
This is the required expression

 

Reflectance or Reflecting Power
     The ratio of the number of thermal radiations reflected by a body in a given time to the total amount of thermal radiations incident on the body in that time is called reflectance or reflecting power of the body. It is denoted by r.

Absorptance or Absorbing Power
    The ratio of the number of thermal radiations absorbed by a body in a given time to the total amount of thermal radiations incident on the body in that time is called absorptance or absorbing power of the body.
It is denoted by a.

Transmittance or Transmitting Power
The ratio of the number of thermal radiations transmitted by the body in a given time to the total amount of thermal radiations incident on the body in that time is called transmittance or transmitting power of the body.
It is denoted by t.

Relation among reflecting power, absorbing power, and transmitting power
r + a + t = l
If body does not transmit any heat radiations, then t = 0|
∴ r + a = 1
(i) r, a and t all are the pure ratio, so they have no unit dimension.
(ii) For perfect reflector, r = 1, a = 0 and t = O.
(iii) For perfect absorber, a = 1, r = 0 and t = 0 (perfect black body).
(iv) For perfect transmitter, t = 1, a = 0 and r = O.

Emissive Power
         The emissive power of a body at a particular temperature is the total amount of thermal energy emitted per unit time per unit area of the body for all possible wavelengths. It is denoted by e_λ. Its SI unit is ‘joule sec^-l metre^-2 or ‘watt-metre^-2‘. Its dimensional formula is [MT^-3].

 

Emissivity
       Emissivity of a body at a given temperature is equal to the ratio of the total emissive power of the body (e_λ) to the total emissive power of a perfectly black body (E_λ) at that temperature.

Emissivity  ε = e_λ / E_λ