The density of an ideal gas can be written in terms of the variables p and T:Mpd =where M is the molar mass of a gas.RT(a) Use the cyclic rule to write an expression for (oden)(%),in terms of a ratio of partialderivatives.(b) show that the cyclic rule in part a is true for an ideal gas.

We see cyclic rule first for the given equation d = MP/RT For solving this problem you must have…

The density of an ideal gas can be written in terms of the variables p and T: Mp where M is the molar mass of a gas. d = RT (a) Use the cyclic rule to write an expression for in terms of a ratio of partial derivatives. (b) show that the cyclic rule in part a is true for an ideal gas.

The density of an ideal gas can be written in terms of the variables p and T: Mp where M is the molar mass of a gas. d = RT (a) Use the cyclic rule to write an expression for in terms of a ratio of partial derivatives. (b) show that the cyclic rule in part a is true for an ideal gas.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter1: Gases And The Zeroth Law Of Thermodynamics

Section: Chapter Questions

Problem 1.66E

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Concept explainers

Kinetic-Theory of Gases

Kinetic theory of gases is the model or method which was developed in the 19th century by Maxwell and Boltzmann. This is possible as the interatomic force which is of short-range forces that are important for solids and liquids can be neglected for gases. This theory or gas law gives a molecular interpretation of the pressure and temperature of a gas and is consistent with gas laws and Avogadro’s hypothesis. This theory is very helpful to correctly explain the specific heat capacities of many gases, kinetic energy and it also explains the transport qualities such as viscosity, thermal conductivity, and diffusion with molecular parameters. As stated in the kinetic-molecular theory, the temperature of a substance or gas particle is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the motion of the particles, called average kinetic energy.

Question

The density of an ideal gas can be written in terms of the variables p and T:
Mp
d =
where M is the molar mass of a gas.
RT
(a) Use the cyclic rule to write an expression for (oden)
(%),
in terms of a ratio of partial
derivatives.
(b) show that the cyclic rule in part a is true for an ideal gas.

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