Randall D. Knight — Work, Heat, and the First Law of Thermodynamics: Problem 81

A satellite to reflect radar is a 2.0-m-diameter, 2.0-mm-thick spherical copper shell. While orbiting the earth, the satellite absorbs sunlight and is warmed to 50°C. When it passes into the earth’s shadow, the satellite radiates energy to deep space. The temperature of deep space is actually 3 K, as a result of the Big Bang 14 billion years ago, but it is so much colder than the satellite that you can assume a deep-space temperature of 0 K. If the satellite’s emissivity is 0.75, to what temperature, in °C, will it drop during the 45 minutes it takes to move through the earth’s shadow?