Thermodynamics Basics: Enthalpy,Entropy, Mollier Diagram and Steam TablesCourse No: M08-005Credit: 8 PDHS. Bobby Rauf, P.E., CEM, MBAContinuing Education and Development, Inc.22 Stonewall CourtWoodcliff Lake, NJ 07677P: (877) [email protected]

Thermodynamics Basics – Enthalpy,Entropy, Molliers Diagram and SteamTables ByS. Bobby Rauf, P.E., CEM, MBAThermodynamics Fundamentals Series 1

PrefaceAs the adage goes, “a picture is worth a thousand words;” this text maximizesthe utilization of diagram, graphs and flow charts to facilitate quick andeffective comprehension of the concepts of thermodynamics by the reader.This text is designed to serve as a tool for building basic engineering skills inthe field of thermodynamics.If your objective as a reader is limited to the acquisition of basic knowledge inthermodynamics, then the material in this text should suffice. If, however, thereader wishes to progress their knowledge and skills in thermodynamics tointermediate or advance level, this text could serve as a useful stepping stone.In this text, the study of thermodynamics concepts, principles and analysistechniques is made relatively easy for the reader by inclusion of most of thereference data, in form of excerpts, within the discussion of each case study,exercise and self assessment problem solutions. This is in an effort to facilitatequick study and comprehension of the material without repetitive search forreference data in other parts of the text.Certain thermodynamic concepts and terms are explained more than once asthese concepts appear in different segments of this text; often with a slightlydifferent perspective. This approach is a deliberate attempt to make the studyof some of the more abstract thermodynamics topics more fluid; allowing thereader continuity, and precluding the need for pausing and referring tosegments where those specific topics were first introduced.Due to the level of explanation and detail included for most thermodynamicsconcepts, principles, computational techniques and analyses methods, this textis a tool for those energy engineers, engineers and non-engineers, who are notcurrent on the subject of thermodynamics.The solutions for end of the segment self assessment problems are explainedin just as much detail as the case studies and sample problems in thepertaining segments. This approach has been adopted so that this text canserve as a thermodynamics skill building resource for not just energyengineers but engineers of all disciplines. Since all segments and topics beginwith the introduction of important fundamental concepts and principles, this2

text can serve as a “brush-up” or review tool for even mechanical engineerswhose current area of engineering specialty does not afford them theopportunity to keep their thermodynamics knowledge current.In an effort to clarify some of the thermodynamic concepts effectively forenergy engineers whose engineering education focus does not includethermodynamics, analogies are drawn from non-mechanical engineeringrealms, on certain complex topics, to facilitate comprehension of the relativelyabstract thermodynamic concepts and principles.Each segment in this text concludes with a list of questions or problems, forself-assessment, skill building and knowledge affirmation purposes. Thereader is encouraged to attempt these problems and questions. The answersand solutions, for the questions and problems, are included under Appendix Aof this text.For reference and computational purposes, steam tables and Mollier(Enthalpy-Entropy) diagrams are included in Appendix B.Most engineers understand the role units play in definition and verification ofthe engineering concepts, principles, equations and analytical techniques.Therefore, most thermodynamic concepts, principles and computationalprocedures covered in this text are punctuated with proper units. In addition,for the reader’s convenience, units for commonly used thermodynamicentities, and some conversion factors are listed under Appendix C.Most thermodynamic concepts, principles, tables, graphs, and computationalprocedures covered in this text are premised on US/Imperial Units as well asSI/Metric Units. Certain numerical examples, case studies or self-assessmentproblems in this text are premised on either the SI unit realm or the US unitsystem. When the problems or numerical analysis are based on only one of thetwo unit systems, the given data and the final results can be transformed intothe desired unit system through the use of unit conversion factors in AppendixC.Some of the Greek symbols, used in the realm of thermodynamics, are listedin Appendix D, for reference.3

What readers can gain from this text: Better understanding of thermodynamics terms, concepts, principles, laws,analysis methods, solution strategies and computational techniques. Greater confidence in interactions with thermodynamics design engineersand thermodynamics experts. Skills and preparation necessary for succeeding in thermodynamics portionof various certification and licensure exams, i.e. CEM, FE, PE, and manyother trade certification tests. A better understanding of the thermodynamics component of heat relatedenergy projects. A compact and simplified thermodynamics desk reference.4

Table of ContentsSegment 1Study of Enthalpy and EntropyEnthalpy, entropy and associated case studySegment 2Understanding Mollier DiagramMollier diagram; the enthalpy-entropy graph, its use and applicationSegment 3Saturated and Superheated Steam TablesUnderstanding of saturated and superheated steam tables; applications,thereof, and associated case studyAppendix ASolutions for self-assessment problemsAppendix BSteam tablesAppendix CCommon units and unit conversion factorsAppendix DCommon symbols5

Segment 1Study of Enthalpy and EntropyTopics- Enthalpy- EntropyIntroductionSimilar to the last segment, the goal in this brief segment is to continue theintroduction of basic, yet critical, concepts in the field of thermodynamics. Inthis segment, we will introduce the concept of entropy and we will expand onthe concept of enthalpy. As we progress through this text, you will notice thatthe discussion on entropy will be limited, reflecting the somewhat limited roleof entropy in practical thermodynamics. On the other hand, our continuedexploration of enthalpy, in this segment, and the ones heretofore, is indicativeof the instrumental and ubiquitous role of enthalpy in the study ofthermodynamics. We received a brief, preliminary, introduction to enthalpy inthe last segment, in the context of energy flow in power generating realm. Inthis segment, we will expand on enthalpy in preparation for its examination inmore complex thermodynamic scenarios.Enthalpy: Enthalpy is defined as the total heat content or total useful energyof a substance. The symbol for enthalpy is “h.” Enthalpy is also considered tobe the sum of internal energy “u” and flow energy (or flow work) p.V. Thisdefinition of enthalpy can be expressed, mathematically, as follows:h u p.VEq. 1.1Where,h Specific enthalpy, measured in kJ/kg (SI Units) or BTU/lbm (USUnits)u Specific internal energy, measured in kJ/kg (SI Units) orBTU/lbm (US Units)p Absolute Pressure measured in Pa (SI Units), or psf (US Units)V Volume measured in m3 (SI Units), or ft3 (US Units)p.V Flow Energy, Flow Work or p-V work, quantified in kJ/kg (SIUnits) or BTU/lbm (US Units)6

In practical saturated or superheated steam systems, internal energy, u,specific enthalpy, h, and specific volume, υ, can be assessed through saturatedsteam tables and superheated steam tables, respectively. The terms saturatedsteam and superheated steam are defined in depth later in this text. Segments 5and 6 cover classifications of steam and associated steam tables in detail.Reference steam tables, in US and SI form, are included in Appendix B of thistext.In order to maintain consistency of units in practical thermodynamicsituations, where computation is performed in US units, a more suitable formof the enthalpy equation Eq. 1.1 would be as follows:h u p.V/JEq. 1.2Where,h Enthalpy, measured in BTU’su Internal energy, measured in BTUp Absolute Pressure measured in psf or lbf/ft2V Volume measured in ft3J Joule’s constant; value of J is 778 ft-lbf/BTUNote that in the SI unit system, an alternate version of enthalpy equation Eq.1.1 is not necessary because units in Eq. 1.1 are congruent.Enthalpy can also be quantified in molar form. In molar form, enthalpy isreferred to as molar enthalpy and represented by the symbol “H”.The units for molar enthalpy H are BTU/lbmole in the US system, andkJ/kmole in the Metric or SI System; where a mole of a substance is definedor calculated through division of the mass of that substance by the atomicweight of the substance, if it is a solid, or by the molecular weight, if it is aliquid or gas.The mathematical equation for molar enthalpy “H,” is as follows:H U p.VEq. 1.3Where,U Molar Internal Energy, can be expressed in BTU/lbmol (USUnits) or kJ/kmol (SI Units)7

p Absolute pressure measured in Pa (SI Units), psf (US Units) orlbf/ft2V Molar specific volume measured in m3/kmol (SI Units), orft3/lbmole (US Units)Example 1.1Calculate the absolute enthalpy, h, in BTU’s, for 1 lbm of vapor under thefollowing conditions:h Enthalpy, measured in BTU’s ?u 1079.9 BTU/lbmp 14.14 psiaV 27.796 ft3J Joule’s constant; value of J is 778 ft-lbf/BTUSolution:The pressure is given in psia, or lbf/in2. In order to streamline the pressure forapplication in Eq. 1.2, we must convert in into lbf/ft2.Therefore,p (14.14 lbf/in2 ).( 144 in2/ ft2) 2,036 lbf/ft2Then, by applying Eq. 1.2, and by substitution of known and derived values:h u p.V/Jh 1079.9 BTU/lbm (2,036 lbf/ft2). (27.796 ft3 )/ 778 ft-lbf/BTUh 1152.67 BTU8

EntropyEntropy is defined as the non-work producing form of energy. It is alsoregarded as the energy that is not available for performing useful work withina certain environment. The symbol for entropy is “s.” Some facts, principlesand laws associated with entropy are summarized below: Increase in entropy is referred to as entropy production. The total absolute entropy of a system is said to be equal to the sum of allabsolute entropies that have occurred over the life of the system.stotal siEq. 1.4Where, si represents change in enthalpy at each object or in eachsubstance. Application of this entropy principle will be demonstratedthrough Case Study 1.1. According to the third law of thermodynamics, the absolute entropy of aperfect crystalline solid, in thermodynamic equilibrium, approaches zeroas the temperature approaches absolute zero.T Limit 0 K s 0In an isothermal (constant temperature) process, the entropy production, s, is a function of the energy transfer rate: s q / T absEq. 1.5Where,s entropy in kJ/kg. K (SI Units System), or in BTU/lbm. R (USUnit System)q Heat transferred in kJ/kg, (SI Units) or BTU/lbm (US Units)T abs Absolute Temperature of the object or substance, in K (SIUnits System), or in R (US Unit System)9

Case Study 1.1 - Entropy AnalysisIn a certain solar system there are four (4) planets oriented in space as shownin Figure #2. Their temperatures are indicated in the diagram, in K as well asin R. As apparent from the orientation of these planets in Figure 1.1, they areexposed to each other such that heat transfer can occur freely throughradiation. All four (4) planets are assumed to be massive enough to allow forthe interplanetary heat transfer to be isothermal for each of the planets.a) Will heat transfer occur, through radiation, from planet Z to planets X andY?b) If the 3,000 kJ/kg of radiated heat transfer occurs from planet X to planetY, what would be the entropy changes at each of the two planets?c) Can convectional heat transfer occur between any of two planets in thissolar system?d) If certain radiated heat transfer between Planets Y and Z causes an entropychange of 11.77 kJ/kg. K at Planet Y and an entropy change of 12.66kJ/kg. K at Planet Z, what would be the overall, resultant, entropy of thisplanetary system?e) Can planet X be restored to its original state? If so, how?Figure 1.1 – Case Study 1.1, Entropy10

Solution - Case Study 1.1:a) Will heat transfer occur, through radiation, from planet Z to planets X andY?Solution/Answer:Heat flows from a body at a higher temperature to one that is at a lowertemperature. The temperature of Planet Z is lower than the temperature ofplanets X and Y. Therefore, NO radiated heat transfer will occur fromplanet Z to planets X and Y.b) If the 3000 kJ /kg of radiated heat transfer occurs from planet X to planetY, what would be the entropy changes at each of the two planets?Solution/Answer:In an isothermal (constant temperature) process, the entropy production, s, isa function of the energy transfer rate and its relationship with heat q andabsolute temperature, T abs and is represented by Eq. 1.5: s q / T abs sX (- 3,000 kJ/kg)/(290 K) - 10.34 kJ/kg. K {Due to heat loss by Planet X}And, sY ( 3,000 kJ/kg)/(280 K) 10.71 kJ/kg. K {Due to heat gain by Planet Y}c) Can convectional heat transfer occur between any of two planets in thissolar system?Solution/Answer:Convectional heat transfer is dependent on bulk movement of a fluid (gaseousor liquid) and, therefore, it can only occur in liquids, gases and multiphasemixtures. Since, the system in this problem is a planetary system, the mediumbetween the bodies is devoid of fluids needed for convectional heat transfer.Heat transfer in this planetary system occurs through radiation, primarily.11

Therefore, the answer is NO.d) If the heat transfer from part (b) occurs simultaneous to a certain radiatedheat transfer between Planets Y and Z, where the entropy change of - 11.77kJ/kg. K is recorded at Planet Y and an entropy change of12.66 kJ/kg. K isrecorded at Planet Z, what would be the overall, resul