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bumblebee08 · Apr 12, 2012, 05:40 PM

I know the basics of rearranging formulas but I am not really sure how to rearrange a more complicated formula. I am trying to rearrange a thermal conductivity formula to solve for T1, but I am not really sure how. I someone could walk me through it that would be great.

Q/T= KA(T1-T2)/d

Am I doing this write?

Q/T - T1= KA(T1- T1 - T2)
----- ----------------------
Q/T Q/T (d)

to become

-T1 = KA-T2
---------
Q/T (d)

ebaines · Apr 13, 2012, 06:00 AM

Not quite right. It looks like you are trying to get the T1 term by itself, correct? Starting with:

$ \frac Q T = \frac {KA (T_1-T_2)} d $

Multiply both sides by d:

$ \frac {dQ} T = \frac {KA (T_1 -T_2)} {\cancel {d}} \times \cancel {d} = KA(T_1-T_2) $

Then expand the right hand side:

$ KA(T_1-T_2) = KAT_1 - KAT_2 $

So you now have:
$ \frac {dQ} T = KAT_1 - KAT_2 $

Now add $KAT_2$ to both sides:

$ \frac {dQ} T + KAT_2 = KAT_1 - \cancel{KAT_2} + \cancel{KAT_2} = KAT_1 $

Finally divide both sides by KA:

$ \frac {dQ}{TKA} - \frac {\cancel{KA}T_2}{\cancel{KA}} = T_1 $

Rearranging:

$ T_1 = \frac {dQ}{KAT} +T_2 $