By Nitin Oke For Safe Hands

Radiation By Nitin Oke For Safe Hands

Flow of heat • Net Heat flow is from body with more heat temperature to body at less heat temperature

• Flow of heat can take place in three ways – Conduction – Conviction – Radiation

Facts about flowHeat flow Conduction

Conviction

Radiation

No Motion of particle

Motion of particle

Electro magnetic wave

Slowest

Moderate

Fastest

Most efficient

Moderate efficient

Least efficient

Cosmic rays Gamma rays UV rays

Facts about RadiationHeat flow

Conduction

Conviction

Radiation

No Motion of particle

Motion of particle

Electro magnetic wave

Slowest

Moderate

Fastest

Visible rays IR rays

Micro Mostwaves Moderate efficient

Radio waves

efficient

Least efficient

More about Electromagnetic spectrum

Properties of heat radiation: • Heat radiation have properties similar to light radiation. • Heat radiation travels in a straight line. • Heat radiation travel with the velocity of light equal to 3 x 108 m/s. • Heat radiation obeys inverse square law i.e. the intensity at a point is inversely proportional to the square of the distance between the point and the point source of radiation.

Properties of heat radiation: • It exhibits the phenomena of reflection, refraction, interference, diffraction and polarization. • Heat radiations can travel through vacuum and other transparent media. • Heat radiations do not affect the medium through which they pass. • Heat radiation consists mostly of infrared rays, which are electromagnetic waves whose wavelength range from 8 x 10 –7m to 4 x 10 –4m.

Facts about Radiation-

• Heat radiation is with wave length ranging between 10-6m to 10-3m in reality the wavelength of heat radiation ranges from 8 x 10 –7 m to 4 x 10 –4 m where as the wave length of visible light ranges from 4 x 10 –7m to 8 x 10 –7m. • These waves are invisible to human • Frequency ranges from 1011Hz to 1014Hz

What means a, r, t • If Q amount of hest is incident on surface. • QR is reflected • QA is absorbed • QT is transmitted • By law of conservation of energy Q = QR+ QA+ QT QR QA QT a= ,r = ,t = Q Q Q

Q

QRA Q T

Classification based on a, r and t • If t = 1 then substances are called as

diathermanous.

• Examples of substances which are transparent to heat radiation are— – Quartz, glass, Rock salt, dry air, O2 , H2, NaCl, CCl4, CHCl3 • If t = 0 then substances are called as

athermanous.

• Examples of substances which are transparent to heat radiation are— – Water, Wood, C6H6, R-OH, Cu, Iron

Classification based on a, r and t • If r = 1 then substances are called as perfect

reflector.

• Bright polished surface may be called as perfect reflector. • If a = 1 then substances are called as perfect black

bodies or perfect absorbers.

• Examples of substances which absorbs heat radiation are— – Lamp black ( absorbs nearly 96%) – Platinum black ( absorbs nearly 98%) – Ferry's black body ( absorbs nearly 100%)

Construction of Ferry's Black body • A Copper sphere is taken. • It is covered by another non conducting concentric sphere of larger radius. • The outer sphere is evacuated. • An aperture is made to both spheres and slightly off the line a conical elevation is created. • Inner part of inner sphere is coated with lamp black, and conical elevation is polished surface.

Facts about Radiation-

• To detect these waves Crook’s radiometer or Boy’s radiometer are used. • Energy of radiation can be measured by “Bolometer” • Heat Radiations spectrum was studied graphically by “Langley” ( Not black body spectrum ) • Spectrum of Black body was studied at different temperatures by Lummer and Prigsheim • The black body used was constructed by Fery • Wien found relation between temperature and maximum corresponding wavelength. • Stefan and Boltzman related area under the curve means total heat and T4 • The graph was explained by Max Plank using Quantum theory.

Study of graph of radiation

T3 T2 T1

Observations of graph

• When radiations of Black body were studied at different temperatures by Lummer and Prigsheim the observations were as follows—

– The graph is different at different temperature – As temperature increases the graph shifts up – The graphs maxima shifts backward as temperature increases. – The area under the curve, means total energy per unit area per unit time means emissive power is proportional to T4 (Stefan’s law) – The Emax is proportional to T5 – The wavelength corresponding to Emax is inversely proportional to T. λmax.T = b The value of b is 0.2892 x 10-2mK ( Wien’s displacement law).

Prevost theory of heat exchange • Every body continuously radiates heat energy at all temperatures except absolute zero. • The amount of radiant energy emitted per unit time depends only on absolute temperature of body and NOT on surrounding temperature.

Heat exchange is as -More Hot

Less Hot

Hot

Hot

Kirchhoff’s Law of radiation • The coefficient of absorption is same as coefficient of emission. • Theoretical proof of Kirchhoff’s law

Theoretical proof of Kirchhoff’s law • As thermal equilibrium is achieved the heat emitted per unit time per unit area of ordinary body equals heat gained per unit time per unit area by it. • E = a.Eb • e=a

Ritchie’s Experiment aAEb 1xAE

aAEb = 1.A.E a =E/Eb = e

Ritchie’s Experiment

Stefan’s Law and its applications • The radiant energy emitted by perfectly black body per unit area per unit time is directly proportional to forth power of absolute temperature. • The constant of proportionality is called as Stefan’s constant and denoted by σ. • The value of σ is 5.67 x 10-8 J/m2.s.K4 (W/m2K4)

Q 4 = σT A.t

Q = A.t.σ.T

Rate of heat radiation by black body dQ = A.σ.T 4 dt Rate of heat radiation by surounding

dQ 4 = A.σ.T0 dt Rate of loss of heat radiation by body dQ = A.σ. T 4 − T04 dt

(

)

4

Generalization of Stefan’s Law • Using Kirchhoff’s law Stefan’s Law can be generalized as— • Emissive power: The amount of heat radiation emitted by a body per unit time per unit area is called as emissive power of the body. • If above body is black body then it is left hand side of Stefan’s law. • Coefficient of emission or emissivity of a body is ratio of emissive power of a body and perfectly black body at same temperature. Denoted by e. e = E/Eb • As a = e Hence E = a. Eb = a .σ.T4 • For ordinary bodies Stefan’s Law will be • Q = a(A.t.σ.T4)

Newton’s Newton’slaw lawofofcooling heat • The rate of loss of heat by a body is directly proportional to the excess temperature of the body over the surrounding. • Please note that the law was stated quite earlier than Stefan’s law and Provost's theory.

dQ dQ α=(θ − θ−0 )θ0 ) k.(θ dt dt dθ m.s. = K(θ k(θ − θ0 ) dt

dQ dθ but = m.s. dt dt

Newton’s law as approximation of Stefan’s Law • Latter on when new theory was developed the Newton’s law was obtained as approximation of Stefan’s Boltzman Law. • Assuming T = T0 + x and using binomial expansion and the fact that T0 > > > x we get • Obviously we need to use T-T0 = θ - θ0

dQ = k.(θ − θ0 ) dt

Solar constant • The solar constant is the amount of radiant energy received per second per unit area by a perfect black body placed on the Earth with its surface perpendicular to the direction of radiation from the Sun. • Solar constant is different for different planets as their distance is different from Sun. • Value of Solar constant is 1.388 x 103W/m2 • Instrument used to measure Solar constant is “Pyro heliometre” • Simplest of all is Angstrong’s Compensation pyro heliometre

Temperature of Sun Using Solar Constant

• If R is distance between Sun and Earth and • r is radius of Sun then

Q 2 S= hence Q = 4πR tS 2 4πR t 2 4 By Stefan's Law Q = 1.4πr .σt(T )

hence 4πr σtT = 4πR tS 2

1 2

1 4

4

2

11 1 2 8

1 4

R S 14.848 x10  1390  T=( )   =( )  = 5730K −8  r σ 6.928 x10  5.67 x10 

Temperature of Sun Using Wien’s Law • If λ is wavelength of radiation for which Solar radiation is maximum ( 4900 x 10-10m) then

Using Wien's law λ max .T = 0.002892 0.002892 T= = 5902 K −10 4900 x10

Note the following—

• If two bodies are of surface area A1 and A2 coefficient of absorption a1 and a2 at temperature T1 and T2 then rate of emission of heat radiation is –  dQ     dt 1 a1A 1T1 = a 2 A 2 T2  dQ     dt  2 A T = 1 1 A 2T2

A 1 r12 = = 2 A 2 r2

If they are of same material then a1 = a2 If they are of same material then a1 = a2 and are at same temperature T1 = T2 If they are of same material then a1 = a2 and are at same temperature T1 = T2 and spherical in shape.

Note the following—

• If two bodies of mass m1 & m2 ,surface area A1 & A2 coefficient of absorption a1 and a2 at temperature T1 & T2 specific heats s1 and s2 and densities ρ1& ρ2 then rate of cooling is –  a1A 1T1   dθ       dt 1  m1s1  a1A 1T1m2s2 If they are of same material = =  dθ   a 2 A 2 T2  a 2 A 2T2m1s1 then a1 = a2 and s1 = s2      dt  2  m2s 2  In addition if are at same A 1T1m2 = temperature T1 = T2 and A 2T2m1 spherical 2 4 3 r1 ( πr2 )ρ2 A 1m2 r 3 = = = 2 A 2m1 r 2 ( 4 πr 3 )ρ r1 2 1 1 3