How to Calculate Time for Temperature Drop in Heat Radiation Problem?

  • Thread starter Thread starter neelakash
  • Start date Start date
  • Tags Tags
    Heat Radiation
Click For Summary
SUMMARY

The discussion focuses on calculating the time required for a spherical black body with a radius of 0.1m and an initial temperature of 1000K to cool to 100K in a vacuum at 0K. The formula derived for this calculation is (CdR/9σ)(T2^(-3) - T1^(-3)), where C is the heat capacity, d is the density, R is the radius, and σ is the Stefan-Boltzmann constant. Participants clarify that Newton's law of cooling is not applicable due to the significant temperature difference, emphasizing the use of Stefan's law instead.

PREREQUISITES
  • Understanding of Stefan-Boltzmann law
  • Knowledge of heat capacity and density concepts
  • Familiarity with black body radiation principles
  • Basic calculus for manipulating equations
NEXT STEPS
  • Study the derivation and applications of Stefan-Boltzmann law
  • Explore the concept of black body radiation in detail
  • Learn about heat transfer mechanisms in thermodynamics
  • Investigate the implications of temperature gradients in cooling processes
USEFUL FOR

Students in physics or engineering disciplines, particularly those studying thermodynamics and heat transfer, as well as educators looking for practical examples of radiation cooling calculations.

neelakash
Messages
491
Reaction score
1

Homework Statement



A spherical black body having R=0.1m and initial temperature T1=10^3 K is cooled by radiation.The surrounding medium is at a temperature T=0K.What time will it take for the temperature of the sphere to drop to T2=100K?
Given heat capacity is C and density d
The answer is :

(CdR/9σ)(T2^(-3) - T1^(-3))

Homework Equations


The Attempt at a Solution



I think just application of Newton's law of cooling will suffice...Isn't it?
 
Physics news on Phys.org
No, u can't use Newton's law of cooling because the temp. difference is large.
U can use stefan's law.
 
OK,I missed...
Then how to proceed?
 

Similar threads

Replies
2
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 41 ·
2
Replies
41
Views
6K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K