Explanation Given: The gas law function is, P V = m R T , where P is pressure, V is volume, m is mass, R is the gas constant and T is temperature. Proof: The given function is, P V = m R T . Obtain the value of ∂ P ∂ V ⋅ ∂ V ∂ T ⋅ ∂ T ∂ P . ∂ P ∂ V ⋅ ∂ V ∂ T ⋅ ∂ T ∂ P = ∂ ∂ V ( m R T V ) ⋅ ∂ ∂ T ( m R T P ) ⋅ ∂ ∂ P ( P V m R ) = − m R T V 2 ⋅ [ m R P ] ( 1 ) ⋅ [ V m R ] ( 1 ) = ( − m R T V 2 ) ( m R P ) ( V m R ) = − m

Bundle: Multivariable Calculus, 8th + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Single-Term

8th Edition

ISBN: 9781305779198

Author: James Stewart

Publisher: Cengage Learning

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Chapter 14.3, Problem 88E

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To show: The function PV=mRT satisfies the equation ∂P∂V⋅∂V∂T⋅∂T∂P=−1 .

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Chapter 14.3, Problem 87E

Chapter 14.3, Problem 89E

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Chapter 14 Solutions

Bundle: Multivariable Calculus, 8th + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Single-Term

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The function P V = m R T satisfies the equation ∂ P ∂ V ⋅ ∂ V ∂ T ⋅ ∂ T ∂ P = − 1 .

Solution Summary: The author explains the gas law function PV=mRT, where P is pressure, V is volume, m is mass, R is gas constant, and T is temperature.

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To show: The function PV=mRT satisfies the equation ∂P∂V⋅∂V∂T⋅∂T∂P=−1 .

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Chapter 14 Solutions