CHAPTER 1 THE NATURE OF THERMODYNAMICS 1 Introduction to thermodynamics: It is probably fair to say that thermodynamics tells us something about everything, but not everything about anything. At a basic level everything behaves as a thermodynamic system: energy flows in and is transformed into something useful and there is an inevitable generation of waste products. The laws of thermodynamics are very general and apply from the microscopic to the cosmic level. The 1st law will seem very familiar to you as it expresses conservation of energy (energy comes from the Greek word for work).

2 The 1st law: you cant win. At best you can break even. Energy is somewhat mysterious, but we are so used to the term that we are comfortable with it. The 2nd law is very different: it is not directly related to other branches of physics. The central concept is entropy S (Greek word for transformation). The 2nd law says that Nature imposes a tax on devices that transform other forms of energy to work. The 2nd law: You can break even only at absolute zero. The 3rd law: You cannot reach absolute zero. 3 Entropy is a rather mysterious concept and we are not as comfortable with it as we are with energy.

Entropy represents the fundamental notion of the inevitable inefficiency when energy is transformed to work (but fundamentally is just a simple statement of statistics). To ignore the second law is folly! Entropy is one of the most profound concepts in science. The idea has found use in fields as diverse as information theory and biology. Now, down to work (so to speak). 4 In dynamics the time, t, is the central variable.

Thermodynamics is the study of the transformation of energy. The central variable (concept) is that of temperature. The study of thermodynamics began at the start of the Industrial Revolution when it became important to understand the conversion of heat to mechanical work. This subject is firmly based on experiment and is very general and so useful in a broad range of situations. 5

Example of Uses: Internal combustion engines Power stations Refrigeration and air conditioning Propulsion systems (robots, missiles, aircraft) Physical chemistry (largely an application of thermodynamics to chemistry)

Production of very low temperatures (thermodynamic principles applied to molecular and nuclear magnets) Communication and information theory Astrophysics (e.g., stars, black holes, systems of stars) Atmospheres and Climate Biology In the study of thermal physics only a small number of principles are used. 6 Thermodynamics: macroscopic properties (P,V etc.) are used. This study gives general relations between quantities, especially as affected by temperature. Kinetic Theory (Maxwell):

uses a model of a system of molecules or atoms. Actual values can be calculated. Statistical Thermodynamics (Boltzmann and Gibbs) not concerned with individual molecules or atoms. Statistical methods are applied to a large number of molecules. 7 We will be concerned with a system, which is a part of the physical world (container of gas, magnet, piece of metal etc). The system might exchange energy with its surroundings. The system and its surroundings constitute the universe.

surroundings Universe boundary (real or mathematical) The boundary is not necessarily fixed. System 8 Open system: can exchange matter and energy with surroundings.

Closed system: cannot exchange mass, but can exchange energy and mechanical work. Isolated system: cannot exchange mass or energy (or in any way interact) with the surroundings. Points of view: Macroscopic: few fundamental measurable properties( P,V,T) Microscopic: concerned with the molecules of the system. Many quantities introduced are not directly measurable. 9 Intensive and extensive Quantities Imagine a system in equilibrium to be divided into two equal parts, each with the same mass:

Those properties of each half of the system that remain the same are said to be intensive. These are independent of mass. Those which are halved are called extensive; i.e., dependent on mass (the extent). Experiment determines whether or not a quantity is intensive or extensive. Experiments show that N, m, n extensive P intensive T intensive V extensive 10 You can verify that:

(I)(I) (I)(E) (I)/(I) (E)/(E) (E)/(I) I E I I E An extensive quantity can be made into an intensive one by dividing by an extensive quantity. kmole: The number of kmoles of a substance is defined to be the mass (expressed in kg) divided by the mass of a molecule (expressed in amu). e.g., 1 kmole of O2 has mass 32 kg.)

11 1 kmole contains Avogadros no. of molecules N A 6.02214179 1026 A little more challenging example: 0.1 kg of H 20 mo = (2 x 1.00794 amu) + (1 x 15.9994 amu) = 18.01528 amu = 18.02 kg kmole-1 m 0.100 kg n 0.0055 kmole 1 m o 18.02 kg kmole no. of molecules N,

N (0.00555) (6.022 1026 ) 3.341024molecules 12 A a lower case letter is often used to represent an intensive variable created by normalizing an extensive variable by another extensive variable. Examples: V v n V v N V v m

(volume per kmole) (volume per molecule) (volume per kg) The variable v is referred to as the specific volume. 13 Definitions concerning the system state: State: is uniquely specified by a set of properties (see figure on next page). State variables: are properties that describe equilibrium states (e.g., P, V, T, U, S). Equation of state (EOS): a functional relationship among the variables describing an equilibrium state. e.g., f(P,V,T) = 0 Path: a path is a series of states through which a system passes. Steady state: energy and/or matter enter and leave the system at the same rate no net changes in time in an otherwise dynamic system. Equilibrium state: the properties of the system are such that they are uniform

throughout and do not change with time a) thermal equilibrium: no T gradients (no heat transfer). b) mechanical equilibrium: e.g., no P gradients (no change in volume). c) chemical/diffusive equilibrium: no chemical potential gradients (no net change in particles). Thermodynamic equilibrium: all three above conditions are met no spatial energy gradients or time dependencies. Local thermodynamic equilibrium (LTE): conditions are locally uniform and changes are slow compared to time scales of interest. Here we will study (near) Equilibrium Thermodynamics. Non-equilibrium thermodynamics is at present frontier physics. 14 It is usual to represent a state as a point on a 3-dimensional

surface. T A Equilibrium state C B f(P,V,T)=0 V

A process is a change in state along a path on P the P-V-T surface. (A to B) A cyclic process is when the initial and final states are the same. (A to B to C to A) Quasi-static process: at any instant the system departs only 15 infinitesimally from an equilibrium state. Reversible process: a process whose direction can be reversed by an infinitesimal change in some property. It is a quasi-static process with no dissipative forces present. i.e., it is an ideal process involving mathematical differential step changes all reversible processes are quasi-static, but vice-versa not always true (e.g., slow leak in tires) Irreversible process: one that involves a finite change in some property and includes dissipation. All natural (real) processes are

irreversible. Holding state a variable constant: Isobaric process: P remains constant Isochoric process: V remains constant Isothermal process: T remains constant Isentropic process: S remains constant 16 (adiabatic and quasi-static) It is found by experiment that only a certain minimum number of macroscopic properties of a thermodynamic system can be given arbitrary values. Once these properties are fixed, all other properties are also fixed.

It is the job of the experimentalist to determine what are the relevant properties and how many of these properties are independent. 17 Change in state: a change in thermodynamic coordinates. Change in phase: transition from solid to liquid etc. It is convenient to introduce two ideal boundaries. Adiabatic boundary: is one across which the flow of heat is zero.

Diathermal boundary: is one in which there is good thermal conduction and energy can be exchanged with the surroundings. 18 Example of a process to do work. We consider a weight divided into three parts and sitting on a piston. shelves Assume no friction and all the walls are adiabatic. We wish to do some work on the system. Suppose we suddenly slide the weights off onto the lowest shelf. The piston will rise rapidly, oscillate, and finally come to rest at some equilibrium position. gas

In this case the piston does no work on the load. However, work can be done if we slide the first of the three weights onto the bottom shelf, then the second weight when the system comes to rest at the second shelf, and finally the last weight when the system comes to rest at the third shelf. The piston comes to rest above the third shelf. 19 We can do better by further subdividing the weight. What is the best that we can do? Imagine replacing the weight by a pile of fine sand of equal total weight. We can imagine removing one grain at a time. Each grain that has been removed is held in place by a vertical strip of sticky tape. Each time we remove a grain, there is only an infinitesimal change in the position of the piston and there is almost no oscillation. We can do better only by making the grains smaller.

This latter process is called a reversible process because we can reverse the process by adding one additional small grain to the piston and then replacing the minute grains of sand from the sticky tape back onto the piston one grain at a time. We can then return the system essentially to its initial condition. 20 The reversible process is of essential importance in thermodynamics. It represents the limit of what is possible (e.g., maximum work may be extracted). The reversible process is amenable to exact mathematical analysis. Often in thermodynamics, a calculation is only possible when we choose a reversible process. The states through which the system passes differ only infinitesimally from equilibrium states. 21

Units. The SI system is used in this course. The unit of pressure is the Pascal (Pa). N 1 Pa 1 2 m 1 bar 105 Pa 1 atm 1.01325 105 Pa 760 torr The SI unit of volume is m3. 1 m3 = 103 = 106 cm3. The SI unit temperature is K (Kelvin). The SI unit of energy is the J (Joule).

1 J = 1.602176487 x 10-19 eV (atomic/molecular energy levels are measured in eV) 1 kcal = 4184 J = heat required to raise T of 1 kg of water from 14.5 C to 15.5 C (equivalent to 1 food calorie c). 22 Consider a system A specified by two macroscopic variables X,Y and a system B specified by X! and Y! Adiabatic boundary A B X,Y X!,Y!

The adiabatic boundary is removed and replaced by a diathermal boundary. At first the properties X,Y and X! and Y! may change. When no further changes take place A and B are said to be in thermal equilibrium. 23 Zeroth Law of Thermodynamics. When two bodies are each separately in thermal equilibrium with a third body, they are in thermal equilibrium with each other.

This law is not a logical deduction but an experimental fact. There exists a property that anticipates when two systems will be in thermal equilibrium, regardless of their composition and size. We call this universal property the temperature. 24 STOP 25 Consider body A to be in some state (X1,Y1) and this state is in thermal equilibrium with body B in

state (X1!,Y1!). Experimentally it is found that there are other states (X2,Y2) etc. of body A that are in thermal equilibrium with the same state (X1!,Y1!) of body B. The locus of such states is called an isotherm of body A. 26 B isotherms

A isotherms Y I! X 1 Y! , Y1

X2 , Y 2 X! , Y! 1 1 I X X! I and I! are corresponding isotherms 27 The property that decides whether or not A and B will be in thermal equilibrium when brought together is the temperature. 28

A thermometer has some thermometric property which changes appreciably as the temperature changes. (An example is Hg in the common Hgin- glass thermometer.) Example of a thermometric property. Resistance (R) of Pt. For temperatures not too low, R changes appreciably with T. At very low temperatures this is no longer true and so this thermometer is not useful at these temperatures. However, at these temperatures one can use the R of Ge (As). Different thermometers are useful in different temperature ranges. 29 We are concerned with an empirical temperature, , that is, a temperature as measured by some thermometer. Historically two points were chosen to define a temperature scale:

Ice point = 00 C Steam point = 1000 C In modern thermometry one uses a single point, the triple point of H2O. At this point vapor, water and ice exist in equilibrium. This occurs at only one temperature. (The P at the triple point is not 1 atmosphere.) The triple point is chosen to be 273.16k (0.010 C). An empirical scale (X) is defined as follows: 30 Y=constant Y isotherm Xtp 273.16K

X Thermometric property 31 For constant Y, as T varies, X varies. We choose (X) = a X (X=0, = 0) Putting in the triple point gives 273.16K = a Xtp (X) = 273.16K so X Xtp Various Xs (different thermometric properties) give

different empirical temperatures! 32 Example: Gas thermometer P (P)273.16K Ptp With V=constant . Example: Pt resistance thermometer R

(R) 273.16K Rtp 33 The empirical temperatures measured by various thermometers disagree! For this reason standard thermometers are defined for various temperature ranges. 34 We consider one thermometer : The constant volume gas thermometer. capillary tube h B

R Hg reservoir Indicial point P 1 ( P ) 273 .16 K Ptp1 manometer 35 In the above sketch: B = bulb containing a gas. B is connected

to the Hg manometer by a capillary tube. R = reservoir of Hg. The reservoir is raised or lowered to adjust the Hg level to the indicial point. The manometer then measures the P of the gas in the bulb at a constant volume. 36 This thermometer is used as follows: For a given quantity of gas in B use a triple point cell and measure the pressure of the gas in B (Ptp1). Remove the triple point cell and place B in contact with the system whose temperature is to be measured. Measure the pressure, P, when B is in thermal equilibrium with the system. Then P

1 ( P)273 .16 K Ptp1 Note: Ptp is not the pressure of the water vapor at the triple point, which is 611 Pa. 37 Repeat the above measurements after removing some gas from B so that Ptp = Ptp2 is lower than Ptp1 P 2 (P) 273.16 K Ptp2 It is found that 2 (P) is different than 1 (P)

(discouraging!) 38 Experimental results for some gases are shown below. 02 ( P) (K ) air N2 H2 Ptp 39

From the above graph we observe the following points: for a given system varies with Ptp ( ) at a given Ptp differs for various gases ( as Ptp 0 all gases give the some result. ( ) ) Because of this behavior we define the T of the system as: P at constant V T 273.16 K P

tp The gas thermometer can be used to measure temperature down to about 2.6 K by using 3He at low pressure. limit Ptp 0 40 Later we will discuss the absolute or thermodynamic temperature, which we will label as T. This temperature does not depend on the properties of the thermometric material.

The temperature defined above is, in fact, an absolute temperature and so we are justified in using the label T. 41 The centigrade (Celsius) scale: (0C) = T - Ti in which Ti represents the temperature at the ice point (273.15K) The normal pressure (N) is one standard atmosphere. NBP = normal boiling point (steam point NMP = normal melting point (freezing point) 42 For H2O we have the following table: T (K)

NMP NBP tp 273.15 373.124 273.16 (0C) 0.00 99.97 0.01 43 Much work has been done to ensure that temperatures measured in different laboratories agree and that they are thermodynamic

temperatures. An international temperature scale was agreed upon in 1990 (ITS-90). A number of reproducible temperatures (triple points for example) that had been carefully measured were assigned standard values. For example the triple point of Ne was assigned the value of 24.5561K. Different thermometers, which must be calibrated, are used in different temperature ranges. 44 Example Pt resistance thermometers Range 13.8033K to 1234.93K

R (T) = Rtp (1+aT+bT2) The constants a and b are determined for a particular thermometer using the ITS- 90 points. From the above it can be seen that it is not trivial to assign a temperature for a system! 45