In: Physics

A body of emissivity (e = 0.75), the surface area of 300 cm2 and temperature 227 ºC are kept in a room at temperature 27 ºC. Using the Stephens Boltzmann law, calculate the initial value of net power emitted by the body.

Concept

According to Stefan Boltzmann law, the amount of radiation emitted per unit time from an area A of a black body at absolute temperature T is directly proportional to the fourth power of the temperature.

u = sAT4 . . . . . . (1)

where s is Stefan’s constant = 5.67 × 10-8 W/m2 k4

A body which is not a black body absorbs and hence emit less radiation, given by equation

For such a body, u = e σ AT4 . . . . . . .

where e = emissivity (which is equal to absorptive power) which lies between 0 to 1.

With the surroundings of temperature T0, net energy radiated by an area A per unit time.

Δu = u – uo = eσA [T4 – T04]

P = rsA (T4 – T04)

= (0.75) (5.67 × 10-8 W/m2 – k4) (300 × 10-4 m2) × [(500 K)4 – (300 K)4]

= 69.4 Watts.

Δu = u – uo = eσA [T4 – T04]

e=0.75

T1=500k

T2=300k

s=Stephen constt=5.67×10^8

A area =300×10^-4 m^2

Net power emitted is -69.4watt

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