Calculating Watts to Air Temperature Rise in a Given Area

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Discussion Overview

The discussion revolves around calculating the temperature rise in air and copper wire based on power input measured in Watts. Participants explore the relationship between energy consumption, specific heat, and temperature changes in different materials, including air and copper, within a defined volume or mass.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant requests help calculating the temperature rise in a sealed container with a 100 Watt heat source, initially assuming 100 Watts of heat is supplied.
  • A correction is made regarding the interpretation of 100 Watts as power consumed rather than heat generated.
  • Another participant provides a calculation for temperature rise in air using specific heat and density values, resulting in a proposed rise of 6.5°C over one minute.
  • Discussion includes assumptions about efficiency, with one participant suggesting that all supplied energy is converted to heat in a resistor.
  • A participant introduces a new question about calculating the maximum surface temperature of a stranded copper wire when subjected to 100 Watts of power, seeking equations and examples.
  • Another participant notes that the calculation method remains the same, substituting specific heat values for different materials.
  • A participant shares findings on specific heat values and expresses appreciation for learning from the forum.
  • One participant questions the correctness of their calculation for temperature rise in copper, using specific heat and density values, and arrives at a result of 0.00174°C.
  • Another participant points out that their wire has a smaller area than the assumed 1m³ block of copper and seeks guidance on how to adjust calculations accordingly.
  • One participant attempts to calculate the heat required to raise the temperature of the copper wire, using mass, specific heat capacity, and temperature change, resulting in a proposed power requirement of 1053 Watts.

Areas of Agreement / Disagreement

Participants express varying interpretations of efficiency in heating calculations and the application of specific heat values. There is no consensus on the correctness of the calculations presented, and multiple approaches are discussed without resolution.

Contextual Notes

Participants rely on specific heat and density values that may vary based on conditions and definitions. Some calculations assume idealized scenarios, and the applicability of results to real-world situations remains uncertain.

Who May Find This Useful

This discussion may be useful for individuals interested in thermodynamics, electrical engineering, or material science, particularly those looking to understand heat transfer and energy calculations in different contexts.

burnit
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Hi All,

Could someone please help me with the calculations & an example of Watts consumed to Air Temperature rise in a given area:

Eg:
If we have a closed sealed container with no outside influences of area say 1 cubic meter, well insulated with an electrical heat source of the best efficiency supplying 100 Watts of heat inside.

What would be the temperature rise in celsius for 1 minute?

Thank You
 
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Sorry, i need to correct something, i should have said with 100 Watts being consumed from the Power supply & not with 100 Watts of heat in the container.
 
The specific heat of air is 716 J/kG K. The density of air is 1.3 kg/m^3. 1 watt is 1 J/sec.

So. In 60 seconds, you'd get a temperature rise of:
100*60/716/1.3=6.5 C
 
Thanks Russ,

So we assume 100% efficiency turning energy to heat with resistance heating elements etc.
 
No, we assume 100% inefficiency:wink:
Remember that heat is just "waste energy", when you use a certain amount of energy you always "produce" the same amount of heat.

In the case of a resistor there is nowhere else for the energy to go, so all of the energy you supple to the resistor is converted into heat.
 
Yes, i get what your saying with inefficiency.


I have another question with Watts Vs Heat in copper wire that i would like to be able to calculate & put some numbers to if someone could help me again with the equations & also an example.

Eg,

I have a length of stranded copper wire 300mm long consisting of 7 strands of "AWG 14" 1.63mm diameter each.
If i apply 100 Watts of power across this as in resistance heating, what will be the maximum surface Temperature of the wire if it stays connected to the 100 Watt supply or after 1 Min if time is applicable.
 
Not sure if AC or DC makes a difference but it is AC that i would like to calculate for.
 
The calculation is the same as what I just went through: just substitute the specific heat of copper in place of the specific heat of air.
 
Thanks Again Russ,

Just did a search & found an excellent chart of specific heat values, i wasn't sure how to go about this with different materials etc until now.

Learn something everyday on this Forum--Excellent!

Thank You Again
 
  • #10
Just need to make sure i have this correct because i just did the calculation & it doesn't seem right?

Ok,

From the figures i found on the Net:

Specific Heat of Copper is 385 J/kg K, Density of Copper is 8940 kg/m^3

100*60/385/8940/m^3= .00174 deg C

Is this correct?
 
  • #11
I Guess as in heating the air example it was heating a 1m^3 area, so the above calculation is also heating a 1m^3 block of Copper.
My wire has a smaller area, how do i calculate the area of my wire example into this equation?
 
  • #12
After tossing & turning all night due to the lack of brain cells i'll give it another go & look at it in another way?

Heat required to raise the temperature of the example copper wire:

Mass of the example wire = .045 kg
Specific Heat Capacity of Copper = .39 KJ/kg K
Final Temp = 100 C
Initial Temp = 40 C

Q = mc(T2 - T1)

Q = .045 * .39 * 60 = 1.053 KJ/sec = 1053 Watts

Is this correct?
 

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