What are the following partial derivatives for the van der Waals equation of state? The number of moles is constant so let's use the molar volume form of the equation: а (2) (V – b) = RT P + да) Provide an interpretation for the partial derivatives in parts a) and b). Be concise! Your explanation should be -1 sentence per partial derivative.
What are the following partial derivatives for the van der Waals equation of state? The number of moles is constant so let's use the molar volume form of the equation: а (2) (V – b) = RT P + да) Provide an interpretation for the partial derivatives in parts a) and b). Be concise! Your explanation should be -1 sentence per partial derivative.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![**Van der Waals Equation Partial Derivatives**
**Question:**
What are the following partial derivatives for the van der Waals equation of state? The number of moles is constant, so let’s use the molar volume form of the equation:
\[
\left( P + \frac{a}{\bar{V}^2} \right) (\bar{V} - b) = RT
\]
**Partial Derivatives:**
a) \(\left(\frac{\partial P}{\partial a}\right)_{\bar{V},T,b}\)
b) \(\left(\frac{\partial P}{\partial b}\right)_{\bar{V},T,a}\)
**Instructions:**
Provide an interpretation for the partial derivatives in parts a) and b).
Be concise! Your explanation should be ~1 sentence per partial derivative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70b600a9-4fe2-43b6-bf71-9653b547ae78%2F019ff286-49b9-4492-9dd8-ed594140fdb6%2Fo2jyb1m_processed.png&w=3840&q=75)
Transcribed Image Text:**Van der Waals Equation Partial Derivatives**
**Question:**
What are the following partial derivatives for the van der Waals equation of state? The number of moles is constant, so let’s use the molar volume form of the equation:
\[
\left( P + \frac{a}{\bar{V}^2} \right) (\bar{V} - b) = RT
\]
**Partial Derivatives:**
a) \(\left(\frac{\partial P}{\partial a}\right)_{\bar{V},T,b}\)
b) \(\left(\frac{\partial P}{\partial b}\right)_{\bar{V},T,a}\)
**Instructions:**
Provide an interpretation for the partial derivatives in parts a) and b).
Be concise! Your explanation should be ~1 sentence per partial derivative.
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