Respuesta :
Answer:
Explanation:
Given
Surface area [tex]A=0.5\ m^2[/tex]
emissivity [tex]\epsilon _0=0.8[/tex]
Temperature of body [tex]T=200^{\circ}C\approx 473\ K[/tex]
Temperature of walls [tex]T_0=25^{\circ}C\approx 298\ K[/tex]
Rate of radiation by surface is given by
[tex]Q=\epsilon _0\sigma AT^4[/tex]
[tex]Q=5.67\times 10^{-8}\times 0.5\times 0.8\times (473)^4[/tex]
[tex]Q=726.11\ W[/tex]
(b)Net rate of radiation exchanged between the surface and the chamber
[tex]Q=\epsilon _0\sigma A(T-T_0)^4[/tex]
[tex]Q=0.8\times 5.67\times 10^{-8}\times 0.5\cdot (473-298)^4[/tex]
[tex]Q=547.25\ W[/tex]
The Stefan–Boltzmann law is used to determine the power of radiation emitted.
Part A: The rate of radiation is emitted by the surface is 1135.23 W.
Part B: The net rate at which radiation is exchanged between the surface and the chamber walls is 21.27 W.
What is the Stefan–Boltzmann law?
The Stefan–Boltzmann law, also known as Stefan's law, states that the total energy radiated per unit surface area of a black body in unit time is directly proportional to its absolute temperature T raised to the fourth power.
Given that the surface area A of the body is 0.5 m^2, emissivity [tex]\epsilon_0[/tex] is 0.8, and temperature T is 200°C. The temperature T' of the wall is 25°C.
The temperatures in kelvin is given as,
T = 200 + 273 = 473 K
T' = 25+273 = 298 K
Part A:
The rate of radiation by the surface is given as,
[tex]P = \epsilon_o\sigma AT^4[/tex]
Where [tex]\sigma[/tex] is Stefan Boltzmann's constant that is [tex]5.67\times 10^{-8}[/tex].
[tex]P = 0.8\times 5.67\times 10^{-8} \times 0.5 \times 473^4[/tex]
[tex]P = 1135. 23\;\rm W[/tex]
The rate of radiation is emitted by the surface is 1135.23 W.
Part B: The net rate at which radiation is exchanged between the surface and the chamber walls is,
[tex]P = \epsilon_o\sigma A(T - T')^4[/tex]
[tex]P = 0.8\times 5.67\times 10^{-8} \times 0.5 \times (473 - 298)^4[/tex]
[tex]P = 21.27 \;\rm W[/tex]
The net rate at which radiation is exchanged between the surface and the chamber walls is 21.27 W.
To know more about Stefan Boltzmann's law, follow the link given below.
https://brainly.com/question/20260974.
