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B. The change in volumetric entropy of a gas explains why it expands spontaneously. Similarly, the increase in entropy due to the mixing of two (or more) different gases explains why such process occurs spontaneously. Here you'll consider the mixing of two distinct ideal gases. The final mixture has a number N of particles in a volume V. The two gases start at the same pressure and temperature, separated by a partition which is then removed. The number of particles in each gas is a fraction of N. Say N₁ = N and N₂ = N. and ). 1. Relate the volumes V₁ and V₂ to the final volume V (calculate P.T 2. Calculate, in terms of N only, the changes AS, and AS, in the entropy of each gas as each expands to a final volume V. Calculate the total entropy change ASmix and explain why the mixing process proceeds spontaneously.

B. The change in volumetric entropy of a gas explains why it expands spontaneously. Similarly, the increase in entropy due to the mixing of two (or more) different gases explains why such process occurs spontaneously. Here you'll consider the mixing of two distinct ideal gases. The final mixture has a number N of particles in a volume V. The two gases start at the same pressure and temperature, separated by a partition which is then removed. The number of particles in each gas is a fraction of N. Say N₁ = N and N₂ = N. and ). 1. Relate the volumes V₁ and V₂ to the final volume V (calculate P.T 2. Calculate, in terms of N only, the changes AS, and AS, in the entropy of each gas as each expands to a final volume V. Calculate the total entropy change ASmix and explain why the mixing process proceeds spontaneously.

Introduction to Chemical Engineering Thermodynamics
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
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B. The change in volumetric entropy of a gas explains why it expands spontaneously. Similarly, the increase in entropy due to the mixing of two (or more) different gases explains why such process occurs spontaneously. Here you'll consider the mixing of two distinct ideal gases. The final mixture has a number N of particles in a volume V. The two gases start at the same pressure and temperature, separated by a partition which is then removed. The number of particles in each gas is a fraction of N. Say N₁ = N and N₂=N. 1. Relate the volumes V₁ and V₂ to the final volume V (calculate and ). P.T 2. Calculate, in terms of N only, the changes AS, and AS, in the entropy of each gas as each expands to a final volume V. Calculate the total entropy change ASmix and explain why the mixing process proceeds spontaneously. P.T 3. Consider now mixing a general fraction of particles of each type, say N₁ = x N and N₂ = y N (the fractions x and y add up to 1). Repeat both previous steps to obtain an expression for ASmix in terms of N, x and y only. Evaluate it for a mol of particles (N = N₁) and for x = and 4 2
Transcribed Image Text:B. The change in volumetric entropy of a gas explains why it expands spontaneously. Similarly, the increase in entropy due to the mixing of two (or more) different gases explains why such process occurs spontaneously. Here you'll consider the mixing of two distinct ideal gases. The final mixture has a number N of particles in a volume V. The two gases start at the same pressure and temperature, separated by a partition which is then removed. The number of particles in each gas is a fraction of N. Say N₁ = N and N₂=N. 1. Relate the volumes V₁ and V₂ to the final volume V (calculate and ). P.T 2. Calculate, in terms of N only, the changes AS, and AS, in the entropy of each gas as each expands to a final volume V. Calculate the total entropy change ASmix and explain why the mixing process proceeds spontaneously. P.T 3. Consider now mixing a general fraction of particles of each type, say N₁ = x N and N₂ = y N (the fractions x and y add up to 1). Repeat both previous steps to obtain an expression for ASmix in terms of N, x and y only. Evaluate it for a mol of particles (N = N₁) and for x = and 4 2
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