How Does a Sphere Exchange Thermal Radiation in Different Temperatures?

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SUMMARY

The discussion focuses on calculating the thermal radiation exchange of a sphere with a radius of 0.5m, an emissivity of 0.85, and a temperature of 27°C in an environment at 77°C. The relevant equation used is P = d(ε)(A)(T^4), where d is the Stefan-Boltzmann constant, ε is emissivity, A is the surface area, and T is temperature. The sphere emits radiation based on its own temperature and absorbs radiation based on the surrounding environment's temperature. The net rate of energy exchange is determined by subtracting the emission rate from the absorption rate.

PREREQUISITES
  • Understanding of the Stefan-Boltzmann Law
  • Knowledge of thermal radiation concepts
  • Familiarity with emissivity and its significance
  • Ability to calculate surface area of a sphere
NEXT STEPS
  • Calculate the surface area of a sphere using the formula A = 4πr²
  • Learn about the Stefan-Boltzmann constant and its value (approximately 5.67 x 10^-8 W/m²K⁴)
  • Explore the concept of emissivity and its impact on thermal radiation
  • Investigate the principles of heat transfer in different environments
USEFUL FOR

Students studying thermodynamics, engineers working on thermal management systems, and anyone interested in the principles of heat transfer and thermal radiation calculations.

bmb2009
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Homework Statement


A sphere of radius .5m, temperature of 27 deg C, and emissivity = .85 is located in an environment of temperature 77 deg C. At what rate does the sphere (a)emit and (b)absorb thermal radiation? (c)What's the sphere's net rate of energy exchange?



Homework Equations





The Attempt at a Solution



(a). I know I must use the equation P = d(ε)(A)(T^4) where d = stefan-Boltz constant, ε= emissivity, A=surface area, T=temperature...but which temperature is it? I believe I should use the Sphere's temp for the emission quantity and the temp of the enviorment for the absorption radiation quantity. Is that correct?

(c) I haven't been given an equation for net rate of energy exchange but wouldn't it just be absorption - emission ?

Thanks for the help!
 
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Yes, that all looks right to me. Degrees K, of course.
 
bmb2009 said:

Homework Statement


a sphere of radius .5m, temperature of 27 deg c, and emissivity = .85 is located in an environment of temperature 77 deg c. At what rate does the sphere (a)emit and (b)absorb thermal radiation? (c)what's the sphere's net rate of energy exchange?



Homework Equations





The Attempt at a Solution



(a). I know i must use the equation p = d(ε)(a)(t^4) where d = stefan-boltz constant, ε= emissivity, a=surface area, t=temperature...but which temperature is it? I believe i should use the sphere's temp for the emission quantity and the temp of the enviorment for the absorption radiation quantity. Is that correct?

(c) i haven't been given an equation for net rate of energy exchange but wouldn't it just be absorption - emission ?

Thanks for the help!

a-ok.
 

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