Heat & Thermodynamics (Thermometry)
Scales of Temperature:
There are three types of scale of temperature which are as given here...
The Celsius Scale:
This scale was devised by Anders Celsius in the year 1710. The interval between the lower fixed point and the upper fixed point is divided into 100 equal parts. Each division of the scale is called one degree centigrade or one degree Celsius (1°C). At normal pressure, the melting point of ice is 0°C. This is the lower fixed point of the Celsius scale. At normal pressure, the boiling point of water is 100°C. This is the upper fixed point of the Celsius scale.
The Fahrenheit Scale:
This scale was devised by Gabriel Fahrenheit in the year 1717. The interval into 180 equal parts. Each division of this scale is called one degree Fahrenheit (1°F). On this scale, the melting point of ice at normal pressure is 32°F. This is the lower fixed point. The boiling point of water at normal pressure is taken as 212°F. This is the upper fixed point.
.The Reaumer Scale:
This scale was devised by R.A. Reaumer in the year 1730.
The interval between the lower and the upper fixed points is divided into 80 equal parts. Each division is called one degree Reaumer (1°R). On this scale, the melting point of ice at normal pressure is 0°R. This is lower fixed point. The boiling point of water at normal pressure is 80°R. This is the upper fixed point.
.Conversion of Temperature:
In order to convert temperature from one scale to another, following relation is used.
.Constant Volume Gas Thermometer:
Suppose the pressure of the gas is p0when the bulb is placed in melting ice (ice point) and it is p100
when the bulb is placed in a steam bath (steam point). We assign 0°C to the temperature of the ice point and 100°C to the steam point. The temperature t corresponding to a pressure p of the gas is defined by
.Constant Pressure Thermometer
Volume of the bulb = V
Volume of the mercury taken out = v'
Temperature of the ice bath = T0
Temperature of the heat bath = T
Platinum resistance Thermometer:
Resistance at the temperature t = Rt
Resistance at the ice point = R0
Resistance at the steam point = R100
Electrical resistance of a metal wire increases gradually and uniformly over a fairly wide range of temperature has been made use of in electrical resistance thermometers. The variation of the resistance thermometers. The variation of the resistance of a metal wire with temperature may be represented by the following approximate relation.
Rt= R0(1 + at) Here, Rtis the resistance at t°C, R0
is the resistance at 0°C and a is the temperature coefficient of resistance. The value of a depends upon the nature of material of the wire.
. Comparison of Different Thermometers:
i.) Platinum Resistance:
can be used between - 180ºC to 1150ºC, Accurate and has a wide range, not suitable for varying temperatures, best thermometer for small steady temperature difference, used as standard between - 183ºC and 630°C.
can be used between - 250°C to 1150°C, temperature is measured in terms of Emf. (electro motive force) between the junction of different metals at different temperatures, fast response because of low heat capacity, has a wide range, can be used for remote reading using long leads, accuracy is lost if emf is measured using a moving coil volt meter, best thermometer for varying temperatures, can be made direct reading by calibrating galvanometer, used as standard between 630°C and 1063°C.
iii.) Radiation Pyrometer:
used for a temperature above 1000°C, colour of radiation emitted by a hot body is used as the property, does not come into contact when temperature is measured, it is cumbersome, a does not give direct reading, it can be used only for high temperatures, used as standard above 1063°C.
Heat is a form of energy which flows between two bodies due to difference in their temperatures.
Heat is the cause and temperature is one of the several effects.
Heat energy is transient form of energy. An isolated body at a temperature will not posses heat energy but possess internal energy.
Heat is a scalar. Units of Heat
a.) S I unit is joule. b) practical unit of heat in C.G.S. is 1 calorie 1 cal = 4.186 J
Dimensional formula : ML2T-2.
Calorie : It is the amount of heat required to raise the temperature of 1 gm of water through 10C.
Mean calorie (or) standard calorie: The amount of heat required to raise the temperature of 1 gm of water from 14.50C to 15.50C.
Specific heat : The amount of heat required to raise the temperature of unit mass of a substance to raise its temperature through 10C is called its specific heat (s).
specific heat S =
Dimensional formula is M°L2T-2K-1S I unit is J kg-1K-1
CGS unit is cal gm-1°C-1
a.) Specific heat for solids and liquids depends upon nature of substance and does not depend upon mass, volume and heat given to the substance. (It is constant for given substance)
b.) Specific heat for gases depends upon degree of freedom, type of process.
c.) Specific heat slightly increases with increase of temperature.
d.) Among solids, liquids and gases, specific heat is maximum for gas.
Of all gases, H2
has highest specific heat.
e.) In liquids specific heat is minimum for mercury. Hence it is used as thermometric liquid.
f.) Specific heat is known as thermal inertia of the body.
The body having higher specific heat cools very slowly and gets heated up very slowly. The body having lower specific heat cools very fast and gets heated up very fast.
i.) Among liquids specific heat is maximum for water. Due to it, water absorbs (or) gives out more heat than any other substance for the same change in temperature. Hence it is used in radiators and hot water bags.
. Latent heat :
The amount of heat energy either absorbed or liberated by unit mass of substance when it undergoes change of state at constant temperature is called Latent heat (or) heat of formation (L).
Cal/gam , K.cal/kg , J/kg.
During the change of state, heat energy supplied is used up in increasing the distance between the molecules, i.e. to increase the P.E. of molecule without increasing the KE and hence the temperature does not change.
The quantity of heat, taken in (or) given out by unit mass of a substance when it changes from solid to liquid state (or) liquid to solid state at constant temperature is known as latent heat of fusion.
Latent heat of fusion of ice = 80 cal/gm = 0.336 x 106J/kg
The quantity of heat taken in (or) given out by unit mass of substance when it changes from liquid to vapour state (or) vapour state to liquid state at constant temperature is known as latent heat of vaporization.
Latent heat of vaporization of water (or) latent heat of steam = 540 cal/gm =
Variation of Boiling Point with pressure:
Boiling point increases with increase of pressure..
I n a pressure cooker, cooking of rice is a quick process as water boils at a temperature above 100o
C due to increase in pressure..
Due to addition of impurities Boiling point of liquid increases..
The heating of liquid above its boiling point is called super heating and cooling of liquid below its freezing point is called super cooling. It is unstable.
Variation of melting point with Pressure:
Melting point varies with the pressure from classius - clayperon equation
The melting point of the substances which expands on melting increases with increase of pressure
Wax, Glass, Gold, Copper, Silver.
The melting point of the substances which contract on melting decreases with increase of pressure.
Ice, Cast Iron, Bismuth, Type Metal.
Addition of impurities decreases with melting point.
Triple point of Water:
The temperature and pressure at which the three states of matter coexists is known as triple point.
Triple point and phase diagram for water
OA - Ice line, OB - steam line, OC- sublimation curve
a.) Triple of water is 273.16k (0.01°C) at a pressure of 610.42pa (4.6 mm of Hg).
b.) Change of state from solid to directly vapour is called sublimation. eg. iodine, camphor etc.
c.) Change of state from vapour directly to solid is called Hoar Frost.
d.) If pressure at triple point is increased then water exists in liquid form. If pressure is decreased, it converts to steam.
Ice at 0°C is much cooler than the water at 0°C.
(1) Steam at 100°C produces more severe burns than water at 100°C.(2) It is not possible to freeze water using ice alone at 0°C.(3) It is not possible to boil water using steam alone at 100°C.
Kinetic Theory of Gases and Thermodynamics:
Internal energy : (U)
a.) U = PE + KE of molecules.
b.) KE of molecule =
where f = degree of freedom, K is Boltzmann constant.
c.) PE of molecules depends upon intermolecular distance (ro).
d.) when ro distances increases or decreases, PE increases.
e.) In case of ideal gases PE of molecules = 0. There by U depends on KE of gas molecules in turn depends on temperature.
f.) In case of real gases U depends upon temperature and volume. Hence is absolute U can not be determined.
g.) For gaseous sample, for any process* dU = change in internal energy = nCvdT* dU purely depends upon temperature.
h.) Two ways of increasing internal energy. By transferring heat and By performing work.
i.) In the process of change of state, internal energy of system increases.
j.) Internal energy is independent of pressure and volume.
k.) The inter energy of water molecules at 0°C is greater than that of ice molecules at 0°C
l.) When unit mass of a substance expands from a volume of V1 to volume V2
at constant temperature, then the change in internal energy is
dU = [L - P (V2- V1)]
m. For an Ideal gas, Change in internal energy dU = 0 for
1. Cyclic process
2. Isothermal process
n. If two systems are at the same temperature, they are said to be in thermal equilibrium.
Zeroth law of thermodynamic :
(1) If the bodies are in thermal equilibrium with a third body separately, then those two bodies are in thermally in equilibrium with each other.
(2) Zeroth law of thermodynamics corresponds to
Existence of temperature of the body
(3) If volume of a system increases in a process then work is done by the system which is +ve. If the volume of a system decreases in a process, then work is done on the system which is - ve.
(4) The amount of work done by a system as it expands (or) contracts is given by
(5) External work done during an Iso choric process is zero
(6) Internal work done : Work done by a part of gas on other part of gas
(7) P - V graph is called indicator diagram. Whose area gives work done.
(8) In a cyclic process work done is +ve if the cycle is clockwise and - ve if the cycle is anti clockwise.
I law of Thermodynamics :
The amount of heat supplied to a system (dQ) capable of doing external work is equal to sum of increase in the internal energy (dU) and external work done by system (dW)
dQ = dU + dW.
Sign convention :
1. d Q = +ve when heat supplied = - ve when heat rejected dU = +ve when temperature increases = -ve when temperature decreases dW = +ve when work is done by system. = - ve when work is done on system.
2. It is a special case of law of conservation of energy.
3. dQ = dU + Pdv
m Cp dT = m Cv dT + m R dT n Cp dT = n Cv dT + n R dT
It in another form of law of conservation of energy.
This law does not indicate the direction of heat flow.
. Specific heats of gases :
1. Amount of Heat required to raise the temperature of whole system by 1°C is Heat capacity of a gas (C)
2. Cv molar specific heat of gas at constant volume.
specific heat of a gas as constant volume.
Cp molar specific heat of gas as constant pressure.
specific heat of gas at constant pressure
units of Cp and Cvare J/mole/k units of Cp and Cvare J/kg/k
3. Relation between molar specific heat and ordinary specific heat is
C = M C (M = Molecular weight of the gas)
4. Relation between Specific heats of the gas
a) Cp- Cv= r =Cp, Cv
Specific heats per unit mass of gas
b) Cp- CV= R
R - universal gas constant.
5. Ratio of specific heats => 1
6. Value of depends on atomicity of gas
7. As atomicity of gas increases, value of decreases
For MAG -=
For DAG -
For TAG -
8. Cp & Cv in terms of
9. Number of degrees of freedom does a gas posses is
10. Based on degree of freedom
11. Fraction of the initial energy supplied that is utilised to
increase the internal energy is
12. Fraction of the initial energy supplied that is utilised to
do the external work is
. Isothermal Process:
1) Isothermal change is that change of pressure and volume when the temperature of the system remains constant.
2) It is a slow process.
3) It should be conducted in good thermally conducted vessel.
4) It follows Boyle's law. P1V1= P2V2
5) During isothermal change, internal energy remains constant. U is constant
Ex. Melting of ice, Boiling of a liquid are isothermal changes.
6) Work done in an isothermal change is given by W = 2.303 nRT log10
= 2.303 nRT log10
7) Work done depends on
a) Number of moles
c) Expansion Ratio
8) Isothermal elastic modulus = P
9) Slope of Isothermal curve
10) Fractional change in pressure
11) No two Isothermals intersect each other
. Adiabatic process :
1) Adiabatic change is that change of pressure and volume during which heat is neither given to the system, nor taken from it.
2) Temperature raises during adiabatic expansion.
3) It is a quick process.
4) Exchange of heat will not takes place between system and surroundings.
5) It should be conducted in perfectly bad conducting vessel.
6) It follows = constant ;
7) During adiabatic process, entropy remains constant. Hence it is also known as isoentropic process.
8) In adiabatic process, dQ = 0
9) In an adiabatic process
10) Work done in an adiabatic process is given by
11) Adiabatic Elastic Modulus =
12) Adiabatic Expansion of Gas is associated with decrease in pressure and temperature
13) Adiabatic compression of a gas associated with increase in pressure and temperature
14) Slope of adiabatic curve
.Slope of isothermal curve
slope of adiabatic curve > slope of isothermal curve.
.Graphs of expansion process
1. isobaric process
2. isothermal process
3. Adiabatic process
1. work done in isobaric process > isothermal > Adiabatic for same change in volume.
2. For same increase in volume, starting from same point, final pressure in adiabatic process is less than that of in isothermal process.
Graphs of compression process.
* isobaric process * isothermal process * Adiabatic process
1. work done in isobaric process > isothermal > Adiabatic process.
2. For same increase in pressure, starting from same point, final pressure in adiabatic process when compared to isothermal process.
3. Either in compression or expansion process, to produce equal change in volume of a gas, more pressure difference is required in adiabatic change.
. II law of Thermodynamics :
Planck statement :
It is impossible to construct a heat engine which can completely convert heat energy into mechanical energy without rejecting heat to surroundings.
Kelvin statement :
It is impossible to extract work from a system by cooling it below surrounding temperature. It is impossible to transfer heat energy from body at lower temperature to body at higher temperature unaided by external agency.
.Heat engine is a device which converts heat energy into mechanical work.
. Reversible and irreversible process :
(a)Reversible process :
Any process which can be made to proceed in reverse direction by variations in its conditions so that all changes occurring in the direct process are exactly reversed in the reverse process, is called a reversible process.
(b) Irreversible process :
Any process which cannot be made to proceed in reverse direction is called an irreversible process. A part of the energy of the system performs work against dissipative forces and it cannot be recovered back. A few examples of irreversible processes are, diffusion of gases, rusting of iron, sudden expansion of a gas, work done against friction etc.
. Carnot's reversible cycle:
It is a reversible engine which absorbs a heat 'Q1' from a source maintained at a constant high temperature 'T1' K and rejects a heat 'Q2' to a sink, which is maintained at a constant low temperature 'T2 'K. The efficiency '' of this engine is given by :
In terms of temperature the efficiency is given by
% Efficiency =
. Efficiency of ideal reversible engine :
(1) depends upon the temperature of the source (T1) and that of the sink (T2) ;
(2) is independent of the nature of the working substance ;
(3) is the same for all reversible engines working between the same two temperatures ;
(4) is directly proportional to the temperature difference (T1- T2) between the source and the sink ;
(5) is always less than 1 or 100% because T2can never be practically zero and hence Q2
can never be zero;
(6) is zero if the temperature of sink happens to be the same as the temperature of source.
. Types of heat engines :
Following two types of heat engines are in common use.1.
External combustion engine:
In this category of heat engines, the source of heat lies outside the engine. that is, heat is produced by burning the fuel outside the engine. Steam engine is the example of this class of heat engines.
2. Internal combustion engine:
In this category of heat engines, the source of heat lies inside the engine. that is, heat is produced by burning the fuel inside the engine. Petrol engine and diesel engine are the example of this class of heat engines.
(i) The working of steam engine is according to
in which Q1 heat is absorbed from the source and Q2
is rejected to sink. The efficiency of steam engine is given by :
(ii) Otto's PETROL ENGINE :
This engine works in FOUR STROKES which gives a reversible Ott-cycle.
. EFFICIENCY OF PETROL ENGINE:
Let Q1 be the heat generated due to the burning of the petrol. Suppose, Q 2
is the heat rejected into the atmosphere during release of the fuel mixture. Then the efficiency of the engine is
If volume of the fuel mixture at the end of the working stroke is V2
and that at the end of compression stroke is V1
, then it is found that
Where '' is the ratio of the specific heat of air at constant pressure to that at constant volume. Generally (V1/V2) is called adiabatic compression ratio. It may be denoted by ''. Then, we may write ;
Hence, equation (i) may be written as :
It is found that in practice cannot be more than 10. Because if we make more that 10 the rise in temperature during compression produces very high temperature. The petrol may be ignited before the completion of the compression stroke, which is not proper for the functioning of the engine. In practice may be around 5. For air
(i) A refrigerator is a reversible engine operating in the reverse direction.
In refrigerator, an amount of heat Q2
is removed from sink at lower rejected at higher temperature T1
to the source.Thus, Q2+ W = Q1
or W = Q1- Q2
Coefficient of performance.
It is defined as the ratio of amount of heat removed from Sink to the amount of work done in removing it. It is denoted by ''
b. A heat engine absorbs heat from a hot body, converts a part of it into work and rejects the rest to a cold body known as sink efficiency of heat engine is
(or) h =
Efficiency of heat engine always less than 1 (or) 100 %.
Temperature of source,
Temperature of sink.
.If the temperature of sink is zero, then
Heat is Transmitted by three methods namely, Conduction, Convection and Radiation.
1. It is the phenomenon of Heat transfer without the actual displacement of the particles of the medium. The particles of the medium execute vibratory motions
Heat Transfer in a metal rod (solid)
Steady State :
In the process of heat conduction through a conductor from hot end to cold end if no heat is absorbed by it along the conductor then it is called steady state of the conductor. The temperatures at different points of the conductor remain same.
(The temperature of each section is constant but not equal) Under steady state of the conductor,
i) Rate of flow of heat =
ii) Temperature gradient along the conductor =
= constant (where
3.Coefficient of Thermal Conductivity : K
The quantity of Heat conducted through a metal rod in steady state is
i) directly proportional to Area of cross section (A)
ii) directly proportional to temperature difference (
1-2) between hot and cold ends
iii) directly proportional to time of flow of heat (t)
iv) inversely proportional to length (l) of the rod.
K is coefficient of Thermal Conductivity of the material of the conductor. It is property of the material of the conductor. It is independent of dimensions of the conductor.
To define K :
It is defined as the Rate of flow of Heat per unit area of cross section per unit Temperature gradient in steady state.
Units of K CGS --- Cal s-1Cm-1°C-1SI --- Wm-1K-1DF of K : - MLT-3-1
Values of K :
For a perfect conductor K =
For a perfect Insulator K = 0
If K value is more, it is a good conductor of Heat
If K value is less, it is a bad conductor of Heat.
(vii) Among metals Silver, Copper, Aluminium, Iron are in decreasing order of good conducting nature.
1) Silver K = 408 Wm-1K-1
2) Copper K = 383Wm-1K-1
3) Aluminium K = 205 Wm-1K-1
4) Iron K = 63 Wm-1K-1
(viii) Mercury is the best conductor among liquids.
4. (i) K of good conductor is determined by
(ii) K of Insulator is determined by
Lee's Disc method.
5.Junction Temperature :
If two metal slabs of equal areas of cross section, having lengthsl1,l2
, coefficients of thermal conductivities k1,k2
and free and Temperatures q1, q2
are kept in contact with each other, then under steady state,
Junction temperature =
Special Case : Ifl1
6. i) Generally Solids are better conductors than Liquids, Liquids are better conductors than Gases.
ii) Metals are much better conductors than Non-Metals, because Metals contain Free electrons.
7.Thermal Diffusivity (or) Thermometric conductivity D :
It is the ratio of coefficient of Thermal conductivity (K) to Thermal Capacity per unit volume (ms/v) of a material.
Thermal Conductance (C) :
For a conductor ,
Thermal conductance =
Here K = Coefficient of thermal conductivity
A = Area of cross section
l = length of conductor
SI Unit : Watt (Kelvin)-1
9. i) Thermal resistance (R) of a conductor of lengthl,
cross - section (A) and conductivity (K) is given by the formula
Thermal Resistance =
SI unit : Kw-1
DF : M-1L-2T3q
ii)Thermal resistance =
iii) Rate of flow of heat in terms of thermal resistance 'R' is
Effective conductivity :
(i) Series Combination :
a) If Two rods of same cross sectional areas, having lengthsl1,l2 and conductivities K1,K2
are connected in Series, then in steady state the Conductivity of the combination() is such that
Special Case :
b) If Three rods of same cross sectional areas having lengths
and conductivities K1, K2, K3
are connected in Series, then in steady state the Conductivity of the combination ()is such that
ii) Parallel combination :
a) If two rods of same length having cross sectional Areas A1, A2 and conductivities K1, K 2
are arranged in Parallel, then in steady state the conductivity of the combination () is such that
Special Case :
If A1= A2
= A then
b) If three rods of same length having cross sectional areas A1, A2
, A3 and conductivities K1, K2, K3
are connected in Parallel, then in steady state, the Conductivity of the combination () is such that
11. i) Cooking utensils are made of metals which are good conductors of heat.
ii) In winter, a metal chair is colder to touch than a wooden chair at the same temperature. The reason is metal is a good conductor and wood is a bad conductor of heat.
iii) In summer, a metal chair is hotter to touch than a wooden chair at the same temperature.
iv) A block of metal and a block of wood can be felt equally cold or hot when touched, if they are at the temperature of the human body.
v) Hot rice cooked in a vessel can be touched while the vessel cannot be touched. Rice is a bad conductor of heat.
vi) Two thin blankets are warmer than a single thick blanket. The reason is air which is trapped in between the blankets is a poor conductor of heat.
vii) Davy's safety lamp used in mines works on the principle of heat conduction.
Growth of thickness of Ice layer on Ponds :
When atmospheric temperature falls below 0°C, water in a lake starts freezing.
i) The time taken to form an Ice layer of thickness x on the Pond is given by the formula
where r is density of Ice
L is latent Heat of Fusion of Ice
K is conductivity of Ice
q is Atmospheric temperature.
ii) To increase the thickness of ice layer from
1. It is the phenomenon of Heat transfer by the actual displacement of the particles of the medium in a fluid.
Ex. : Heat Transfer in Liquids & Gases
2. Convection which results from difference in densities is called natural convection.
Ex: A fluid heated in a container.
3. If a heated fluid is forced to move by a blower (or) pump then the phenomenon is called forced convection [induced convection]
Ex: Temperature of human body is kept constant by pumping blood with heart pump. Here the transfer of heat is by forced convection.
4. The rate of heat convection from an object is such that
Here A = Contact area
= Temperature difference between
the object and conductive fluid.
h = constant called convection coefficient. It depends on the properties of the fluid such as density, viscosity, specific heat and thermal conductivity.
5. In case of natural convection, convection currents move warm fluid upwards and cool fluid downwards. Hence, heating is done from base to top while cooling is from top to base.
6. Natural convection takes heat from the bottom to the top while forced convection may take heat in any direction.
7. Natural convection cannot take place in a gravity free region.
Orbiting satellite, freely falling lift
8. Natural convection is the principle in working of ventilator, working of a chimney, changes in climatic conditions, formation of Land & Sea breezes, Trade winds, ocean currents etc.,a
1. Radiation is the phenomenon of transfer of heat without necessity of a material medium. It is by virtue of electromagnetic waves.
Energy radiated from a body is called Radiant energy.
Rate of emission of radiant energy depends on
i) Nature of surface of the body
ii) Surface area of the body
iii) Temperature of the body and surroundings
Properties of Thermal Radiation:
(i) It is the invisible electromagnetic radiation emitted from a hot body.
(ii) It lies in I.R. region of wavelength range from 4 × 10-4m to 7.5 × 10-7m
(iii) It travels in vacuum with velocity of light (3 × 108ms-1). It can also travel through a medium without affecting it.
(iv) It exhibits the Phenomena of Reflection, Refraction, Interference, Diffraction and Polarisation like light.
(v) It obeys Inverse square law
where I = Intensity of radiation
d = distance from source.
(vi) It can be detected by Thermocouple, Thermopile, Bolometer, Pyrometer, Radio-micrometer, Differential air thermoscope etc.,
(vii) Its spectrum can be formed by prisms of Rock-salt, KCl etc.,
(viii) Rough and black surfaces are good absorbers while shining and smooth surfaces are good reflectors of heat radiation.
Ex : Transmission of heat from Sun to Earth.
3. i) The substances which absorb heat radiations and get themselves heated up are called athermanous substances
Eg: wood, water vapour, water, , metals, glass.
ii) The substances which allow heat radiations to pass through them are called diathermanous substances
Eg: dry air, rocksalt, quartz, sylvine
4. Prevost's theory of Heat Exchange :
i) Every body emits and absorbs heat radiations at all temperatures except at absolute zero (-273ºC)
ii) If a body emits more heat energy than what it absorbs from the surroundings, then its temparature falls.
iii) If a body absorbs more heat energy than what it emits then its temperature rises.
iv) If a body emits & absorbs heat in equal amounts, then it is said to be in Thermal equilibrium.
v) When the temperatures of body and surroundings are equalized, conduction and convection stop but the radiation exchange takes place.
5. Perfect blackbody:
i) It is a body which absorbs all the heat radiations incident on it.
ii) On heating, it emits radiations of all possible wavelengths at a given temperature.
iii) The wavelengths of the emitted heat radiations depend only on the temperature but are independent of the material of the blackbody.
Ex : Lamp black (96%), platinum black (98%) Fery's and Wien's black bodies are artificial black bodies.
'Sun' is natural blackbody.
6. Spectral emissive power () :
i) It is the amount of energy radiated by unit surface area per second per unit wavelength range at a given temperature.
ii) Emissive power depends upon Nature of the surface and temperature of the body.
iii) It is maximum for a perfect blackbody (
). It is minimum for a smooth, shining white surface.
7. Spectral absorptive power :
i) For a given wavelength and temperature, it is the ratio of radiant energy absorbed by unit surface area per second to that incident on it in the same time.
al = Qa/Qi
ii) For a perfect blackbody,
= 1 (Qi= Qa)
iii) Absorptive power depends upon
nature of the surface and temperature of the body.
Emissivity or relative emittance (e) :
For a perfect blackbody e = 1
For anybody 0 < e < 1
9. For a surface if a = Absorptive power,
r = Reflecting power, and t = Transmitting power then
a + r + t =1
for a black body r =0 , t = 0, a=1
Kirchoff's law :
For a given temperature and wavelength, the ratio of emissive power to absorptive power of all bodies is always a constant. The constant is equal to emissive power of a perfect blackbody at the same temperature and wavelength.
i) Good emitters are good absorbers and vice versa.
ii) With increase of temperature increases.
i) A white china cup with a black spot is heated to high temperature and kept in a dark room. The spot appears brighter than the remaining part, because black is good absorber and hence good emitter.
ii) A Red glass when heated to high temperature kept in a dark room, appears Green and vice versa
iii) A Yellow glass when heated to high temperature and kept in a dark room appears Blue and vice versa
The above pairs of colour are called complementary colours.
iv) Dark lines in solar spectrum are called Fraunhoffer lines. Some wave lengths of white light from photosphere are absorbed by some elements in chromosphere
On the day of solar eclipse, absorption spectrum is not seen, rather emission spectrum which is complimentary to earlier absorption spectrum is seen.
i) The amount of heat radiated per second from unit surface area of a black body (E) is proportional to Fourth Power of its absolute temperature (T).
=AT4(watt)where '' is Stefan's constant
= 5.67 × 10-8w/m2/K4
ii) If the body is not a black body, then
= e s AT4
('e' lies between 0 & 1)
e = Emissivity of the body.
Q = e At s 4
Stefan - Boltzmann Law :
i) If a blackbody at absolute temperature 'TB
' is in an enclosure at absolute temparature 'Ts
' then the loss of thermal energy by the body per unit time is
=A (TB4- TS4)ii) If it is not a blackbody, then
= eA (TB4- TS4) where e = emissivity
Newton's Law of cooling:
(i) The rate of cooling (the rate of fall of temperature) of a hot body is directly proportional to the difference between mean excess temperature of the body and the temperature of its surroundings
= Temperature of surroundings.
The body is cooling from
under forced convection
Where k is a constant, independent of time of cooling.
(ii) As the body cools, its rate of cooling goes on decreasing
(iii) Cooling curve of a hot body with time is exponential
To compare specific heats of two liquids with their cooling curves, the liquid with cooling curve of less slope is of more specific heat.
(iv)The body never cools below the temperature of surroundings.
(v) Newtons law of cooling is a special case of Stefan-Boltzman's Law.
When the heat loss by radiation is considered
Here m = mass of of the body
s = specific heat of the material of the body
(ii) Using Stefan - Boltzman's Law
(iii) Rate of cooling by radiation depends upon :
a) Nature of the radiating surface i.e., greater the emissivity, faster will be the cooling.
b) Area of the radiating surface , i.e., greater the area of radiating surface, faster will be the cooling
c) Temperature of the radiating body, i.e., greater the temperature faster will be the cooling.
d) Temperature of the surroundings i.e., greater the temperature of surroundings slower will be the cooling
e) Mass of the body i.e., greater the mass of the radiating body slower will be the cooling.
f) Sp.heat of the body i.e., greater the specific heat of the radiating body slower will be the cooling.
(iv). For a spherical body,
(v) A solid sphere and a hollow sphere of same material are of equal radii. They are heated to the same temperature and allowed to cool in the same environment. Now
a) The hollow sphere cools faster
b) The rate of loss of heat is same for both the spheres.
Energy Distribution in the Spectrum of black body radiation:
i.) At different temperatures graphs are drawn taking wavelengths (l) along x-axis and Energy density per unit wavelength range (i.e,) energy radiated per unit area per unit time per unit wavelength range (El) along y-axis.
ii.) The energy is not distributed uniformly at a given temperature
iii.) At any temperature, the radiations of wavelength 0 to
iv.) With the increase of temperature, the wavelength corresponding to maximum intensity decreases.
v.) The area under the curve gives the total radiant energy at that temperature. Increase of area with temperature is according to Stefan's law.
Laws of Distribution of Energy radiated:
Three laws were proposed to explain the distribution of energy radiated by a black body
1.) Wien's Law:
i.) Spectral energy density (El)
ii.) Energy distribution can be explained by the formula
iii.) This law is applicable to shorter wavelengths only (it is based upon classical mechanics)
2.) Rayleigh - Jean's law :
i.) Spectral Energy density El - 4
ii.) Energy distribution can be explained by the formula
K = 1.38 x 10
iii.) This law is applicable to longer wavelengths only (it is based upon statistical mechanics)
3.) Plank's law :
i.) A blackbody emits discrete energy packets called quanta, each having energy E = h
ii.) The Energy distribution can be explained by the formula
iii.) This law is applicable to all wavelength ranges (it is based upon quantum mechanics)
Wien's fifth power law :
The monochromatic energy density (El) of a blackbody corresponding to wavelength of maximum energy is directly proportional to fifth power of its absolute temperature
Where K = 1.29x10-5W
Wien's Displacement law :
In blackbody, radiations spectrum the wavelength corresponding to maximum energy (maximum intensity) is inversely proportional to its absolute temperature.
T = constant = b
where b = 2.9 × 10-3
mk = wein's constant
m- T graph is a Rectangular hyperbola
- T' graph is a
straight line passing through the origin.