# Thread: Urgent Help Needed: solving integration

1. ## Urgent Help Needed: solving integration

Hello I am trying to solve for Tf in the problem below. Ti = 298, Pf = 10, Pi =1

Integration from Ti to Tf of (Cp/T)dt = integration of Pi to Pf dP/P, where Cp = 22.243 + 5.97710^-2*T - 3.499*10^-5*T^2 + 7.464*10^-9*T^3

I am stuck at:
Evalution from 298 to Tf for Ln (Tf/298) - 3.499*10^-5/2*Tf^2 + 7.464*10^(-9)/3*Tf^3 + 5.979*10^-2*Tf = 19.23

2. I just can't read this. So many decimals and confusing coefficients. Try writing in Latex. Use the "math" tags. Here is a model that will help you. Click on the image for the code and substitute your own information as needed.

$\displaystyle \int_{a_0}^{a_f} \frac{x^2+x+1}{5}dx$

3. ## Urgent Help Needed: solving integration

What is the best way to get Latex? I have surfed around and it seems that I will be required to pay a fee. Can you send me a link to a free download of Latex?

Thanks,

Gordon

4. ## Urgent Help Needed: solving integration

I decided to attach the problem written with microsoft equation editor, while I wait to hear from you regarding the use of Latex.

Thanks, GN

5. Originally Posted by gnameni

What is the best way to get Latex? I have surfed around and it seems that I will be required to pay a fee. Can you send me a link to a free download of Latex?

Thanks,

Gordon
LaTeX Online Equation Editor

6. $\displaystyle \int_{Ti}^{Tf}\left(\frac{Cp}{T} \right)dT=\int_{Pi}^{Pf}\left(\frac{dP}{P} \right)$
$\displaystyle Where Cp(T) = 2.243+5.977\bullet {10}^{-2}T - 3.499\bullet {10}^{-5}{T}^{2} + 7.464\bullet {10}^{-9}{T}^{3}$
$\displaystyle {T}_{i}=298, {P}_{i}=1, {P}_{i}=10$
$\displaystyle solve for {T}_{f}$
$\displaystyle \int_{Pi}^{Pf}\left(\frac{dP}{P} \right)= ln \left(\frac{{P}_{f}}{{P}_{i}} \right)=2.3$
$\displaystyle \left(\frac{Cp}{T} \right)= 22.243\bullet {T}^{-1} - 3.499\bullet {10}^{-5}T + 7.464\bullet {10}^{-9}{T}^{2}+5.979\bullet {10}^{-2}dT$
$\displaystyle \int_{298}^{Tf}\left(\frac{Cp}{T} \right)dT = 22.243ln\left(\frac{{T}_{f}}{298}\right) - 3.499\bullet {10}^{-5}\frac{{T}^{2}}{2} + 7.464\bullet {10}^{-9}\frac{{T}^{3}}{3} + 5.979\bullet {10}^{-2}T$
$\displaystyle 22.243ln\left(\frac{{T}_{f}}{298}\right) - \frac{3.499\bullet {10}^{-5}}{2}\left( {{T}_{f}}^{2}-{{298}^{2}}\right)$ +
$\displaystyle \frac{7.464\bullet {10}^{-9}}{3}\left( {{T}_{f}}^{3}-{{298}^{3}}\right) + 5.979\bullet {10}^{-2}\left( {{T}_{f}}-{{298}}\right)=2.3$

This is where I am stuck. Can someone walk me through how to solve for $\displaystyle {T}_{f}$?

7. ## Urgent Help Needed! solving integration

Can someone PLEASE help me solve this integration!? Or, just point me to more resources that I can use to solve the problem! Is anyone familiar with Maple? I need to solve this problem in the next 3 hours!

Thank you! Thank you!