Ask Me Help Desk - Need help rearranging termal conductivity formulas

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Need help rearranging termal conductivity formulas

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)

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

$<br /> \frac Q T = \frac {KA (T_1-T_2)} d<br />$

Multiply both sides by d:

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

Then expand the right hand side:

$<br /> KA(T_1-T_2) = KAT_1 - KAT_2<br />$

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

Now add $KAT_2$ to both sides:

$<br /> \frac {dQ} T + KAT_2 = KAT_1 - \cancel{KAT_2} + \cancel{KAT_2} = KAT_1<br />$

Finally divide both sides by KA:

$<br /> \frac {dQ}{TKA} - \frac {\cancel{KA}T_2}{\cancel{KA}} = T_1<br />$

Rearranging:

$<br /> T_1 = \frac {dQ}{KAT} +T_2<br />$

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