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(a) Derive the change in the entropy for adiabatic reversible expansion of a diatomic ideal gas from V; to V, starting with the Tinitial temperature (neglect the temperature dependence of the heat capacity). (b) Verify that the same entropy change is obtained if the gas is first expanded reversibly and isothermally the final volume followed by (reversible) cooling at constant V.

(a) Derive the change in the entropy for adiabatic reversible expansion of a diatomic ideal gas from V; to V, starting with the Tinitial temperature (neglect the temperature dependence of the heat capacity). (b) Verify that the same entropy change is obtained if the gas is first expanded reversibly and isothermally the final volume followed by (reversible) cooling at constant V.

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
Problem 1.1P
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(a) Derive the change in the entropy for adiabatic reversible expansion of a diatomic ideal gas from \( V_i \) to \( V_f \), starting with the \( T_i \) initial temperature (neglect the temperature dependence of the heat capacity). (b) Verify that the same entropy change is obtained if the gas is first expanded reversibly and isothermally to the final volume followed by (reversible) cooling at constant \( V \).
Transcribed Image Text:(a) Derive the change in the entropy for adiabatic reversible expansion of a diatomic ideal gas from \( V_i \) to \( V_f \), starting with the \( T_i \) initial temperature (neglect the temperature dependence of the heat capacity). (b) Verify that the same entropy change is obtained if the gas is first expanded reversibly and isothermally to the final volume followed by (reversible) cooling at constant \( V \).
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Step 1: Given Data

(a) An adiabatic reversible expansion is given of a diatomic ideal gas fom Vi to Vf

The initial temperature is Ti

We need to derive the change in etropy  

(b) We need to verify if the same entropy change is obtained if the gas is first expanded reversibly and isothermally  and the final volume followed by reversible cooling  at constant V 

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