(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
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
Related questions
Question
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 \( V \).
Expert Solution
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
Step by step
Solved in 6 steps with 18 images
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The