What is the transfer of net power from the oven in this problem?
An oven with an inside temperature T0 = 227°C is in a room having a temperature T, = 27°C. There is a small opening of area 5.0 cm2 in one side of the oven. How much net power is transferred from the oven to the room?
The power emitted by a black body, per unit area depends on absolute temperature of that certain body. It is given by the Stefan-Boltzmann law:
`P = sigma*T^4` ,
where `sigma =5.67*10^-8 W/(m^2*K^4)` . For the oven in the problem, there is an emitted power from inside to outside due to oven temperature an absorbed power from outside to inside due to outside temperature.
`P_("tot") =P_("out") -P_("in") =sigma*(T_1^4 -T_2^4)`
`P_("tot") =5.67*10^-8*[(227+273)^4 -(27+273)^4] =5.67*10^-8*(6.25*10^10 -0.81*10^10) =30.845*10^2 =3084.5 W/m^2`
Now all we have to do is to multiply this value with the given surface area to find the power transferred from the oven to the room:
`P =P_("tot")*S =3084.5*5*10^-4 =1.542 W`
Answer: the power transferred from the oven to the room is 1.542 W