Thread: 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

Originally Posted by j-lee00

I dont know the latex format for pd

Basically the same thing that you have, except replace [tex] with [tex] and [/tex] with [/tex] .

-Dan

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

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

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

B(T) not a constant

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