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TRANSFER OF HEATTRANSFER OF HEAT
CONTENTS• MODES OF TRANSMISSION OF HEAT• THERMAL RADIATIONS• CONDUCTION, CONVECTION, RADIATION• STEADY STATE• REFLECTANCE, ABSORPTANCE AND
TRANSMITTANCE• SOLAR CONSTANT • SURFACE TREMPERATURE OF SUN • NEWTONS LAW OF COOLING• KIRCHOFF’S LAW• STEFAN’S LAW• WIEN’S DISPLACEMENT LAW • ENERGY DISTRIBUTION OF BLACK BODY
RADIATIONS
TRANSFER OF HEAT
C O N D U C TIO N C O N V E C TIO N R A D IA TIO N
TY P E S
M O D E S O F TR A N S M IS S IO N O F H E A T
THERMAL RADIATIONS
THERMAL RADIATION ARE THOSE WHICH PROVIDE US I N THE SENSATION OF WARMTH. THEY ARE EMITTED BY A
BODY ON ACCOUNT OF ITS TEMPERATURE.
THE ENERGY EMITTED DEPENDS ON:-•THE TEMPERATURE OF THE BODY
•NATURE OF RADIATING SURFACE OF THE BODY.IT WAS ESTABLISHED LATER THAT EVERY OBJECT
WHOSE TEMPERATURE IS ABOVE 0 KELVIN, EMITS THERMAL RADIATIONS.
THERMAL RADIATIONSLET THEIR BE THERMAL RADIATIONS FALLING
ON A METALLIC CONTAINER, THEN
• A PART OF RADIATIONS WILL BE ABSORBED BY THE CONTAINER.
• A PART WILL BE TRANSMITTED BY THE METALLIC BODY.
• A PART OF THE RADIATIONS WILL BE REFLECTED BACK TO THE SURROUNDINGS
(as shown in the diagram)
THERMAL RADIATIONS
PROPERTIES(THERMAL
RADIATIONS)
» THEY TRAVEL WITH THE SPEED OF LIGHT.» TRAVEL IN STRAIGHT LINE.» DONOT HEAT THE INTERVEANING MEDIUM INFACT
THEY DONOT REQUIRE ANY MEDIUM FOR PROPAGATION.
» OBEY INVERSE SQUARE LAW.» OBEY THE LAWS OF REFRACTION AND
REFLECTION.» ALSO EXHIBIT THE PHENOMENON OF
INTERFERENCE AND DIFFRACTION.
CONDUCTION
IT IS THE MODE OF TRANSFERENCE OF HEAT IN WHICH THE HEAT TRANSFERS FROM PARTICLE TO PARTICLE IN THE
DIRECTION OF FALL OF TEMPERATURE WITHOUT THE MOVEMENT OF THE
PARTICLES OF THE MEDIUMIN CONDUCTION PARTICLES DO NOT TRANSFER, JUST HEAT TRANSFERS.
CONVECTION
IT IS THE MODE OF TRANSFERENCE OF HEAT IN
WHICH THE ACTUAL MOVEMENT OF THE PARTICLES OF THE
MEDIUM TAKES PLACE.
RADIATION
IT IS A MODE OF HEAT TRANSFER IN WHICH HET REACHES THE RECIEVER OR OBSERVER DIRECTLY FROM THE SOURCE WITHOUT HEATING THE INTERVEANING/
MIDDLE MEDIUM.
STEADY STATE(THERMAL CODUCTIVITY)
STEADY STATE IS THE STATE WHEN THERE IS NO MORE ABSORPTION OF
HEAT AND THE TEMPERATURE BECOMES CONSTANT.
DURING STEADY STATE, DIFFERENT PARTICLES MAY HAVE DIFFERENT TEMPERATURES BUT DIFFERENT
PARTICLES HAVE CONSTANT TEMPERATURE.
REFLECTANCE• THE REFLECTANCE OR REFLECTING POWER
OF A BODY IS DEFINED AS THE RATIO OF THE AMOUNT OF THERMAL RADIATIONS REFLECTED BY THE BODY IN A GIVEN TIME TO THE TOTAL AMOUNT OF THERMAL RADIATIONS INCIDENT ON THE BODY AT THAT TIME.
• IT IS REPRESENTED BY “r”
• FOR EXAMPLE, THE REFLECTANCE OR REFLECTING POWER OF POLISHED SURFACES IS LARGE
ABSORPTANCE• ABSORPTANCE OR ABSORPING POWER IS DEFINED AS
THE RATIO OF THE AMOUNT OF THERMAL RADIATIONS ABSORBED BY THE BODY IN A GIVEN TIME TO THE
TOTALAMOUNT OF THERMAL RADIATIONS INCIDENT ON THE BODY IN THE SAME TIME. IT IS REPRESENTED
BY “a”.
• E.g-ABSORBING POWER OF DULL COPPER IS 13%, OF INDIAN INK IS 85%. AS NO REAL BODY CAN ABSORB
100% OF THE RADIATIONS FALLING ON IT, THEREFORE THE VALUE OF a IS ALWAYS LESS THAN UNITY.
TRANSMITTANCE
• THE TRANSMITTANCE OR THE TRANSMITTING POWER OF A BODY IS
DEFINED AS THE RATIO OF THE AMOUNT OF THERMAL RADIATIONS TRANSMITTED
BY THE BODY IN A GIVEN TIME TO THE TOTAL AMOUNT OF THARMAL
RADIATIONS INCIDENT ON THE BODY IN THE SAME TIME. IT IS REPRESENTED
BY”t”.
• SOLAR CONSTANT IS DEFINED AS THE
AMOUNT OF RADIENT ENERY RECEIVED PER SECOND BY A UNIT
AREA OF TA PERFECTLY BLACK BODY SURFACE HELD AT RIGHT ANGLES TO
THE DIRECTIONS OF THE SUN RAYS AT THE MEAN DISTANCE OF EARTH FROM
THE SUN • THE VALUE OF SOLAR CONSTANT IS
1388 WATT sq. METERS OR 2 CAL.sq.CM PER MINUTE
EXPRESSION FOR SURFACE TEMPERATURE OF THE SUN
EXPRESSION FOR SURFACE TEMPERATURE OF THE SUN
cONSIDER THE SUN TO BE A BLACK BODY AT TEMPERATURE “T “AND RADIUS “R” AT THE CENTRE OF THE
HOLLOW SPHERE OF RADIUS r AS GIVEN IN FIG. 1 , WHERE r=1 A.U and r>R
ACCORDING TO STEFAN’S LAW , THE ENERGY EMITTED PER SECOND PER UNIT AREA BY THE SUN IS GIVEN BY
E= T4
SURFACE AREA OF THE SUN = 4R2
TOTAL ENERGY EMITTED PER SECOND BY THE SUN = 4R2 E= 4R2 T4
SINCE SOLAR LUMINOSITY IS ALSO EQUAL TO THE
TOTAL ENERGY RADIATED PER SECOND BY THE SUN, 4R2 T4 = 4r2 S
T=[r2 S / R2 ]1/4
NEWTON’S LAW OF COOLING
• ACCORDING TO THIS LAW, THE RATE OF LOSS OF HEART OF A LIQUID IS DIRECTLY PROPORTIONAL TO THE DIFFERENCE IN THE TEMPERATURES OF THE LIQUID AND THE SURROUNDINGS , PROVIDED THE DIFFERENCE IN TEMPERATURES IS SMALL,SAY OF THE ORDER OF 30 DEGREES.
• .i.e E (T-T0)
• THE LAW MEANS THAT A HOTTER LIQUID WILL COOL
DOWN MORE QUICKLY THAN A WARM LIQUID , IN THE
SAME SURROUNDINGS.
KIRCHOFF’S LAW• KIRCHOFF’S LAW STATES THAT THE
RATIO OF EMMISIVE POWER TO THE ABSORPTIVE POWER CORRESPONDING TO A
PARTICULAR WAVELENGTH AND AT ANY GIVEN TEMPERATURE BLACK
BODY AT THE SAME TEMPERATURE AND CORRESPONDING TO THE
SAME WAVELENGTH.
STEFAN’S LAW• IT STATES THAT THE AMOUNT OF HEAT
ENERGY(E) RADIATED PER SECOND BY UNIT AREA OF APERFECTLYBLACK BODY IS DIRECTLY PROPORTIONAL TO THE FOURTH POWER OF ABSOLUTE TEMPERATURE (T) OF THE BODY.
• ET4
• E= T4
WHERE IS A CONSTANT OF PROPORTIONALITY AND IS CALLED STEFAN’S CONSTANT.ITS VALUE IS
5.67X10-8 Wm-2 K-4
WIEN’S DISPLACEMENT LAW
ACCORDING TO THIS LAW, THE WAVELENGTH (M) OF MAXIMUM INTENSITY
OF EMISSION OF THE BLACK BODY RADIATION IS INVERSELY PROPORTIONAL
TO ABSOLUTE TEMPERATURE OF THE BLACK BODY,I.E
m1/T or m = b/T
WHERE ‘ b’ IS THE CONSTANT OF PROPORTIONALITY AND IS CALLED WIEN’S
CONSTANT.
FOR A BLACK BODY , THE VALUE OF
b=2.898 X10-3 m K.
CONCLUSION : WITH THE RISE IN TEMPERATURE OF THE BLACK BODY, THE WAVELENGTH OF MAXIMUM INTENSITY OF EMISSION SHIFTS TOWARDS LOWER WAVELENGTH SIDE.
THIS LAW IS USED TO FIND THE TEMPERATURE OF SUN AND STARS.
•THE WIEN’S DISPLACEMENT LAW ACCOUNTED FOR THE CHANGE
IN COLOUR OF A BODY FROM RED TO YELLOW AND THEN TO
WHITE AS ITS TEMPERATURE IS INCREASED.
ENERGY DISTRIBUTION OF BLACK BODY RADIATIONS
• E
•
ENERGY DISTRIBUTIONS OF BLACK BODY RADIATIONS
• BODY EACH CURVE IN THE GRAPH REPRESENTS THE VARIATION OF
MONOCHROMATIC EMITTANCE (E) OF THE BLACK BODY WITH THE WAVELENGTH (0 OF
THE RADIATION EMITTED.
• DIFFERENT CURVES HAVE BEEN SHOWN FOR DIFFERENT TEMPERATURES OF THE BLACK
BODY.
OBSERVATIONS [ ENERGY DISTRIBUTION OF BLACK BODY RADIATIONS ]
• AT A GIVEN TEMPERATURE OF BLACK BODY 1.ENERGY EMITTED IS NOT
DISTRIBUTED UNIFORMLY AMONGST ALL WAVELENGTHS.
• 2.ENERGY EMITTED IS MAXIMUM CORESSPONDING TOA CERTAIN WAVELENGTH (m ) AND IT FALLS ON EITHER SIDE OF IT.
• WITH RISE IN TEMPERATURE OF BLACK BODY
• 1.TOTAL ENERGY EMITTED INCREASES RAPIDLY FOR ANY GIVEN WAVELENGTH.
m 1/T or m T= a constant.
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