Serway & Jewett — The First Law of Thermodynamics: Problem 30.

You are reading your textbook on Greek mythology. You find a story about Daedalus and Icarus. Daedalus built two sets of wings out of feathers and wax, one set for him and one for his son Icarus. The father and son planned to use the wings to escape from their imprisonment on the island of Crete. The father warned Icarus not to fly too high because the proximity to the Sun might melt the wax in his wings. Of course, Icarus was overtaken by the thrill of flying and flew too close to the Sun. His wings melted and he fell into the sea. While reading this information, you think about your physics class, where your instructor has just discussed the equilibrium temperature of an object with no atmosphere at a given distance from the Sun. You look in your notes and find the following equation for this equilibrium temperature: \[ T = (255 \text{ K}) \sqrt{\frac{R}{r}} \] where \( R \) is the distance from the Sun to the Earth, \( r \) is the distance from the Sun to the object, and \( T \) is in kelvins. This raises a conundrum in your mind: If Icarus flew so close to the Sun that the wax in his wings melted, would there still be air at that location to allow him to fly to that location? Take the melting point of wax to be \( 65^\circ\text{C} \).