Moufid Hilal - Graphical Thermodynamics

GRAPHICAL
THERMODYNAMICS
AND IDEAL GAS
POWER CYCLES

GRAPHICAL
THERMODYNAMICS
AND IDEAL GAS
POWER CYCLES

IDEAL GAS THERMODYNAMICS IN BRIEF

MOUFID I. HELAL

Graphical Thermodynamics and Ideal Gas Power Cycles: Ideal Gas Thermodynamics in Brief

Copyright Momentum Press, LLC, 2017.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any meanselectronic, mechanical, photocopy, recording, or any otherexcept for brief quotations, not to exceed 250 words, without the prior permission of the publisher.

First published in 2017 by

Momentum Press, LLC

222 East 46th Street, New York, NY 10017

www.momentumpress.net

ISBN-13:978-1-60650-506-9 (print)

ISBN-13: 978-1-60650-507-6 (e-book)

Momentum Press Thermal Science and Energy Engineering Collection

Cover and interior design by S4Carlisle Publishing Service Private Ltd.

Chennai, India

10 9 8 7 6 5 4 3 2 1

A BSTRACT

In this book, an almost new approach to modern thermodynamics has been applied. One or more useful qualitative discussion statements have been extracted from each equation. These and other important statements were numbered and their titles were situated in an index entitled Helal and Others statements, definitions and rules. This ensures very quick obtaining of the required (for discussing and solving problems) statements, rules, definitions, equations, and their theoretical base that much eases readers qualitative discussions and calculations. Almost all ideal gas closed system thermodynamic topics are either discussed in depth or deeply abbreviated. The topics discussed in depth are either new original ones or valuable classical ones that increase readers ability for better understanding but are overlooked or deeply abbreviated in modern thermodynamic books. In both cases, they are significantly improved. The main five new ideas that are discussed in depth in this book are: (1) The ideal gas polytropic process for Cv = f(T) and its analysis (Chapter 6, Part I), (2) The theoretical realization of reversible gas state change processes (5-10), (3) Helal cycle (s 7-5-2), (4) Helal graphical method for comparing and discussing power cycles ( 7-5-4), and (5) the imperfection in the classical proof of Carnots efficiency (theorem) and its exclusion (Chapter 7, final section). The deeply abbreviated topics are rigorously discussed in depth in the majority of modern thermodynamic books. To dissipate any misunderstanding, the equations and statements that can be misunderstood are followed by explanatory sentences (see equation 1-38 and the paragraph following it).

KEYWORDS

absolutely reversible cycle;Carnot; Carnots efficiency; closed thermodynamic system; cycles ability for heat regeneration; the equivalent thermodynamic cycles; Ericsson and Dual cycles; Helal air standard cycle; Helal method; heat regeneration; ideal gas property tables; the imperfection in the classical proof of Carnots efficiency (theorem) and its exclusion; a new, polytropic ideal gas state change process; polytropic state change process; the regeneratability condition; reversible cycle recognizing thermodynamic properties; second law of thermodynamics; Stirling cycle; the theoretical realization of reversible gas state change processes; thermal efficiency.

C ONTENTS

This book Graphical Thermodynamics and Ideal Gas Power Cycles is based on authors book in Arabic Technical Thermodynamics, Volume 1, Third Edition, Second Revision, Published in 2006 by Damascus University Press-Damascus University in Damascus-Syrian Arab Republic. We will refer to this book as the base book.

The base book discusses in depth many topics including the following five original topics in addition to a number of traditional topics that are useful for better understanding thermodynamics and that are rarely met in modern thermodynamics:

1. The analysis of the ideal gas polytropic process for Cv = f(T): A new analysis making possible executing exact solutions of the polytropic process problems by using the already existing ideal gas property tables.

2. The theoretical realization of reversible gas state change processes: This topic consists of two parts: (1) the first part is traditional, but it was not successfully explained, and it does not exist in modern books. This part enables better understanding of concepts relating to equilibrium and reversibility. (2) The second part is new and original. It enables best understanding of concepts relating to equilibrium, reversibility, irreversibility, ability for heat regeneration, and so on.

3. Helal graphical method for comparing heat engine cycles. This method is more flexible and inclusive than the previous methods. It allows to examine qualitatively the influence of cycles characteristics (r, rp, and rc) on the thermal efficiency of the dual cycle and enables additionally better understanding of T_s diagram.

4. Helal cycle (a new common case ideal gas ideal thermodynamic cycle): Five of its seven special case cycles have counterparts in reality. These are the Carnot, Otto, Brayton, Stirling, and Ericsson cycles.

5. Detecting and excluding the imperfection in the classical proof of Carnots efficiency (theorem): The classical proof of the Carnots efficiency ( theorem ) is imperfect. It did not prove that the arbitrary reversible cycle used in the proof represents all ever possible engine cycles.

In the base book and especially in its new original topics, an almost new approach was applied. One or more statements, which are useful for qualitative discussions, were extracted from each equation. These statements were numbered as rules or definitions, and their titles were situated in a special index entitled Helal definitions and rules. This ensured the quick finding of the required (for discussing and solving problems) rules, definitions, equations, and their theoretical base. The reduction in the required time and efforts to find the necessary tools for discussing and solving problems comforts the readers and eases their efforts. In this book:

1. The new approach that is partially applied in the base book is applied in the whole book. One or more statements, which are useful for qualitative discussions, were extracted from each equation. These and other important statements were numbered as rules or definitions, and their titles were situated in a special index entitled Helal and Others statements, definitions, and rules. This will ensure the very quick finding of the required (for discussing and solving problems) statements, rules, definitions, equations, and their theoretical base. The reduction in the required time and efforts to find the necessary tools for discussing and solving problems comforts the readers and eases their efforts. According to my experience, it will be much easier to the reader to use the rules instead of relations in qualitative discussions. Readers will benefit from the following: (1) Helal and others statements, definitions, and rules, which will be included in the appendix, (2) the new topics, and (3) some traditional topics that are unusually explained.

2. Almost all ideal gas closed system thermodynamic topics are either discussed in depth or deeply abbreviated. (1) The topics discussed in depth are either new original ones that are based on the base book or valuable classical ones that increase readers ability for better understanding but are overlooked or deeply abbreviated in modern thermodynamic books. And in both cases, they are significantly/gregariously improved. (2) The deeply abbreviated topics are significantly/gregariously discussed in depth in the majority of modern thermodynamic books. The following main new ideas that were discussed in the base book are discussed here in depth: (1) the analysis of the ideal gas polytropic process for Cv =