Final answer:
To calculate the rates of heat loss by radiation and convection from the burner, use the formulas Q = εσA(Ts^4 - T?^4) and Q = hA(Ts - T?) respectively. The electric power requirement can be calculated using P = Q/η.
Step-by-step explanation:
To calculate the rates of heat loss by radiation and convection from the burner, we need to use the Stefan-Boltzmann law for radiation and Newton's law of cooling for convection.
For radiation, we can calculate the rate of heat loss using the formula:
Q = εσA(Ts^4 - T?^4)
where Q is the rate of heat loss, ε is the emissivity of the burner (assumed to be 1 for a blackbody), σ is the Stefan-Boltzmann constant (5.67x10^-8 W/m^2 K^4), A is the surface area of the burner, Ts is the surface temperature of the burner, and T? is the ambient temperature.
For convection, we can calculate the rate of heat loss using the formula:
Q = hA(Ts - T?)
where Q is the rate of heat loss, h is the heat transfer coefficient for convection, A is the surface area of the burner, Ts is the surface temperature of the burner, and T? is the ambient temperature.
To calculate the electric power requirement, we can use the formula:
P = Q/η
where P is the power requirement, Q is the rate of heat loss, and η is the efficiency of the energy transfer from the heaters to the burners.