Q-5. This problem focuses on the thermal expansion coefficient for a van der Waals gas. a) Derive an expression for the thermal expansion coefficient of a van der Waals gas [Hint; you can't solve the VDW equation for the molar volume, so use either the reciprocal identity or the method of implicit differentiation to evaluate the partial derivative]. Warning: this formula may not be very simple! b) Show that your equation reduces to the ideal gas formula in the limit that a and b vanish. c) Calculate the thermal expansion coefficient of ammonia, modeled as a van der Waals gas, at 300K and 0.5 L/mole . Compare this to the coefficient of an ideal gas.
Q-5. This problem focuses on the thermal expansion coefficient for a van der Waals gas. a) Derive an expression for the thermal expansion coefficient of a van der Waals gas [Hint; you can't solve the VDW equation for the molar volume, so use either the reciprocal identity or the method of implicit differentiation to evaluate the partial derivative]. Warning: this formula may not be very simple! b) Show that your equation reduces to the ideal gas formula in the limit that a and b vanish. c) Calculate the thermal expansion coefficient of ammonia, modeled as a van der Waals gas, at 300K and 0.5 L/mole . Compare this to the coefficient of an ideal gas.
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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![Q-5. This problem focuses on the thermal expansion coefficient for a van der Waals gas.
a) Derive an expression for the thermal expansion coefficient of a van der Waals gas [Hint; you
can't solve the VDW equation for the molar volume, so use either the reciprocal identity or the
method of implicit differentiation to evaluate the partial derivative]. Warning: this formula may
not be very simple!
b) Show that your equation reduces to the ideal gas formula in the limit that a and b vanish.
c) Calculate the thermal expansion coefficient of ammonia, modeled as a van der Waals gas, at
300K and 0.5 L/mole . Compare this to the coefficient of an ideal gas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12c18db6-f6e8-4129-b933-2f1b3972f7de%2F68a834d4-c188-40fc-9055-c2923d94e67a%2Fotb1j0k.png&w=3840&q=75)
Transcribed Image Text:Q-5. This problem focuses on the thermal expansion coefficient for a van der Waals gas.
a) Derive an expression for the thermal expansion coefficient of a van der Waals gas [Hint; you
can't solve the VDW equation for the molar volume, so use either the reciprocal identity or the
method of implicit differentiation to evaluate the partial derivative]. Warning: this formula may
not be very simple!
b) Show that your equation reduces to the ideal gas formula in the limit that a and b vanish.
c) Calculate the thermal expansion coefficient of ammonia, modeled as a van der Waals gas, at
300K and 0.5 L/mole . Compare this to the coefficient of an ideal gas.
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