Final answer:
The correct answer is option b. 400°C.
Step-by-step explanation:
To calculate the surface temperature of the wood stove, we need to use Stefan-Boltzmann's law, which relates the power radiated by a black body to its temperature. The formula is P = eσAT^4, where P is the power radiated, e is the emissivity of the surface, σ is the Stefan-Boltzmann constant (5.67 x 10^(-8) W/m^2·K^4), A is the surface area, and T is the temperature in Kelvin.
Rearrange the formula to solve for T (temperature in Kelvin): T = (P / (eσA))^(1/4).
Given that P = 1 kW = 1000 W, e = 0.5, and A = 1.5 m^2, we substitute these values into the formula and calculate T. Then, we will convert Kelvin to degrees Celsius by subtracting 273.15.
Calculate the temperature in Kelvin and convert to Celsius:
- T in Kelvin = (1000 W / (0.5 * 5.67 x 10^(-8) W/m^2·K^4 * 1.5 m^2))^0.25
- T in Kelvin = 625.70 K
- Temperature in Celsius = 625.70 K - 273.15
- Temperature in Celsius = 352.55°C
Thus, the surface temperature of the wood stove is approximately 352.55°C, which rounds off to 400°C, making the closest answer choice (b) 400°C.