The Power of Heat: 16x More Energy at 550°C

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Homework Help Overview

The discussion revolves around the energy emitted from a black body at two different temperatures: 550°C and 22°C. The original poster is attempting to understand how to calculate the ratio of energy emissions based on temperature differences, referencing the Stefan-Boltzmann law.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between temperature and energy emission, with one suggesting that doubling the temperature increases energy by a factor of 16. Another participant introduces the proportionality of radiant heat flux to the fourth power of temperature. There is also a focus on the importance of using absolute temperature in calculations.

Discussion Status

The discussion is ongoing, with participants clarifying concepts and questioning assumptions, particularly regarding temperature units and the relevance of surface area in the energy output calculations. Some guidance has been offered about unit conversion and the implications of surface area, but no consensus has been reached.

Contextual Notes

Participants note the necessity of converting Celsius to Kelvin for accurate calculations and question whether the problem specifies equal surface areas for the two black bodies involved.

lilkrazyrae
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How many times more energy is emitted from a black body at 550. degrees C than at a room temperature of 22.0 degrees C.
So I know that a double in temperature increases energy by 2^4=16 so would I just do 25^4=390625 for this problem?
 
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Well assuming the radiant heat flux is given by Q is proportional to T4, then Q1/Q2 = (T1/T2)4.
 
lilkrazyrae said:
How many times more energy is emitted from a black body at 550. degrees C than at a room temperature of 22.0 degrees C.
So I know that a double in temperature increases energy by 2^4=16 so would I just do 25^4=390625 for this problem?

Careful with your units. Whenever you plug a temperature into the blackbody formula (or pretty much any other physics-related formula), you'll want to make sure the temperature is in kelvin. This is an important distinction because the zero-point of the celsius scale is defined to be the freezing point of water (roughly), not absolute zero. Once you convert to these units, you should find a much more reasonable value for the ratio of energy outputs. Do you know how to convert to kelvin?

By the way, the rate of energy output also depends on the surface area. Does the problem specify that the surface areas of the two objects are the same?
 
Ok that makes more sense! And the problem reads just as I wrote it.
 

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