453 Chapter 17 Engineering Fundamentals: Part 2 Thermodynamics 17.1 Introduction Thermodynamics is an aspect of physics which deals with the energy characteristics of materials and with the behavior of systems under- going changes in system energy levels. The field of thermodynamics is quite broad as well as deep, and can vary in presentation and in application from relatively simple to very complex. For the purposes of this book, a relatively simple presentation is adequate. The concepts of thermodynamics presented here are common to virtually all text- books and reference books. For those who want greater detail, Chap. 1 of the ASHRAE Handbook Fundamentals is one presentation writ- ten at a college upper-division or graduate-student level. 1,2 17.2 Thermodynamics Terms One problem with understanding thermodynamics is that the basic terms energy and entropy are defined in relatives rather than abso- lutes. Energy can be reduced to the concepts of heat and work and can be found in various forms: potential energy, kinetic energy, thermal or internal energy, chemical energy, and nuclear energy. Potential energy is the energy of location or position of a mass in a force field. A body or a volume of water at the top of a hill has potential energy with respect to the bottom of the hill. Source: HVAC Systems Design Handbook Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 454 Chapter Seventeen Kinetic energy is the energy of motion and is proportional to the square of the velocity as well as to the mass of the moving body. Internal energy has to do with activity within the molecular struc- ture of matter, and is typically observed with temperature measure- ments. Chemical energy is related to the relationships between molecules in chemical compounds. When different molecules combine in chemical reaction, they may give off heat (exothermic reaction) or require heat (endothermic reaction). Electric energy is related to electrons moving along a conductor. Nuclear energy is the energy of atomic relationships between the fundamental particles of matter. Nuclear fission and fusion are reac- tions which release stored nuclear energy. Heat is observed as energy in motion from one region to another resulting from temperature difference. Work is an energy form which can be equated to the raising of a weight. This may be mechanical work, such as moving a mass in a force field, or it may be flow work, such as moving a liquid against a resisting force. Enthalpy is a term used with energy units that combines internal energy with a pressure/volume or flow work term. Property is a measurable characteristic of a system or a substance. Temperature, pressure, and density (the inverse is the specific volume) are all properties. The different kinds of energy, enthalpy, and entropy are all considered properties. Temperature is a term used to quantify the difference between warm and cold or the level of internal energy of a substance. The original numerical designations were based on the difference between the freezing point and boiling point of water. The Celsius scale defined the difference in terms of 100 units with 0 as the freezing point and 100 as the boiling point. The Fahrenheit scale uses the freezing point of a salt solution as the 0 point with pure water freezing and boiling at 32 and 212ЊF, respectively. The lowest possible temperature, the condition at which molecular motion ceases, is called absolute zero. The absolute scale which uses the Celsius increment is called the Kelvin scale. It places absolute zero at Ϫ273ЊC, or the ice melting point of water at ϩ273K. The absolute scale which uses the Fahrenheit increment is called the Rankine scale. It places absolute zero at Ϫ460ЊF, or the ice melting point of water at ϩ492ЊR. There is no upper limit to a possible temperature. 17.3 First Law of Thermodynamics The first law of thermodynamics sounds like the law of the conser- vation of mass, with different vocabulary. If the law of mass conser- Engineering Fundamentals: Part 2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Engineering Fundamentals: Part 2 455 vation asserts that matter can be neither created nor destroyed, then the first law of thermodynamics states that energy cannot be created or destroyed. This implies that the various forms of energy may be converted, one to another. It means that we can account for all energy conversions in a system with accuracy. Energy in Ϫ Energy out ϭ Change in stored energy Entropy is used to define the unavailable energy in a system. In another sense, entropy defines the relative ability of one system to act on another. As things move toward a lower energy level, where one is less able to act upon the surroundings, the entropy level is said to increase. If we look at the universe as a whole, things are running down, so the entropy of the universe is said to be increasing. 17.4 Second Law of Thermodynamics There are two classical statements of the second law of thermodynam- ics. The first was expressed by Kelvin and Planck: No (heat) engine whose working fluid undergoes a cycle can absorb heat from a single reservoir, deliver an equivalent amount of work, and produce no other effect. To understand this statement, recognize that for energy to be available at all, there must be a region of high energy level compared to a region of lower energy level. Useful work must be derived from the energy that would flow from the high potential region to the lower potential region. But 100 percent of the energy cannot be converted to work. If it were, the process would be dealing only with a single energy region, in violation of the Kelvin-Planck statement. The reality of this statement can be seen in our inability to extract energy from the en- vironment unless there is a second, colder region to relate to. The theoretical maximum efficiency ␩ of a heat machine working between two energy regions is defined in terms of temperatures on an absolute scale as T Ϫ TT HL L ␩ ϭϭ1 Ϫ TT HH where T H is the temperature of the high energy region, and T L is the temperature of the low energy region. As the temperatures approach equilibrium (T L ϭ T H ), the process efficiency tends toward zero. The second statement of the second law is credited to Clausius, who said, ‘‘No machine whose working fluid undergoes a cycle can absorb heat from one system, reject heat to another system and produce no other effect.’’ Engineering Fundamentals: Part 2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 456 Chapter Seventeen Both statements of the second law place constraints on the first law by identifying that under natural conditions, things (including energy) run downhill. We must expend energy to make it happen otherwise. It takes energy to drive cold to hot, e.g., a refrigerator. It takes energy to raise a weight against gravity. A corollary is that there is no such thing as a perpetual-motion machine. We cannot get something for nothing. This means that in all the energy balances of the first law, we know that some things will not happen unless we expend or give up something to make them happen. Ⅲ Example: A heat resource cannot be fully converted to work. Work can be withdrawn from heat moving from a high-energy region to another, but not completely. This makes work (kinetic energy, elec- tric energy, etc.) more valuable than conventional heat resources. Hence it is generally better to use fuels for heating and electricity for power, rather than to use power for resistance heating. Ⅲ Example: Refrigeration is a process of moving heat (thermal energy) from a cold region to a warmer region. Since this is counter to the nature of things, which is to run downhill, we must expend energy to make it happen (i.e., power to the compressor; steam or fuel to the absorption chiller). 17.5 Efficiency Efficiency is simply defined for an energy conversion process as how much is obtained compared to how much was expended. For example, in a gas-fired hot water boiler, of every unit of fuel burned, approxi- mately 80 to 90 percent is transferred to the circulated hot water while 10 to 20 percent goes up the chimney as products of combustion and uncaptured heat. The efficiency of the boiler is 80 to 90 percent. Note that a heat transfer process in a heat exchanger does not uti- lize the word efficiency. All the heat taken from one side of the ex- changer winds up on the other side. Even if the exchanger is fouled, there is an energy balance. However, a fouled exchanger will not transfer as much heat as a clean one. A comparison of fouled capacity to clean capacity is sometimes called efficacy, or effectiveness, but not efficiency. 17.6 Coefficient of Performance The coefficient of performance (COP) is defined as useful heat moved or obtained COP ϭ energy required to drive process For a refrigeration cycle, the useful heat is the refrigeration effect Engineering Fundamentals: Part 2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Engineering Fundamentals: Part 2 457 Q evap COP ϭ cool Q in In the classical sense, similar to the definition of efficiency, there is a theoretical limit to the COP defined in terms of the temperature (low) of the cold region T L related to the temperature (high) of the warm region T H T L COP ϭ (17.1) max T Ϫ T HL For a building chiller evaporating at 40ЊF (500ЊR) and condensing at 100ЊF (560ЊR), the maximum COP would be 500 COP ϭϭ8.3 (17.2) max 560 Ϫ 500 The actual COP of these machines is on the order of 4 to 6, which reveals the inefficiencies of the real world. Studying the defining equa- tion reveals that it takes more energy to refrigerate at lower temper- atures, and it takes more energy to drive a process with a higher temperature differential between evaporator and condenser. We need to minimize the differential (often called thermal lift) as much as pos- sible for the purposes of energy conservation. For the heat pump cycle, the energy input becomes a benefit. Q ϩ Q evap in COP ϭϭCOP ϩ 1 heat cool Q in In heat pump systems, the system designer should again try to work with the smallest possible thermal lift to get maximum beneficial ef- fect for least input. 17.7 Specific Heat C p The specific heat of a substance is the amount of energy it takes to raise a unit mass of the substance by one degree in temperature. For HVAC work, the specific heat of water in the liquid state is 1 Btu / (lb ⅐ ЊF). Water in the solid state (ice) has a specific heat of 0.487 to 0.465 Btu / (lb ⅐ ЊF), which is easy to remember as 0.5 Btu/(lb ⅐ ЊF). Water as a vapor has a specific heat of 0.489 Btu / (lb ⅐ ЊF) which can also be rounded to 0.5 Btu/(lb ⅐ ЊF) as for ice. In a process where energy is added to or taken from a flowing stream of water, the specific heat term evolves to Engineering Fundamentals: Part 2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 458 Chapter Seventeen [1 Btu/(lb ⅐ ЊF)](8.3 lb/gal)(60 min/h ϭ 500 Btu/[h ⅐ (gal/min) ⅐ ЊF] The heat-carrying capacity of a flowing stream of water is then ˙ Q ϭ MC (T Ϫ T ) ϭ GPM(500)(T Ϫ T ) Btu/h p 21 12 where ϭ ˙ M mass flow rate Q ϭ energy transported, Btu/h C p ϭ specific heat of water T 1 , T 2 ϭ temperature in, temperature out GPM ϭ fluid flow rate (water), gal/min The same equation (a variation of the Bernoulli equation) can be adapted for any fluid (such as a glycol antifreeze solution) by substi- tuting the specific heat and density of the substance for that of water. The same derivation for air, which at standard conditions has a den- sity of 0.075 lb/ft 3 and a specific heat of 0.24 Btu/(lb ⅐ ЊF), yields 3 [0.24 Btu/(lb ⅐ ЊF)](0.075 lb/ft )(60 min / h) 3 ϭ 1.08 Btu/[h ⅐ (ft / min) ⅐ ЊF] Q ϭ CFM(1.08)(T Ϫ T )Btu/h 12 17.8 Summary Thermodynamics is an interesting and valuable study for the HVAC designer. Its principles define the concept of energy and identify which energy processes are possible and which are impossible unless forced. The first law of thermodynamics allows us to count and keep track of energy as if it were money in the bank. The second law of thermody- namics confirms that energy processes run downhill. This knowledge helps an HVAC designer to identify reality among the often overstated claims of overenthusiastic inventors and salespeople. The mathemat- ical relationships of thermodynamics allow the designer to quickly and confidently calculate the energy flows in a process. References 1. William J. Coad, ‘‘Fundamentals to Frontiers (Fundamentals of Thermodynamics),’’ Heating / Piping / Air Conditioning, February 1981. 2. William J. Coad, ‘‘Fundamentals to Frontiers (Unavailable Energy),’’ Heating / Piping / Air Conditioning, March 1982. Engineering Fundamentals: Part 2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. . potential energy with respect to the bottom of the hill. Source: HVAC Systems Design Handbook Downloaded from Digital Engineering Library @ McGraw-Hill. 453 Chapter 17 Engineering Fundamentals: Part 2 Thermodynamics 17. 1 Introduction Thermodynamics is an aspect of physics