i am stuck again with this problem. Can you guys please help me rearranging this equation for T?
ln (P) = A + (B/T) + C ln (T) solve for T
Thanks in advance. :?
Where are you getting these problems? This has T both "inside" and "outside" a transcendental function (ln) so there is no "algebraic" way to solve for T. You might be able to do it in terms of the "Lambert W function" which is defined as the inverse function to \(\displaystyle f(x)= xe^x\).
We can write this as \(\displaystyle ln(T)= A/C+ B/(TC)- ln(P)/C\) and take the exponential of both sides:
\(\displaystyle T= e^{A/C} e^{B/(TC)} P^{-1/C}\)
Divide both sides by \(\displaystyle e^{B/TC}\)
\(\displaystyle Te^{-B/TC}= e^{A/C}P^{-1/C}\)
Let x= B/TC so that T= B/(Cx) and the equation becomes
\(\displaystyle [B/(Cx)]e^{-x}= e^{A/C}P^{-1/C}\)
Multiply both sides by \(\displaystyle xe^{x}\) and divide both sides by \(\displaystyle e^{A/C}P^{-1/C}\):
\(\displaystyle xe^{x}= (B/C)e^{-A/C}P^{1/C}\)
Then \(\displaystyle B/(TC)= x= W((B/C)e^{-A/C}P^{1/C})\) so
\(\displaystyle T= \frac{CW\left((B/C)e^{-A/C}P^{1/C}\right)}{B}\)
