Question

How do you calculate the time required to change the temperature of a room by 10C by radiation? Given: Emissivity: 0.91 A: 2.0 T2: 292.5K T1:282.4K

I just need to know what formula to use in order to calculate the time.

Answer 1

According to Stefan - Boltzmann law , the total power radiated by a black body across all wavelengths is directly proportional to the fourth power of the black body's thermodynamic temperature T:

  

For a general body (grey body), the total power radiated by the body across all wavelengths is given by

Where, is emissivity of the body

is Stefan - Boltzmann constant

A is surface area of the body

If the energy contained by the body is E then

(by chain rule)

If the number of particles in the room is N then from equipartition of energy, the energy of the room at temperature T is given by   

then

or,

or,   

or,   

or,   

After integration, we get

  

Where, k is Boltzmann constant

This is the required equation for calculation of time if temperature is changing by radiation. (But you have to know the value of N) .

For any doubt please comment .