Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 34

34 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. 18-36). Assume the following: 500 bees form a ball of radius R = 1.8 cm for a time t = 18 min, the primary loss of energy by the ball is by thermal radiation, the ball’s surface has emissivity ε = 0.80, and the ball has a uniform temperature. On average, how much additional energy must each bee produce during the 18 min to maintain 47°C?