Question

A wood stove is used to heat a single room. The stove is cylindrical in shape, with a diameter of D=0.400 m and a length of L=0.500 m, and operates at a temperature of Tₛ =200° C. (a) If the temperature of the room is Tᵣ =20° C, determine the amount of radiant energy delivered to the room by the stove each second if the emissivity of the stove is e=0.920.

Answer 1

The wood stove delivers 1326.44 Watts of radiant energy to the room each second.

Step-by-step explanation:

To determine the amount of radiant energy delivered to the room by the wood stove each second, we can use the Stefan-Boltzmann Law. The equation for the radiant power emitted by an object is given by P = εσAT⁴, where P is the power, ε is the emissivity, σ is the Stefan-Boltzmann constant, A is the surface area, and T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin by adding 273.15. So the temperature of the stove is Tₛ = 200 + 273.15 = 473.15 K. The temperature of the room is Tᵣ = 20 + 273.15 = 293.15 K.

The surface area of the stove is A = πr² + 2πrh, where r is the radius (half of the diameter) and h is the length. Substituting the given values, we get A = π(0.400/2)² + 2π(0.400/2)(0.500) = 0.1257 m².

Now we can calculate the power using the equation P = εσAT⁴. Substituting the values, P = (0.920)(5.67×10⁻⁸)(0.1257)(473.15⁴ - 293.15⁴) = 1326.44 W. Therefore, the wood stove delivers 1326.44 Watts of radiant energy to the room each second.