Heat Transfer Laws Assignment Help

Thermodynamics - Heat Transfer Laws

Heat Transfer Laws

Kirchhoff’s law according to this aw, the ratio of emissive power to adsorptive power is same for all surfaces at the same temperature and is equal to the emissive power of a perfectly black body at that temperature. Thus for a body having e and a as emissive and absorptive power

e/a = E/ A = E/1 = E

Where E = emissive power of a black body

It implies a good absorber and is also a good emitter (radiator)

Fraunhofer lines they are the dark lines in the spectrum of the sun and are explained on the basis of kirchoff’s law. White light emitted from core (photosphere) of the sun when passes through its atmosphere (chromospheres) radiations of those wavelengths will be absorbed by the gases present there, which they usually emit (in emission spectrum) resulting in dark lines in the spectrum of sun.

Stefan’s law radiant energy emitted per unit area per second (or emissive power or intensity) of a black body is directly proportional to the fourth power of temperature.

ER ∝ Tor ER = σT4

If the body is not perfectly black then 

ER = eσTwhere σ = 5.67 x10-8 Wm-2 K-4

Energy radiated per second or radiant power

PR = eAσTor ∫Rλdλ αT4

Cooling by radiation if a body is at temperature T in an environment of temperature T0 (< T), then body loses energy by emitting radiations at a rate

P1 = eAσT4

And it receives energy by absorbing radiation at a rate 

P2 = eAσT40

So the net rate of loss is p = p1 – p2

Or p = eA σ(T– T40)

When a body cools by radiation, that rate of cooling depends upon the following factors:

Nature of the radiating surface, that is, emissivity

Breather the emissivity faster will be the cooling

Area of the radiating surface more the surface area of the radiating surface, faster will be the cooling.

Mass of the radiating surface greater the mass of the radiating body slower will be the cooling.

Specific heat of the radiating body more the specific heat slower will be the cooling.

Temperature of radiating body higher the temperature faster will be the cooling. 

Temperature of the surrounding lesser the temperature of the surrounding faster is the cooling

Newton’s law of cooling the rate of cooling is proportional to the temperature difference between body and the surroundings provided the temperature difference is not very large from the surroundings. That is, 

Dθ/dt = - K (θ – θ0)

Or ∫_θ2^θ2¦?(dθ? / θ )– θ0 = ∫t0- Kdt

Loge (θ2 – θ2) / (θ1 – θ0) = -K

Show the temperature vs time curve.

If time intervals are equal and successive then

2 – θ0) /( θ1 – θ0) = (θ3 – θ0) /( θ1 – θ0)

Assuming temperature at t =0 is θ1, after first interval it is θand after second equal interval of time it isθ3.

Solar constant the sun is a perfectly black body as it emits all possible radiations (e = 1) solar consent s is defined as the intensity of solar radiation at the surface of the earth. That is, 

S = pR / 4πr2 = 4πr2 σT4 / 4πr2

R = 1.5 x 1011 km

(Distance between the sun and the earth R = 7 x 108 km (radius of the sun)

S = 2cal / cmmin = 138 W/m2

Wien’s displacement law when a body is heated it emits all possible radiations. However, intensity of different wavelengths is different. According to wine’s law the product of wavelength (corresponding to maximum intensity of radiations) and temperature of the body in Kelvin id constant

λmT = b (constant)

b = 2.89 x 10-3 
– K

Planck’s law Planck assumed that electromagnetic radiations are not emitted or absorbed continuously but in energy associated with each photon is 

E = hv

Where is Planck’s constant (= 6.625 x 10-34 j – s). On the basis of quantum theory Planck showed that 

ER(λ) = 2πhc2 / λ5 /1 [ehc / λKT – 1] 

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