Radiation Problem: Solving Homework to Maintain 47°C for Bees

[lordloss]

Homework Statement

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.

Homework Equations

P=\sigma\epsilonAT^{4}

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.

 

[Dadface]

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