Burning Calories by radiation (Stefan-Boltzman law)

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SUMMARY

The discussion centers on calculating the time required to radiate away 290 Calories from an ice cream cone using the Stefan-Boltzmann law. The skin temperature is 32.7°C, and the air temperature is 19.9°C, with an emissivity of 0.915 and a skin surface area of 1.25 m². The participant initially confuses the definitions of power and energy, needing clarification on applying Stefan's law to derive the time from power calculations. The correct approach involves using the Stefan-Boltzmann law to determine the power emitted and then relating it to the energy to find the time.

PREREQUISITES
  • Understanding of the Stefan-Boltzmann law
  • Basic knowledge of thermodynamics and heat transfer
  • Familiarity with the concepts of power and energy
  • Ability to manipulate equations involving mass, specific heat, and temperature change
NEXT STEPS
  • Study the application of the Stefan-Boltzmann law in thermal radiation calculations
  • Learn how to convert energy (Calories) to power (Watts) using the appropriate formulas
  • Explore the relationship between emissivity and heat transfer in different materials
  • Investigate practical examples of heat loss in biological systems
USEFUL FOR

Students in physics or engineering, thermodynamics enthusiasts, and anyone interested in understanding heat transfer and energy conservation in biological contexts.

fordy314
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Homework Statement


An ice cream cone has 290 Calories. Assuming the temperature of your skin is 32.7 C and the temperature of the air is 19.9 C, how long (hours) will it take to radiate away the energy of the ice cream cone. The emissivity of the average body is 0.915 and the average surface area of your skin is 1.25 m2.


Homework Equations


Stefan's law to get Watts
P=(J/Δt)
Q=mCΔT


The Attempt at a Solution


I'm all set with just plugging in the numbers into Stefan's Law to get watts, I'm having trouble trying to figure out how to get from watts to time though. All I can think of is

P=(J/Δt)=(Q/Δt) and Q=mCΔT, but I don't have enough information to solve for Q. Any help on this?

Thanks.
 
Physics news on Phys.org
You need Stefan-Boltzmann law.
What you wrote is just the definition of power (P=Energy/time) and not Stefan's law.
 

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