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

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In summary, the giant hornet Vespa mandarinia japonica can be stopped by a compact ball of Japanese bees, who raise their body temperatures to a lethal level for the hornet but not for themselves. To maintain a temperature of 47°C for 24 minutes, each of the 519 bees in the ball must produce an additional 22.84 joules per second, taking into account the thermal radiation loss with an emissivity of 0.85 and the Stefan-Boltzmann constant.
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lordloss
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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=[tex]\sigma[/tex][tex]\epsilon[/tex]AT[tex]^{4}[/tex]

The Attempt at a Solution



(5.6704X10[tex]^{-8}[/tex])(.85)(4[tex]\pi[/tex])(.036)[tex]^{2}[/tex](320)[tex]^{4}[/tex]

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)
 

What is radiation?

Radiation is a form of energy that is emitted in the form of waves or particles from a source. It can be found naturally in sunlight and in the form of electromagnetic waves, such as X-rays and microwaves. Radiation can also be man-made, such as in nuclear power plants.

How does radiation affect bees?

Bees are sensitive to radiation because it can damage their DNA and impair their ability to navigate and communicate. This can lead to a decline in their population and impact pollination and agriculture.

What is the ideal temperature for bees?

The ideal temperature for bees is between 35-37°C. This is the temperature at which they can properly regulate their body temperature and perform their essential tasks, such as foraging and caring for the hive.

Why is it important to maintain a temperature of 47°C for bees?

Maintaining a temperature of 47°C is important for bees because it is the optimal temperature for their brood, which are the developing eggs, larvae, and pupae. If the temperature falls below this, it can affect their growth and survival.

How can we solve the radiation problem to maintain 47°C for bees?

There are a few ways to solve the radiation problem and maintain a temperature of 47°C for bees. One option is to use insulation and reflective materials to minimize radiation exposure. Another is to use natural cooling methods, like ventilation or shading. Additionally, implementing radiation protection measures and monitoring radiation levels can also help mitigate the problem.

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