Question

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.

 

Answer 1

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