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Table of 1....................................................................................................................................................... Macroscopic Point of View ...................................................................................................................

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Table of Contents Chapter 1....................................................................................................................................................... 3 1.1 Macroscopic Point of View ................................................................................................................. 3 1.2 Microscopic Point of View .................................................................................................................. 3 1.3 Macroscopic vs. Microscopic Points of View ...................................................................................... 3 1.4 Scope of Thermodynamics .................................................................................................................. 3 1.5 Thermal Equilibrium and the Zeroth Law ........................................................................................... 4 1.6 Concept of Temperature..................................................................................................................... 4 1.7 Thermometers and Measurement of Temperature ........................................................................... 4 1.10 Ideal-Gas Temperature ..................................................................................................................... 4 Chapter 2....................................................................................................................................................... 4 2.1 Thermodynamic Equilibrium............................................................................................................... 4 2.2 Equation of State ................................................................................................................................ 5 2.3 Hydrostatic Systems ............................................................................................................................ 5 2.4 Mathematical Theorems ..................................................................................................................... 6 2.5 Stretched Wire .................................................................................................................................... 6 2.6 Surfaces ............................................................................................................................................... 6 Chapter 3....................................................................................................................................................... 6 3.1 Work.................................................................................................................................................... 6 3.2 Quasi-static Process ............................................................................................................................ 6 3.3 Work in Changing the Volume of a Hydrostatic System ..................................................................... 6 3.4 PV Diagram .......................................................................................................................................... 7 3.5 Hydrostatic Work Depends on the Path,, ........................................................................................... 7 3.6 Calculation of ∫P dV for Quasi-static Processes .................................................................................. 7 3.7 Work in Changing the Length of a Wire .............................................................................................. 8 3.8 Work in Changing the Area of a Surface Film ..................................................................................... 8 Chapter 4....................................................................................................................................................... 8 4.1 Work and Heat .................................................................................................................................... 8 4.2 Adiabatic Work.................................................................................................................................... 8 4.3 Internal-Energy Function .................................................................................................................... 8 4.4 Mathematical Formulation of the First Law ...................................................................................... 8 4.5 Concept of Heat .................................................................................................................................. 9

4.6 Differential Form of the First Law ....................................................................................................... 9 4.7 Heat Capacity and Its Measurement .................................................................................................. 9 4.8 Specific Heat of Water; The Calorie .................................................................................................. 10 4.9 Equations for a Hydrostatic System .................................................................................................. 10 4.10 Quasi-static Flow of Heat; Heat Reservoir ...................................................................................... 10 Chapter 5..................................................................................................................................................... 10 5.1 Equation of State of a Gas................................................................................................................. 10 5.2 Internal Energy of a Real Gas ............................................................................................................ 11 5.3 Ideal Gas ............................................................................................................................................ 11 5.4 Experimental Determination of Heat Capacities .............................................................................. 11 5.5 Quasi-static Adiabatic Process .......................................................................................................... 12 Chapter 6..................................................................................................................................................... 12 6.1 Conversion of Work into Heat and Vice Versa.................................................................................. 12 6.2 The Gasoline Engine .......................................................................................................................... 12 6.3 The Diesel Engine .............................................................................................................................. 12 6.6 Heat Engine; Kelvin-Planck Statement of the Second Law ............................................................... 13 Chapter 8..................................................................................................................................................... 13 8.1 Reversible Part of the Second Law....................................................................................................13 8.4 Entropy of the Ideal Gas ...................................................................................................................13 8.6 Entropy and Reversibility .................................................................................................................. 14 Chapter 10................................................................................................................................................... 14 Sections 1-8................................................................................................ Error! Bookmark not defined. 10.1 Characteristic Functions.................................................................................................................. 14 10.2 Enthalpy .......................................................................................................................................... 14 10.3 Helmholtz and Gibbs Functions ...................................................................................................... 14 Chapter 11................................................................................................................................................... 15 Sections 3, 6 ............................................................................................... Error! Bookmark not defined. Other ........................................................................................................................................................... 15 Natural logarithm rules ........................................................................................................................... 15 Material after chapter 11........................................................................................................................ 15 To do: .......................................................................................................................................................... 15

Chapter 1 1.1 Macroscopic Point of View • •

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Separation of a restricted region of space or a finite portion of matter from its surroundings by means of a closed surface is called the boundary The region within the arbitrary boundary and on which the attention is focused is called the system, and everything outside the system that has a direct bearing on the system’s behavior is known as the surroundings, which could be another system If no matter crosses the boundary, then the system is closed If there is an exchange of matter between system and surroundings, then the system is open The macroscopic point of view considers variables or characteristics of a system at approximately the human scale, or larger The microscopic point of view considers variables or characteristics of a system at approximately the molecular scale, or smaller Quantities of mass, composition, volume, pressure, and temperature refer to the large-scale characteristics, or aggregate properties, of the system and provide a macroscopic description o The quantities are called macroscopic coordinates Macroscopic coordinates, in general, have the following properties in common: o They involve no special assumptions concerning the structure of matter, fields, or radiation o They are few in number needed to describe the system o They are fundamental, as suggested more or less directly by our sensory perceptions o They can, in general, be directly measured A macroscopic description of a system involves the specification of a few fundamental measurable properties of a system Thermodynamics is the branch of natural science that deals with the macroscopic properties or characteristics of nature and always includes the macroscopic coordinates of temperature for every system

1.2 Microscopic Point of View •

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A microscopic description of a system involves the following properties o Assumptions are made concerning the structure of matter, fields, or radiation o Many quantities must be specified to describe the system o These quantities specified are not usually suggested by our sensory perceptions, but rather by our mathematical models o They cannot be directly measured, but must be calculated A microscopic description of a system involves various assumptions about the internal structure of the system and then calculations of system-wide characteristics

1.3 Macroscopic vs. Microscopic Points of View •

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1.4 Scope of Thermodynamics

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Position and time and a combination of both, such as velocity, constitute some of the macroscopic quantities used in classical mechanics and are called mechanical coordinates Macroscopic quantities, including temperature, having a bearing on the internal state of a system are called thermodynamic coordinates. Such coordinate serve to determine the internal energy of a system

1.5 Thermal Equilibrium and the Zeroth Law •

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Thermal equilibrium is the state achieved by two (or more) systems, characterized by restricted values of the coordinates of the systems, after they have been in communication with each other through a diathermic wall An adiabatic wall prevents two systems from communicating with each other and coming to thermal equilibrium with each other o Ideally does not communicate heat A diathermic wall is a boundary through which heat is communicated from one system to another system, yet remains closed to the transport of matter Zeroth law of thermodynamics: two systems in thermal equilibrium with a third are in thermal equilibrium with each other

1.6 Concept of Temperature • • •

Temperature is a measure of the hotness of a given macroscopic object, as felt by the human body An isotherm is the locus of all points representing states in which a system is in thermal equilibrium with one state of another system The temperature of a system is a property that determines whether or not a system is in thermal equilibrium with other systems o The necessary and sufficient condition for thermal equilibrium between two systems is that they have the same temperature

1.7 Thermometers and Measurement of Temperature 1.10 Ideal-Gas Temperature •

Ideal-gas law: 𝑃𝑉 = 𝑛𝑅𝑇

(1.5)

𝑃

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Ideal-gas temperature T: 𝑇 = 273.16𝐾 lim ( 𝑃 ) , constant V

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In the temperature region in which a gas thermometer may be used, the ideal-gas scale and the Kelvin thermodynamic scale are identical

𝑃𝑇𝑃 →0

𝑇𝑃

(1.7)

Chapter 2 2.1 Thermodynamic Equilibrium • • •

When these coordinates change in any way whatsoever, either spontaneously or by virtue of outside influence, the system is said to undergo a change of state When a system is not influenced in any way by its surroundings, it is said to be isolated When there is no unbalanced force or torque in the interior of a system and also none between a system and its surroundings, the system is said to be in mechanical equilibrium

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When a system in mechanical equilibrium does not tend to undergo a spontaneous change of internal structure (chemical reaction or transfer of matter from one part of the system to another, e.g. diffusion or solution), then it is in chemical equilibrium Thermal equilibrium exists when there is no spontaneous change in the coordinates of a system in mechanical and chemical equilibrium when it is separated from its surroundings by diathermic walls o There is no exchange of heat between the system and its surroundings o In thermal equilibrium, all parts of a system are at the same temperature, and this temperature is the same as that of the surroundings When the conditions for all three types of equilibrium are satisfied, the system is in thermodynamic equilibrium o There will be no tendency whatever for any change of state, either of the system or of the surroundings, to occur States of thermodynamic equilibrium can be described in terms of macroscopic coordinates that do not involve the time, that is, in terms of thermodynamic coordinates When the conditions for mechanical and thermal equilibrium are not satisfied, the states traversed by a system cannot be described in terms of thermodynamic coordinates referring to the system as a whole

2.2 Equation of State • •

Of the three thermodynamic coordinates P, V, and T, only two are independent variables There exists an equation of equilibrium which connects the thermodynamic coordinates and which robs one of them of its independence. Such an equation, called an equation of state, is a mathematical function relating the appropriate thermodynamic coordinates of a system in equilibrium o For a closed system, the equation of state relates the temperature to two other thermodynamic variables

2.3 Hydrostatic Systems •

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Any isotropic system of constant mass and constant composition that exerts on the surroundings of a uniform hydrostatic pressure, in the absence of gravitational, electric, and magnetic effects is called a hydrostatic system o A pure substance, which is a single chemical compound in the form of a solid, liquid, gas mixture, of any two, or mixture of all three o A homogeneous mixture of different compounds, such as a mixture of inert gases, a mixture of chemically active gases, a mixture of liquids, or a solution o A heterogeneous mixture, such as a mixture of different gases in contact with a mixture of different liquids The state of equilibrium of a hydrostatic system of a single phase can be described in an equation of state by three coordinates: P (Pa = N/m2), V (m3), T (K) If the system undergoes a small change of state whereby it passes from an initial state of equilibrium to another state of equilibrium very near the initial one, then all three coordinates, in general, undergo slight changes

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If the change of V is very small in comparison with V and very large in comparison with the space occupied by a few molecules, then this change of V may be written as a differential dV Every infinitesimal in thermodynamics must satisfy the requirement that it represents a change in a quantity which is small with respect to the quantity itself and large in comparison with the effect produced by the behavior of a few molecules

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If dz is an exact differential of a function of x and y, then 𝑑𝑧 = ( 𝜕𝑥) 𝑑𝑥 + ( 𝜕𝑦) 𝑑𝑦

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An infinitesimal that is not the differential of an actual function is called an inexact differential

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𝜕𝑧

𝜕𝑧

𝑦

𝑥

2.4 Mathematical Theorems •

See formula sheet

2.5 Stretched Wire 2.6 Surfaces Chapter 3 3.1 Work •

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If a system undergoes a displacement under the action of a force, work is said to be done, the amount of work being equal to the product of the force and the component of the displacement parallel to the force If a system as a whole exerts a force on its surroundings and a displacement takes place, the work that is done either by the system or on the system is called external work The work done by one part of a system on another part is called internal work o Work considered here is only external work unless stated otherwise When the resultant force exerted on a mechanical system is in the same direction as the displacement of the system, the work of the force is positive, work is done on the system, and the energy of the system increases o Positive work when work is done on the system o Negative work when work is done by the system

3.2 Quasi-static Process •

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A system in thermodynamic equilibrium satisfies the following o Mechanical equilibrium: no unbalanced forces/torques o Thermal equilibrium: no temperature differences o Chemical equilibrium: no chemical reactions/motion of chemical constituents within system During a quasi-static process, the system is at all times infinitesimally near a state of thermodynamic equilibrium

3.3 Work in Changing the Volume of a Hydrostatic System •

Imagine any hydrostatic system contained in a closed cylinder equipped with a frictionless movable piston on which the system and the surroundings may act

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If the piston moves in an infinitesimal distance dx during compression, and the force F from the surroundings differs only slightly from the force PA of the system, then the surroundings perform an infinitesimal amount of positive work đW on the system, equal to đ𝑊 = 𝐹𝑑𝑥 = 𝑃𝐴𝑑𝑥 o During compression, the volume of the system is decreasing: 𝐴𝑑𝑥 = −𝑑𝑉 o Hence, đ𝑊 = −𝑃𝑑𝑉 (3.1) In a finite quasi-static process in which the volume changes from Vi to Vf, the amount of work W 𝑉

done by the system is 𝑊 = − ∫𝑉 𝑓 𝑃𝑑𝑉 (3.2) 𝑖

3.4 PV Diagram • • • • ...