Unlike most other plants, a special type of cabbage called skunk cabbage can regulate its internal temperature ( set at T = `22^(@)C` )by altering the rate at which it produces energy. If it becomes covered with snow, it can increase that its thermal radiation metls the snow in order to re-expose the plant to sunlight. Let's model a skunk cabbage with a cylinder of height h = 5.0 cm and radius R = 1.5 cm and assume it is surrounded by a snow wall at temperature `T_("env") = - 3.0^(@)C` (Figure) . If the emissivity `epsilon` is 0.80, what is the net rate of energy exchange via thermal radiation between the plant's curved side and the snow ?

Explanation

(1) In a steady-state situation, a surface with area A, emissivity `epsilon`, and temperature T loses energy to thermal radiation at th erate given by Equation `( P_("rad") =sigma epsilon A T)` (2) Simultaneously , it gains energy by thermal radiation from its environment at temperature `T_("env")` at the rate given by Equation `( P_("abs") =sigma epsilon A T_("env")^(4))`
Calculations `:` To find the net rate of energy exchange, we subtract Equation from Equation to write
`P_("net") = P_("abs")-P_("rad")`
`=sigma epsilon A ( T_("env")^(4)-T^(4))` ( 19 - 27)
We need the area of the curved surface of the cylinder, which is `A = h ( 2pi R )` . We also need the temperature in kelvins. `T_("env") = 273K - 3K = 270 K ` and `T = 273 K + 22K = 295 K`. Substituting in Equation for A and then substituting known values in SI units ( which are not displayed here ). we find
`P_("net") = ( 5.67 xx 10^(-8)) ( 0.80 ) ( 0.050) ( 2pi ) ( 0.015) ( 270^(4) - 295^(4)) = - 0.48 W`
Thus, the plant has a net loss of energy via thermal radiation of 0.48 W. The plant.s energy production rate is comparable to that of a hummingbird in flight.