What is initial slopes of the plot Z versus P ?

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Homework Help Overview

The discussion revolves around calculating the initial slopes of the compressibility factor Z versus pressure P using the van der Waals constants for hydrogen (H2) and oxygen (O2). The original poster attempts to apply the virial expansion to derive the relationship between Z and P.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the derivation of the initial slope using the virial expansion and question the relevance of temperature (T) in the context of the calculated slopes. There is a focus on understanding how T influences the results and which specific value should be used to align with reference answers.

Discussion Status

The discussion is ongoing, with participants confirming the calculations and exploring the implications of temperature on the results. There is no explicit consensus on the value of T to use, and multiple interpretations regarding its role are being examined.

Contextual Notes

Participants are navigating the constraints of the problem, particularly the lack of clarity on the temperature value needed to achieve the expected results. The original poster's question about the initial slope and its dependence on T remains a focal point of inquiry.

Buffu
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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 ## ?
 
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What you calculated is the initial slope.
 
Chestermiller said:
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 ?
 
Buffu said:
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?
 

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