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

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SUMMARY

The discussion focuses on calculating the additional energy required for 519 Japanese bees to maintain a temperature of 47°C while forming a protective ball around a giant hornet (Vespa mandarinia japonica). The bees' ball has a radius of 3.6 cm and an emissivity of 0.85, with the primary energy loss occurring through thermal radiation. The Stefan–Boltzmann constant is utilized in the calculations, and the initial attempts to solve the problem yield incorrect results due to not accounting for the bees' normal temperature of 35°C. The correct approach requires calculating the additional energy produced by each bee over a 24-minute period.

PREREQUISITES
  • Understanding of thermal radiation principles
  • Familiarity with the Stefan–Boltzmann law
  • Basic knowledge of emissivity and its impact on heat transfer
  • Ability to perform unit conversions and energy calculations
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  • Study the Stefan–Boltzmann law in detail
  • Learn about emissivity and its role in thermal radiation
  • Explore energy conservation principles in biological systems
  • Practice solving thermal energy problems involving phase changes and temperature variations
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This discussion is beneficial for students studying thermodynamics, biology enthusiasts interested in bee behavior, and educators looking for practical applications of thermal radiation concepts in real-world scenarios.

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

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