# Equation measuring heat with temperature change, time and specific heat

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
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Does anyone know any equation that would include time (z)???

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)

ohh, I'm really sorry, :(,