Question

In the equation for heat transfer where Q/t=(kA(Thot-Tcold))/d, I understand that heat is being transferred over time, but what value is assigned to the denominator, t, in this instance? Thank you!

Answer 1

Where did you get that equation?

Answer 2

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Answer 3

Hyper-Physics is host by the University of Georgia Department of Physics and Astronomy

Answer 4

t is simply the time taken for the amount of heat Q to be transferred, so t will depend on the value of Q.
Or taking Q and t together, the equation gives you the rate of heat transfer.

Answer 5

So what you are saying then is...whatever the result for "Q", I can simply take that over any period of time for "t" and come up with an answer??? Sorry...that just doesn't seem logical.

Answer 6

No that is not what I'm saying. Actually I don't see how to say it any simpler, t is the time taken to transfer an amount of heat Q.
For a given value of Q, t is determined by the other quantities, kappa, A, difference in T's and d.

Answer 7

I understand what you are saying, thank you

Answer 8

In this equation heat \(Q\) (which isn't a substance) is changing with time
\[\frac Qt=\frac{\kappa A}d(T_\text{hot}-T_\text{cold})\]

If we rearrange \[Q=\frac{\kappa A}d(T_\text{hot}-T_\text{cold})t\]

And take the derivative with respect to time
\[\frac{\mathrm d Q}{\mathrm dt}=\frac{\mathrm d}{\mathrm dt}\left(\frac{\kappa A}d(T_\text{hot}-T_\text{cold})t\right)\]
And make the assumption the none of the variables are changing during the transfer
\[\frac{\mathrm d Q}{\mathrm dt}=\frac{\kappa A}d(T_\text{hot}-T_\text{cold})\frac{\mathrm d}{\mathrm dt}\left(t\right)\\\qquad=\frac{\kappa A}d(T_\text{hot}-T_\text{cold})\]

We see the derivative of heat; the rate that heating is occurring is constant, ie for any given length of time the same amount of heating will occur.

Answer 9

Thank you for the clarification. There have been so many differing approaches to this, I have become wary. I have been looking for an approach that would allow for any substance using the same variable, in this case thermal conductivity, and not have to use different equations for different substances, in this particular case steel vs. polypropylene.