# What is initial slopes of the plot Z versus P ?

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1. Jun 2, 2017

### Buffu

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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 ? $T = 0$ ?

2. Jun 2, 2017

### Staff: Mentor

What you calculated is the initial slope.

3. Jun 4, 2017

### Buffu

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 ?

4. Jun 4, 2017

### Staff: Mentor

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?