Transfer of heat

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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