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 )
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 eλ. 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 (eλ) to the total emissive power of a perfectly
black body (Eλ) at that temperature.
Emissivity ε = eλ / Eλ
