α = alpha A possible equation of state for a gas takes the form PV = RT * exp (-α / VRT) in which α and R are constants. Calculate expressions for (∂P/∂V)T, (∂V/∂T)P, (∂T/∂P)V, and show that their product is −1.

α = alpha A possible equation of state for a gas takes the form PV = RT * exp (-α / VRT) in which α and R are constants. Calculate expressions for (∂P/∂V)T, (∂V/∂T)P, (∂T/∂P)V, and show that their product is −1.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter16: Temperature And The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 67P

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Concept explainers

Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.

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α = alpha

A possible equation of state for a gas takes the form
PV = RT * exp (-α / VRT)
in which α and R are constants. Calculate expressions for
(∂P/∂V)_T, (∂V/∂T)_P, (∂T/∂P)_V,
and show that their product is −1.

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