Temperature Coefficient of Resistance and Specific Heat

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Discussion Overview

The discussion revolves around estimating the electrical power required to heat a material from 20°C to 1000°C in a specified time frame. Participants explore the relationship between specific heat, temperature coefficient of resistance, and the discrepancies between calculated and manufacturer-specified power requirements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant calculates the power needed for heating based on specific heat and estimates heat losses, arriving at a total of 1400W.
  • The manufacturer claims that 12600W is required initially due to the temperature coefficient of resistance (TCR) of 0.0015, which raises questions about the relationship between TCR and specific heat.
  • Another participant clarifies that TCR relates to electrical resistance, not specific heat.
  • There is a correction regarding the mass of the sample, suggesting it is 113g instead of 11.39g.
  • Several participants inquire about the heating method, geometry of the heater, and whether the heating is applied from one or both sides.
  • One participant notes that the effect of TCR on power calculations is small and emphasizes the importance of consistent units in calculations.
  • A participant expresses confusion over the significant difference between their calculations and the manufacturer's specifications, indicating a need for further clarification.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the relationship between specific heat and TCR, and there are multiple competing views regarding the calculations and the heating method. The discussion remains unresolved with respect to the discrepancies in power requirements.

Contextual Notes

Participants express uncertainty about the assumptions made in the calculations, the definitions of terms like "sqin," and the specifics of the heating setup. There are unresolved mathematical steps and potential dependencies on the geometry of the heater and the material properties.

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I am trying to estimate the amount of electrical power needed to heat up a material from 20C to 1000C in 20 seconds. Assuming it is 18sqin and 3mm thick, I used the specific heat which was given as 0.78 J/gC and weight 11.39g (from the destiny of 3.26).

0.78 J/gC x 11.39g x (1000C - 20C) / 20sec = 435 J/s = 435 W.

Now I know I've left out some heat losses.
I estimate Radiation at 1000C with an emissivity of 0.85 would be around 1470W
Convective loss around 377W with a 25mph wind
If heatup is linear, I would expect maybe half of that would be the losses during warmup are around 950W
so perhaps a total of 1400W needed for the heatup

Reading data from the manufacturer, they tell me that 700W/sqin (12600W total) are required to heat it from 20C to 1000C in 20sec. I asked them why so much and they say it has a "Temperature Coefficient of Resistance" of 0.0015. I showed them my calculation, they tell me that will give an average power needed, but 12600W is required at the start.

That makes no sense to me as I would expect the power to be constant and I am unfamiliar with this TCR coefficient. How is TCR related to Specific Heat?
What am I missing?
 
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It is not related to specific heat but to the electrical resistance.
http://www.allaboutcircuits.com/textbook/direct-current/chpt-12/temperature-coefficient-resistance/

What is "sqin"?
 
nasu said:
What is "sqin"?

' square inches ' .
 
I think the mass of your sample is 113 g rather than 11.3 g.
Isn't it?
 
Exactly how is this plate being heated - it is not at all clear what you are doing from your initial description .
 
What is the material that you are trying to heat up? Are you heating it from one side or from both sides? Is the heater in contact with the sample? What is the geometry of the heater?
 
the temperature coefficient of resistance tells you how much the resistance of the specimen will change as it warms up (or cools down) this could effect your calculations of power supplied by electrical means.
The effect is small and I think that you have more to worry about before temperature coefficient of resistance becomes a significant aspect in your calculations.
By the way, it is very bad to mix up units in calculations...square inches and mm do not work well together.
 
It material is being heated electrically, it is a square plate in geometry. I thought that using my calculation using specific heat and then including losses from convection and radiation, I should arrive at an answer fairly close (ie. within 25%). However, the numbers I'm getting from the spec are an order of magnitude different.
 
See nasu's post #4.
 
  • #10
AH, I see, I must have missed that post. Now I'm only about 3X off from their estimate. A 3X safety factor seems resonable
 

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