Physics
Physics
Problem
(Emissivity and temperature change combined) A cast-iron plate of area initially has an emissivity of and is maintained at . It is later coated with a special paint that increases its emissivity to , while at the same time the plate cools to . Keeping all other conditions identical, answer the following. a. (i) Obtain the ratio of the final total power radiated by the plate to its initial power. b. (ii) Express the change in power as a percentage increase or decrease relative to the initial value.Intuitive explanation
The key is recognizing that Stefan–Boltzmann radiation depends on both emissivity and the fourth power of absolute temperature. When emissivity increases, the plate radiates more power; when temperature drops, it radiates much less. You need to compare the radiated power in both states to see which effect dominates—this reveals how the plate's thermal behavior changes despite the competing influences.
Intuitive explanation
The key is recognizing that Stefan–Boltzmann radiation depends on both emissivity and the fourth power of absolute temperature. When emissivity increases, the plate radiates more power; when temperature drops, it radiates much less. You need to compare the radiated power in both states to see which effect dominates—this reveals how the plate's thermal behavior changes despite the competing influences.