Equation measuring heat with temperature change, time and specific heat

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Discussion Overview

The discussion revolves around the relationship between heat transfer, temperature change, time, and specific heat in a substance. Participants explore equations related to heat exchange and how time factors into the temperature change of a substance exposed to a different ambient temperature.

Discussion Character

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

Main Points Raised

  • One participant seeks a simple equation to determine the final temperature of a substance after heating, incorporating time and specific heat.
  • Another participant suggests that if the substance is heated from T1 to T2, the final temperature is T2, questioning the relevance of time.
  • A different participant describes a scenario where a substance at a lower temperature is placed in a warmer environment and asks how to calculate its temperature after a specific time, given its specific heat and heat capacity.
  • One participant introduces the concept of heat flow and provides a formula relating heat flow to the temperature difference between the substance and its surroundings, mentioning the need for a transient analysis rather than a steady-state solution.
  • There is a discussion about the thermal resistance at the interface and how it relates to the heat transfer coefficient and surface area.
  • A participant expresses confusion about terms used in the equations and seeks clarification on the meaning of T∞ and T.
  • Another participant asks about the heat transfer coefficient (h) and acknowledges its complexity, providing a link for further reading.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of time in determining the final temperature of the substance. While some suggest time is not a factor, others argue that it is essential for understanding the heat transfer process. The discussion remains unresolved regarding the best approach to incorporate time into the calculations.

Contextual Notes

The discussion highlights limitations in the participants' understanding of heat transfer concepts, particularly regarding transient versus steady-state solutions and the definitions of variables used in the equations.

Who May Find This Useful

This discussion may be useful for students and individuals interested in thermodynamics, heat transfer, and related mathematical modeling in physics and engineering contexts.

jc.int
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hello,
If I had a substance (k) and heated it from Temperature1 to Temperature2, for z seconds, is there any (simple) equation that would give me the temperature (x) of this substance at the end? (knowing, of course, the substance's specific heat(C))

I found that:
Q(energy exchanged during the process)= C*(T2-T1)

thereby:

T2=Q/C + T1

BUT TIME (z) is never mentionned
[

Does anyone know any equation that would include time (z)?
 
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I thought you said you heated the substance from T1 to T2...therefore the temperature at the end is T2 :-)

Anyway, I don't think time matters...
 
well, I mean that if a put a 10ºC/50ºF substance outdoors where the temperature is about 30ºC/86ºF, how can I find the temperature of the substance 10 minutes after, knowing the substance specific heat & heat capacity.
thanks
Jaimie
 
Oh, that's much better explained, now...not that that makes me know the answer :-)

In any case, along with finding out Q=C*(T2-T1), where I presume C is the heat capacity of the substance and include its total mass (specific heat x mass)...you should have found out that the heat flow Q is

Q = (T - T)/R

In words, the heat flow (J/s) from the surrounding ambient into your substance is proportional to the difference between temperature of ambient and temperature of substance and inversely proportional to the thermal resistance at the interface.

The thermal resistance at the interface is a result of the heat transfer coefficient, h, and the amount of surface area, A, exposed to the ambient:

R = 1/(hA)

Needless to say, you have a transient problem at hand (as opposed to a steady state solution) in which you need to calculate the amount of heat being transferred to your substance at some temperature during a time step dt, at time t, then you need to increase your substance's temperature and calculate the amount of heat that will be transfer in the next dt, etc.

In other words, the amount of heat being transferred will keep getting less and less as the substance temperature continues to increase.

You easily model this in a spreadsheet, without getting into mathematics or differential equations...just simple time-stepping.

I don't have it at hand but I think it is simply an exponential profile, where eventually, the substance reaches the ambient's temperature, of course.Hope this helps.
 
thank you very much for you answer :D
I'm afraid I still have a doubt: what does T∞ and T represent? (sorry but I'm still at high school)
 
I explained that in english right below the formula, please read.
 
ohh, I'm really sorry, :(,

thanks again for your time and your answer
 
I still have another (and I hope this time it is the last one) question:
Is there any simple way to get h (heat transfer coefficient)?

I've seen that it is quite complicated: http://goo.gl/Ol6Qj
 
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