# Thread: A Partial differetial question

1. ## A Partial differetial question

PV = RT(1+B(T)/V)

Code:
$\displaystyle \beta$ = (1/V)*($\displaystyle \frac{dV}{dT}$)
at constant P

show
Code:
$\displaystyle \beta$ =$\displaystyle \frac{1}{T}$*$\displaystyle \frac{V + B + T\frac{dB}{dT}}{V + 2B}$
I got to

Code:
$\displaystyle \beta$ =$\displaystyle \frac{PV}{VRT+PRTB}$*($\displaystyle \frac{R}{P}$+$\displaystyle \frac{d}{dT}$$\displaystyle \frac{RTB}{V}) I need help with Code: \displaystyle \frac{d}{dT}$$\displaystyle \frac{RTB}{V}$)
I dont know the latex format for pd

2. Originally Posted by j-lee00
I dont know the latex format for pd
Basically the same thing that you have, except replace $$with [tex] and$$ with [/tex] .

-Dan

3. To use TeX here use [ MATH] and [ /MATH] without the spaces.

Here is what you posted:

PV = RT(1+B(T)/V)

$\displaystyle \beta = (1/V)*(\frac{dV}{dT})$

at constant P

show

$\displaystyle \beta = \frac{1}{T}*\frac{V + B + T\frac{dB}{dT}}{V + 2B}$

I got to

$\displaystyle \beta=\frac{PV}{VRT+PRTB}*(\frac{R}{P}+\frac{d}{dT }\frac{RTB}{V}$)

I need help with

$\displaystyle \frac{d}{dT}\frac{RTB}{V}$

4. I need help with

$\displaystyle \frac{d}{dT}\frac{RTB}{V}$
I haven't look at the rest of it, but since R and B are constant it would seem to be that
$\displaystyle \frac{d}{dT} \left ( \frac{RTB}{V} \right ) = \frac{RB}{V} - \frac{RTB}{V^2}~\frac{dV}{dT}$

-Dan

5. B(T) not a constant

6. Originally Posted by j-lee00
B(T) not a constant
Okay, then
$\displaystyle \frac{d}{dT} \frac{RTB}{V} = R \left ( \frac{B}{V} + \frac{T}{V} \frac{dB}{dT} - \frac{TB}{V^2}\frac{dV}{dT} \right )$

(This is a rather messy problem you've got here, isn't it?)

-Dan