Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 56

The giant hornet Vespa mandarinia japonica preys on Japanese bees. However, if one of the hornets attempts to invade a beehive, several hundred of the bees quickly form a compact ball around the hornet to stop it. They don’t sting, bite, crush, or suffocate it. Rather they overheat it by quickly raising their body temperatures from the normal 35°C to 47°C or 48°C, which is lethal to the hornet but not to the bees (Fig. 18.21). Assume the following: 500 bees form a ball of radius \(R = 2.0\text{ cm}\) for a time \(t = 20\text{ min}\), the primary loss of energy by the ball is by thermal radiation, the ball’s surface has emissivity \(\epsilon = 0.80\), and the ball has a uniform temperature. On average, how much additional energy must each bee produce during the 20 min to maintain 47°C?