Question

If you are designing a space heater to warm a room and are required by safety codes to keep its surface temperature below 350 K (170 F or 77 C), the only variable you have to work with is the surface area, and you want to minimize that to make it convenient and inexpensive. Neglecting convection entirely, and assuming all the heat is transferred as infrared light, suppose it is to radiate 1200 W. How much area would it have

Answer 1

A = 1.41 m²

Step-by-step explanation:

The ara can be found out by using Stefan Boltzman Law:

`P = \sigma AT^4`

where,

A = Area = ?

P = Radiation Power = 1200 W

σ = Stefan Boltzman Constant = 5.6703 x 10⁻⁸ W/m².k⁴

T = surface temperature = 350 k

Therefore:

`1200\ W = (5.6703\ x\ 10^(-8)W/m^2.k^4)(A)(350\ k)^4\\\\A = (1200\ W)/(850.9\ W/m^2)`

A = 1.41 m²