What is initial slopes of the plot Z versus P ?

[Buffu]

Homework Statement

Use the van der waals constant for $H_2$ and $O_2$ to calculate the initial slopes of the plots of compressibility factor Z versus P.

Homework Equations

The Attempt at a Solution

Using virial expansion for van der waal gas in terms of $P$

I get $Z = 1 + \dfrac{1}{RT}\left(b - \dfrac{a}{RT} \right)P + \cdots$

Using first approximation,

Then $\dfrac{dZ}{dP} = \dfrac{1}{RT}\left(b - \dfrac{a}{RT} \right)$.

What is initial slope in this context ? $T = 0$ ?

 

[Chestermiller]

What you calculated is the initial slope.

 

[Buffu]

What you calculated is the initial slope.

But the answer does not involve $T$.

For $O_2$ it is $-4.07 \times 10^{-3} bar^{-1}$ and for $H_2$ it is $-6.92 times 10^{-4} bar^{-1}$.

Which value of $T$ should I take ?

 

[Chestermiller]

But the answer does not involve $T$.

For $O_2$ it is $-4.07 \times 10^{-3} bar^{-1}$ and for $H_2$ it is $-6.92 times 10^{-4} bar^{-1}$.

Which value of $T$ should I take ?

I confirm you virial expansion for Z in terms of P and T. Can you please determine the value of T that gives the "book" answers?