Question

A wood stove has a total surface area of 1.5 m^2 and radiates a power of 1.0 kw. calculate the surface temperature in °c for emissivity = 0.5.

a. 200°C
b. 400°C
c. 600°C
d. 118.6°C

Answer 1

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:

1. T in Kelvin = (1000 W / (0.5 * 5.67 x 10^(-8) W/m^2·K^4 * 1.5 m^2))^0.25
2. T in Kelvin = 625.70 K
3. Temperature in Celsius = 625.70 K - 273.15
4. 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.