A question on heat transfer and blackbodys

  • Context: Graduate 
  • Thread starter Thread starter pastro
  • Start date Start date
  • Tags Tags
    Heat Heat transfer
Click For Summary
SUMMARY

The discussion centers on the relationship between the Stefan-Boltzmann law, represented by the equation \(\frac{dQ}{dt} = \sigma A T^{4}\), and the specific heat equation \(Q = mc\Delta T\). The user inquires whether taking the time derivative of the second equation and equating it to the power emitted by a blackbody can yield a temperature function for a blackbody radiator cooling in a vacuum. The consensus is that these equations pertain to different heat transfer mechanisms, with the first addressing radiation and the second focusing on convective heat transfer, indicating that they cannot be directly equated.

PREREQUISITES
  • Understanding of the Stefan-Boltzmann law
  • Familiarity with the concept of specific heat capacity
  • Knowledge of differential equations
  • Basic principles of heat transfer mechanisms
NEXT STEPS
  • Study the derivation and applications of the Stefan-Boltzmann law
  • Explore the principles of convective heat transfer
  • Learn about the differences between radiation and convection in heat transfer
  • Investigate the cooling laws for blackbody radiators in vacuum
USEFUL FOR

Students and professionals in physics, particularly those focusing on thermodynamics and heat transfer, as well as engineers working with thermal systems and blackbody radiation concepts.

pastro
Messages
15
Reaction score
0
Hello,

I was wondering:
\frac{dQ}{dt} = \sigma A T^{4}
for a perfect blackbody.

Also
Q = mc\DeltaT

If I take the time derivative of the above equation, set it equal to the power emitted by a blackbody, and solve the resulting differential equation for temperature, does that give me the temperature with which a blackbody radiator of a given mass and material cools in vacuum as a function of time?

Just curious...

Thanks!
 
Last edited:
Science news on Phys.org
Ummm, I doubt it.

Equation 1 is for, well, radiation.

Equation 2, as I understand it, is for convective heat transfer.

The two are not really the same thing.
 

Similar threads

Undergrad Questions about Jean-Rayleigh's derivation of Ultraviolet Catastrophe
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Blackbody radiation and the cosmic microwave background
  • · Replies 29 ·
Replies
29
Views
5K
Graduate Practical use of an overall heat transfer coefficient?
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Calculating the heat loss of an open water tank (aquarium)
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Heat Equilibrium in elliptical cavities, and the second Law
  • · Replies 17 ·
Replies
17
Views
4K
Undergrad Temperature change due to mixing liquids, heating and heat losses
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Warm-up time for a hollow cylinder
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Heat exchange in a thermal storage based on phase change materials
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How to measure average thermal conductivity of a metallic material?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Blackbody radiation with frequency filter
  • · Replies 3 ·
Replies
3
Views
2K