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Thermodynamics Notes
Thermodynamics Notes Steven K. Krueger Department of Atmospheric Sciences, University of Utah August 2020 Contents 1 Introduction 1 1.1 What is thermodynamics? . .1 1.2 The atmosphere . .1 2 The Equation of State 1 2.1 State variables . .1 2.2 Charles' Law and absolute temperature . .2 2.3 Boyle's Law . .3 2.4 Equation of state of an ideal gas . .3 2.5 Mixtures of gases . .4 2.6 Ideal gas law: molecular viewpoint . .6 3 Conservation of Energy 8 3.1 Conservation of energy in mechanics . .8 3.2 Conservation of energy: A system of point masses . .8 3.3 Kinetic energy exchange in molecular collisions . .9 3.4 Working and Heating . .9 4 The Principles of Thermodynamics 11 4.1 Conservation of energy and the first law of thermodynamics . 11 4.1.1 Conservation of energy . 11 4.1.2 The first law of thermodynamics . 11 4.1.3 Work . 12 4.1.4 Energy transferred by heating . 13 4.2 Quantity of energy transferred by heating . 14 4.3 The first law of thermodynamics for an ideal gas . 15 4.4 Applications of the first law . 16 4.4.1 Isothermal process . 16 4.4.2 Isobaric process . 17 4.4.3 Isosteric process . 18 4.5 Adiabatic processes . 18 5 The Thermodynamics of Water Vapor and Moist Air 21 5.1 Thermal properties of water substance . 21 5.2 Equation of state of moist air . 21 5.3 Mixing ratio . 22 5.4 Moisture variables . 22 5.5 Changes of phase and latent heats . -
Thermodynamic State Variables Gunt
Fundamentals of thermodynamics 1 Thermodynamic state variables gunt Basic knowledge Thermodynamic state variables Thermodynamic systems and principles Change of state of gases In physics, an idealised model of a real gas was introduced to Equation of state for ideal gases: State variables are the measurable properties of a system. To make it easier to explain the behaviour of gases. This model is a p × V = m × Rs × T describe the state of a system at least two independent state system boundaries highly simplifi ed representation of the real states and is known · m: mass variables must be given. surroundings as an “ideal gas”. Many thermodynamic processes in gases in · Rs: spec. gas constant of the corresponding gas particular can be explained and described mathematically with State variables are e.g.: the help of this model. system • pressure (p) state process • temperature (T) • volume (V) Changes of state of an ideal gas • amount of substance (n) Change of state isochoric isobaric isothermal isentropic Condition V = constant p = constant T = constant S = constant The state functions can be derived from the state variables: Result dV = 0 dp = 0 dT = 0 dS = 0 • internal energy (U): the thermal energy of a static, closed Law p/T = constant V/T = constant p×V = constant p×Vκ = constant system. When external energy is added, processes result κ =isentropic in a change of the internal energy. exponent ∆U = Q+W · Q: thermal energy added to the system · W: mechanical work done on the system that results in an addition of heat An increase in the internal energy of the system using a pressure cooker as an example. -
Novel Hot Air Engine and Its Mathematical Model – Experimental Measurements and Numerical Analysis
POLLACK PERIODICA An International Journal for Engineering and Information Sciences DOI: 10.1556/606.2019.14.1.5 Vol. 14, No. 1, pp. 47–58 (2019) www.akademiai.com NOVEL HOT AIR ENGINE AND ITS MATHEMATICAL MODEL – EXPERIMENTAL MEASUREMENTS AND NUMERICAL ANALYSIS 1 Gyula KRAMER, 2 Gabor SZEPESI *, 3 Zoltán SIMÉNFALVI 1,2,3 Department of Chemical Machinery, Institute of Energy and Chemical Machinery University of Miskolc, Miskolc-Egyetemváros 3515, Hungary e-mail: [email protected], [email protected], [email protected] Received 11 December 2017; accepted 25 June 2018 Abstract: In the relevant literature there are many types of heat engines. One of those is the group of the so called hot air engines. This paper introduces their world, also introduces the new kind of machine that was developed and built at Department of Chemical Machinery, Institute of Energy and Chemical Machinery, University of Miskolc. Emphasizing the novelty of construction and the working principle are explained. Also the mathematical model of this new engine was prepared and compared to the real model of engine. Keywords: Hot, Air, Engine, Mathematical model 1. Introduction There are three types of volumetric heat engines: the internal combustion engines; steam engines; and hot air engines. The first one is well known, because it is on zenith nowadays. The steam machines are also well known, because their time has just passed, even the elder ones could see those in use. But the hot air engines are forgotten. Our aim is to consider that one. The history of hot air engines is 200 years old. -
Thermodynamics the Goal of Thermodynamics Is to Understand How Heat Can Be Converted to Work
Thermodynamics The goal of thermodynamics is to understand how heat can be converted to work Main lesson: Not all the heat energy can be converted to mechanical energy This is because heat energy comes with disorder (entropy), and overall disorder cannot decrease Temperature v T Random directions of velocity Higher temperature means higher velocities v Add up energy of all molecules: Internal Energy of gas U Mechanical energy: all atoms move in the same direction 1 Mv2 2 Statistical mechanics For one atom 1 1 1 1 1 1 3 E = mv2 + mv2 + mv2 = kT + kT + kT = kT h i h2 xi h2 yi h2 z i 2 2 2 2 Ideal gas: No Potential energy from attraction between atoms 3 U = NkT h i 2 v T Pressure v Pressure is caused because atoms T bounce off the wall Lx p − x px ∆px =2px 2L ∆t = x vx ∆p 2mv2 mv2 F = x = x = x ∆t 2Lx Lx ∆p 2mv2 mv2 F = x = x = x ∆t 2Lx Lx 1 mv2 =2 kT = kT h xi ⇥ 2 kT F = Lx Pressure v F kT 1 kT A = LyLz P = = = A Lx LyLz V NkT Many particles P = V Lx PV = NkT Volume V = LxLyLz Work Lx ∆V = A ∆Lx v A = LyLz Work done BY the gas ∆W = F ∆Lx We can write this as ∆W =(PA) ∆Lx = P ∆V This is useful because the body could have a generic shape Internal energy of gas decreases U U ∆W ! − Gas expands, work is done BY the gas P dW = P dV Work done is Area under curve V P Gas is pushed in, work is done ON the gas dW = P dV − Work done is negative of Area under curve V By convention, we use POSITIVE sign for work done BY the gas Getting work from Heat Gas expands, work is done BY the gas P dW = P dV V Volume in increases Internal energy decreases .. -
Thermal Equilibrium State of the World Oceans
Thermal equilibrium state of the ocean Rui Xin Huang Department of Physical Oceanography Woods Hole Oceanographic Institution Woods Hole, MA 02543, USA April 24, 2010 Abstract The ocean is in a non-equilibrium state under the external forcing, such as the mechanical energy from wind stress and tidal dissipation, plus the huge amount of thermal energy from the air-sea interface and the freshwater flux associated with evaporation and precipitation. In the study of energetics of the oceanic circulation it is desirable to examine how much energy in the ocean is available. In order to calculate the so-called available energy, a reference state should be defined. One of such reference state is the thermal equilibrium state defined in this study. 1. Introduction Chemical potential is a part of the internal energy. Thermodynamics of a multiple component system can be established from the definition of specific entropy η . Two other crucial variables of a system, including temperature and specific chemical potential, can be defined as follows 1 ⎛⎞∂η ⎛⎞∂η = ⎜⎟, μi =−Tin⎜⎟, = 1,2,..., , (1) Te m ⎝⎠∂ vm, i ⎝⎠∂ i ev, where e is the specific internal energy, v is the specific volume, mi and μi are the mass fraction and chemical potential for the i-th component. For a multiple component system, the change in total chemical potential is the sum of each component, dc , where c is the mass fraction of each component. The ∑i μii i mass fractions satisfy the constraint c 1 . Thus, the mass fraction of water in sea ∑i i = water satisfies dc=− c , and the total chemical potential for sea water is wi∑iw≠ N −1 ∑()μμiwi− dc . -
25 Kw Low-Temperature Stirling Engine for Heat Recovery, Solar, and Biomass Applications
25 kW Low-Temperature Stirling Engine for Heat Recovery, Solar, and Biomass Applications Lee SMITHa, Brian NUELa, Samuel P WEAVERa,*, Stefan BERKOWERa, Samuel C WEAVERb, Bill GROSSc aCool Energy, Inc, 5541 Central Avenue, Boulder CO 80301 bProton Power, Inc, 487 Sam Rayburn Parkway, Lenoir City TN 37771 cIdealab, 130 W. Union St, Pasadena CA 91103 *Corresponding author: [email protected] Keywords: Stirling engine, waste heat recovery, concentrating solar power, biomass power generation, low-temperature power generation, distributed generation ABSTRACT This paper covers the design, performance optimization, build, and test of a 25 kW Stirling engine that has demonstrated > 60% of the Carnot limit for thermal to electrical conversion efficiency at test conditions of 329 °C hot side temperature and 19 °C rejection temperature. These results were enabled by an engine design and construction that has minimal pressure drop in the gas flow path, thermal conduction losses that are limited by design, and which employs a novel rotary drive mechanism. Features of this engine design include high-surface- area heat exchangers, nitrogen as the working fluid, a single-acting alpha configuration, and a design target for operation between 150 °C and 400 °C. 1 1. INTRODUCTION Since 2006, Cool Energy, Inc. (CEI) has designed, fabricated, and tested five generations of low-temperature (150 °C to 400 °C) Stirling engines that drive internally integrated electric alternators. The fifth generation of engine built by Cool Energy is rated at 25 kW of electrical power output, and is trade-named the ThermoHeart® Engine. Sources of low-to-medium temperature thermal energy, such as internal combustion engine exhaust, industrial waste heat, flared gas, and small-scale solar heat, have relatively few methods available for conversion into more valuable electrical energy, and the thermal energy is usually wasted. -
Laws of Thermodynamics
Advanced Instructional School on Mechanics, 5 - 24, Dec 2011 Special lectures Laws of Thermodynamics K. P. N. Murthy School of Physics, University of Hyderabad Dec 15, 2011 K P N Murthy (UoH) Thermodynamics Dec 15, 2011 1 / 126 acknowledgement and warning acknowledgement: Thanks to Prof T Amaranath and V D Sharma for the invitation warning: I am going to talk about the essential contents of the laws of thermodynamics, tracing their origin, and their history The Zeroth law, the First law the Second law .....and may be the Third law, if time permits I leave it to your imagination to connect my talks to the theme of the School which is MECHANICS. K P N Murthy (UoH) Thermodynamics Dec 15, 2011 2 / 126 Each law provides an experimental basis for a thermodynamic property Zeroth law= ) Temperature, T First law= ) Internal Energy, U Second law= ) Entropy, S The earliest was the Second law discovered in the year 1824 by Sadi Carnot (1796-1832) Sadi Carnot Helmholtz Rumford Mayer Joule then came the First law - a few decades later, when Helmholtz consolidated and abstracted the experimental findings of Rumford, Mayer and Joule into a law. the Zeroth law arrived only in the twentieth century, and I think Max Planck was responsible for it K P N Murthy (UoH) Thermodynamics Dec 15, 2011 3 / 126 VOCALUBARY System: The small part of the universe under consideration: e.g. a piece of iron a glass of water an engine The rest of the universe (in which we stand and make observations and measurements on the system) is called the surroundings a glass of water is the system and the room in which the glass is placed is called the surrounding. -
Supercritical CO 2 Cycles for Gas Turbine
Power Gen International December 8-10, Las Vegas, Nevada SUPERCRITICAL CO2 CYCLES FOR GAS TURBINE COMBINED CYCLE POWER PLANTS Timothy J. Held Chief Technology Officer Echogen Power Systems, LLC Akron, Ohio [email protected] ABSTRACT Supercritical carbon dioxide (sCO2) used as the working fluid in closed loop power conversion cycles offers significant advantages over steam and organic fluid based Rankine cycles. Echogen Power Systems LLC has developed several variants of sCO2 cycles that are optimized for bottoming and heat recovery applications. In contrast to cycles used in previous nuclear and CSP studies, these cycles are highly effective in extracting heat from a sensible thermal source such as gas turbine exhaust or industrial process waste heat, and then converting it to power. In this study, conceptual designs of sCO2 heat recovery systems are developed for gas turbine combined cycle (GTCC) power generation over a broad range of system sizes, ranging from distributed generation (~5MW) to utility scale (> 500MW). Advanced cycle simulation tools employing non-linear multivariate constrained optimization processes are combined with system and plant cost models to generate families of designs with different cycle topologies. The recently introduced EPS100 [1], the first commercial-scale sCO2 heat recovery engine, is used to validate the results of the cost and performance models. The results of the simulation process are shown as system installed cost as a function of power, which allows objective comparisons between different cycle architectures, and to other power generation technologies. Comparable system cost and performance studies for conventional steam-based GTCC are presented on the basis of GT-Pro™ simulations [2]. -
Removing the Mystery of Entropy and Thermodynamics – Part II Harvey S
Table IV. Example of audit of energy loss in collision (with a mass attached to the end of the spring). Removing the Mystery of Entropy and Thermodynamics – Part II Harvey S. Leff, Reed College, Portland, ORa,b Part II of this five-part series is focused on further clarification of entropy and thermodynamics. We emphasize that entropy is a state function with a numerical value for any substance in thermodynamic equilibrium with its surroundings. The inter- pretation of entropy as a “spreading function” is suggested by the Clausius algorithm. The Mayer-Joule principle is shown to be helpful in understanding entropy changes for pure work processes. Furthermore, the entropy change when a gas expands or is compressed, and when two gases are mixed, can be understood qualitatively in terms of spatial energy spreading. The question- answer format of Part I1 is continued, enumerating main results in Key Points 2.1-2.6. • What is the significance of entropy being a state Although the linear correlation in Fig. 1 is quite striking, the function? two points to be emphasized here are: (i) the entropy value In Part I, we showed that the entropy of a room temperature of each solid is dependent on the energy added to and stored solid can be calculated at standard temperature and pressure by it, and (ii) the amount of energy needed for the heating using heat capacity data from near absolute zero, denoted by T process from T = 0 + K to T = 298.15 K differs from solid to = 0+, to room temperature, Tf = 298.15 K. -
Ch 19. the First Law of Thermodynamics
Ch 19. The First Law of Thermodynamics Liu UCD Phy9B 07 1 19-1. Thermodynamic Systems Thermodynamic system: A system that can interact (and exchange energy) with its surroundings Thermodynamic process: A process in which there are changes in the state of a thermodynamic system Heat Q added to the system Q>0 taken away from the system Q<0 (through conduction, convection, radiation) Work done by the system onto its surroundings W>0 done by the surrounding onto the system W<0 Energy change of the system is Q + (-W) or Q-W Gaining energy: +; Losing energy: - Liu UCD Phy9B 07 2 19-2. Work Done During Volume Changes Area: A Pressure: p Force exerted on the piston: F=pA Infinitesimal work done by system dW=Fdx=pAdx=pdV V Work done in a finite volume change W = final pdV ∫V initial Liu UCD Phy9B 07 3 Graphical View of Work Gas expands Gas compresses Constant p dV>0, W>0 dV<0, W<0 W=p(V2-V1) Liu UCD Phy9B 07 4 19-3. Paths Between Thermodynamic States Path: a series of intermediate states between initial state (p1, V1) and a final state (p2, V2) The path between two states is NOT unique. V2 W= p1(V2-V1) +0 W=0+ p2(V2-V1) W = pdV ∫V 1 Work done by the system is path-dependent. Liu UCD Phy9B 07 5 Path Dependence of Heat Transfer Isotherml: Keep temperature const. Insulation + Free expansion (uncontrolled expansion of a gas into vacuum) Heat transfer depends on the initial & final states, also on the path. -
Thermodynamic State, Specific Heat, and Enthalpy Function 01 Saturated UO Z Vapor Between 3000 Kand 5000 K
Februar 1977 KFK 2390 Institut für Neutronenphysik und Reaktortechnik Projekt Schneller Brüter Thermodynamic State, Specific Heat, and Enthalpy Function 01 Saturated UO z Vapor between 3000 Kand 5000 K H. U. Karow Als Manuskript vervielfältigt Für diesen Bericht behalten wir uns alle Rechte vor GESELLSCHAFT FÜR KERNFORSCHUNG M. B. H. KARLSRUHE KERNFORSCHUNGS ZENTRUM KARLSRUHE KFK 2390 Institut für Neutronenphysik und Reaktortechnik Projekt Schneller Brüter Thermodynamic State, Specific Heat, and Enthalpy Function of Saturated U0 Vapor between 3000 K 2 and 5000 K H. U. Karow Gesellschaft für Kernforschung mbH., Karlsruhe A summarized version of s will be at '7th Symposium on Thermophysical Properties', held the NBS at Gaithe , 1977 Thermodynamic State, Specific Heat, and Enthalpy Function of Saturated U0 2 Vapor between 3000 K and 5000 K Abstract Reactor safety analysis requires knowledge of the thermophysical properties of molten oxide fuel and of the thermal equation-of state of oxide fuel in thermodynamic liquid-vapor equilibrium far above 3000 K. In this context, the thermodynamic state of satu rated U0 2 fuel vapor, its internal energy U(T), specific heats Cv(T) and C (T), and enthalpy functions HO(T) and HO(T)-Ho have p 0 been determined by means of statistical mechanics in the tempera- ture range 3000 K .•• 5000 K. The discussion of the thermodynamic state includes the evaluation of the plasma state and its contri bution to the caloric variables-of-state of saturated oxide fuel vapor. Because of the extremely high ion and electron density due to thermal ionization, the ionized component of the fuel vapor does no more represent a perfect kinetic plasma - different from the nonionized neutral vapor component with perfect gas kinetic behavior up to about 5000 K. -
“Fabrication of Stirling Engine”
“Fabrication of Stirling Engine” Sibabrata Mohanty*,Debasis Pattnayak** , Ashik Dash*** ,Raju Singh**** , Chandrakant Bhardwaj***** , Sk Firdosh Akhtar****** *Assistant Professor, Department of Mechanical Engineering, Gandhi Institute of Engineering and Technology, Gunupur, Rayagada Odisha, **,***,****,*****,&****** B.Tech Mechanical Students, Gandhi Institute of Engineering and Technology, Gunupur, Rayagada Odisha ABSTRACT The performance of Stirling engines meets the demands of the efficient use of energy and environmental security and therefore they are the subject of much current interest. Hence, the development and investigation of Stirling engine have come to the attention of many scientific institutes and commercial companies. The Stirling engine is both practically and theoretically a significant device, its practical virtue is simple, reliable and safe which was recognized for a full century following its invention by Robert Stirling in 1816. The engine operates on a closed thermodynamic cycle, which is reversible. The objective of this project paper is to provide fundamental information and present a detailed review of the efforts taken by us for the development of the Stirling cycle engine and techniques used for engine analysis. A number of attempts have been made by us to build and improve the performance of Stirling engines. It is seen that for successful operation of engine system with good efficiency a careful design, proper selection of drive mechanism and engine configuration is essential. This project paper indicates that a Stirling cycle engine working with relatively low temperature with air or helium as working fluid is potentially attractive engines of the future, especially solar-powered low-temperature differential Stirling engines. Keywords: Stirling engines, Stirling cycle, thermodynamic cycle 1.