Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 104

Skunk cabbage. Unlike most other plants, a skunk cabbage can regulate its internal temperature (set at \( T = 22^{\circ}\text{C} \)) by altering the rate at which it produces energy. If it becomes covered with snow, it can increase that production so that its thermal radiation melts the snow to re-expose the plant to sunlight. Let’s model a skunk cabbage with a cylinder of height \( h = 5.0\text{ cm} \) and radius \( R = 1.5\text{ cm} \) and assume it is surrounded by a snow wall at temperature \( T_{\text{env}} = -3.0^{\circ}\text{C} \) (Fig. 18.39). 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?