1. Feb 21, 2010

### lordloss

1. The problem statement, all variables and given/known data

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. below). Assume the following: 519 bees form a ball of radius R = 3.6 cm for a time t = 24 min, the primary loss of energy by the ball is by thermal radiation, the ball's surface has emissivity ε = 0.85, and the ball has a uniform temperature. On average, how much additional energy must each bee produce during the 24 min to maintain 47°C? The Stefan–Boltzmann constant is 5.6704 × 10-8 W/m2-K4.

2. Relevant equations

P=$$\sigma$$$$\epsilon$$AT$$^{4}$$

3. The attempt at a solution

(5.6704X10$$^{-8}$$)(.85)(4$$\pi$$)(.036)$$^{2}$$(320)$$^{4}$$

Which comes out to 8.24635 and I took this to be joules per second.

(8.24635 X 1440)/519

=22.84

So far, I can't seem to get the correct answer. I have tried finding the answer with only the increased temp rise from 35 to 47 instead of the overall temp of 47 and its still wrong.

2. Feb 21, 2010

Hello lordloss did you calculate the ADDITIONAL energy?Remember the bees still radiate at their normal temperature of 35C(308K)

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