Theory of thermodynamics1.1 The goals of thermodynamicsThermodynamics is the branch ofphysics that studies the macroscopic systems in which the thermal affects aretaken into account. These systems areconsidered to be in equilibrium. Whenthe systems are in equilibrium it is easier to study them both experimentallyand theorically. A system is a thermodynamicevent such as some liquid that is inside a closed container for which we haveto measure the pressure volume temperature and other physical properties. The system has also its surroundings, whichmeans that it is not enough to know the system in order to get accurate valuesfor the quantities involved in the study. We have also to take into consideration even the surroundings in orderto the study the situation described.When studying thermodynamics weoften neglect the interaction between particles.
For this reason we are more interested inmacroscopic systems rather than in microscopic ones. So, thermodynamics represents a very generalapproach for the study of a System Properties. However, with a good approximation it is very useful when studying thedaily life phenomenon regarding properties such as heat, temperature, thermalexpansion and contraction, pressure, volume, internal energy etc.
1.2 The universe and its componentsFirst let’s give somedefinitions:The thermodynamic system is confinedalways with some boundary. The externalpart of this boundary is called surroundings as we said before. So, everything that exists is either a partof the system, a boundary or surroundings.
Hence, we can say that the system plus surroundings plus boundariesgives the universe. We must not neglect theimportance of boundary. It is equallyimportant as the system and the surroundings. Without the boundary we can’t have heat-exchange, thermal interactionsetc.
The boundary is called adiabatic whenit prevents any exchange of heat between the system and the surroundings. On the other hand, the diathermal boundarythe walls heat exchange between the system and its surroundings. In Thermodynamics there arethree types of systems: open systems, closed systems and insulatedsystems. In open systems will particlesare thermally interacting. 1.3 EquilibriumA system is in equilibrium whenits physical properties do not change with time. For example, when no heat is supplied to someliquid, its temperature will remain constant all the time.
The liquid will have the same temperature asthe environment if no heat is supplied to it. On the other hand, when heat is given to the liquid, its mass willdecrease because some liquid will turn into a vapor. So this system is not anymore in equilibrium.How can this equilibrium bereached? Let’s consider some gas whichinitially is allowed to slowly fill a box. As long as the gas is filling the box, the system is not in equilibrium. This equilibrium will be reached after thegas flow is stopped and the gas fills all the volume of the box.
Now the system is in equilibrium. The gas will continue to flow within the boxbut this is a microscopic process and we are not interested in that. And as we said before, we are interested in macroscopicprocesses. Imagine if we are measuring thepressure in two different moments. Firstwe measure the pressure during the gas entrance into the box. In this moment the pressure is changeablebecause the gas flow is not uniform. Ifwe measure of the gas pressure after the gas has stopped flowing inside thebox, we will find that the pressure is almost constant. So, we can conclude that the pressure isuniform only when the equilibrium of the system has been reached.
Therefore, equilibrium isverified in two conditions: the absence of macroscopic flows and the constantpressure. If the gas pressure is notuniform within the box, so that the pressure in one side of the box is notequal to the pressure on the other side of net force will appear as P = F / A where A it is the side area of the box. Therefore F = (P2 – P1) xAHence, if there is a net forcethere is no equilibrium and this comes because of non-uniform pressure.
So, we obtain an important property of the system:”Non -uniform pressure resultsin macroscopic flow and this one results in absence of equilibrium.”And also we can say that equilibriumis reached only at constant pressure. 1.4 Thermodynamic variablesA variable is a quantity thatcan change during the process in thermodynamics. There are several variables in thermodynamicswhich characterize the system as a whole. The values that these variables will take during the process will notdepend on the place where these values are measured. The thermodynamic variables can be definedonly when the system is in equilibrium.
Variables are necessary to describe the physical state of the thermodynamicsystem in equilibrium.Let’s take an example with afluid. There are two variables that haveto be considered when studying this system. These two variables are pressure and volume. There are other thermodynamic variables suchas temperature, entropy, and internal energy etc.
. They are common to all thermodynamic systems.Thermodynamic variables can bedivided into two main categories: extensive and intensive variables.
Let’s imagine that a thermodynamic system isdivided into two equal parts where each of these parts carries its ownthermodynamic variables. The question is:how to the variables of the splitted system, compare to the variables of theoriginal system? Some quantities womenbe affected while some others will be halved. The quantities that are not affected are intensive variables while theothers are extensive variables. Forexample the pressure is not affected by the division, so it is an intensive upvariable, but the volume has been halved, so the volume is an extensivevariable.1.5 Zeroth law of thermodynamicsLet’s imagine that the systemsA and B and are placed on both sides of the diathermal wall so that heat isallowed to be exchanged. These systemsare in thermal contact with each other.
Let’s consider both systemsinitially in equilibrium but these equilibriums are internal equilibriums ofthe separate systems and not equilibrium of the joint system. When we placed in contact both objects, theprevious equilibriums will change until both objects will reach a new equilibrium. In this case, the physical properties ofobjects A and B had changed and the new equilibrium has established new valuesof their physical properties. This newequilibrium of both systems is known as thermal equilibrium which appears whentwo systems are brought in thermal contact. This fact is known as the first principle of thermodynamics or zerothlaw of thermodynamics. It states thatWhen asystem A is in thermal equilibrium with a system B, and the system B is inthermal equilibrium with a system C, the system A is also in equilibrium withthe system C.
1.6 TemperatureWe can feel the differencebetween a hot object and a cold object. We may say that the temperature is the degreeof hotness of an object. But this definition is intuitive and makes referenceto our senses. We cannot use this approach to assign a numerical value to temperature.A cup of tea can be “warm” according to one person and “veryhot” according to another. We must find a universally applicable way tomeasure the numerical value of temperature. The device used to measure thetemperature is called a “thermometer”.
There are different types ofthermometers utilizing different physics laws as their working principle. It ispossible to measure the temperature by using resistance of a wire, expansion propertiesof solids, or even an infrared camera. But the common thermometer we are so familiarwith utilizes expansion of liquids to measure the temperature.1.7Scales of temperatureThe mercury thermometer was invented by Gabriel D. Fahrenheit. Itconsists of a thin glass tube sealed at both ends (capillary tube) and partlyfilled with mercury.
Above the mercury column is vacuum, for the mercury toexpand freely. As the temperature increases the mercury column in the tubesrises. Assigning numerical values to different heights of the mercury column iscalled “calibrating the thermometer”. Using different criteria forcalibration gives rise to different temperature scales. Two commonly usedtemperature scales in daily life are Celsius and Fahrenheit scales. Swedishastronomer Celsius used the freezing and boiling points of water under 1 atm pressureas the reference points for his scale.Temperature of ice-water mixture is taken as 0 °C and temperatureof boiling water is taken as 100 °C in Celsius scale.
Between these tworeference points is divided into 100 equal parts. This is why the Celsius scaleis also called centigrade (=100 grades) scale. Germanphysicist Fahrenheitused the temperatures of hottest andcoldest days in his country to calibrate his scale. In scientific studies Kelvin scale is used to express temperature.Kelvin scale is also named as “absolute temperature scale”. Later inthis chapter we will learn further about Kelvin scale.The correspondenceamong the three temperature scales is given below.Betweenfreezing and boiling points of water, temperature increases from 0 to 100 inCelsius scale, from 273.
15 to 373.15 in Kelvin scale and from 32 to 212 in Fahrenheitscale. Consequently the conversion formulas must be TK= TC + 273.15 and Capillary tube thermometers havea problem. Two thermometers calibrated in the same way gives us different temperaturereadings, if the liquids used in the thermometers are different. Supposefreezing and boiling points of water are marked on a mercury thermometer and aglycerin thermometer.
The two thermometers agree on 0 °C and 100 °C, but theywill show different values for intermediate temperatures. This effect is causedby the different expansion properties of different liquids.Toovercome this difficulty and reach a universal agreement on the full range of temperaturescale, “constant volume gas thermometer” is used. This thermometer isalso used in defining the Kelvin scale.1.8Thermal ExpansionSolid, liquid, gas, all substances expand (become larger) withincreasing temperature.
Power lines sagging in the summer and tightening in thewinter is a common observation. We will investigate three types of expansion: linear,area and volume expansion.For long and thin objects like long copper wire, change inthickness is very smalland can be neglected.
If we assume the object to be one dimensional, expansionis linear.a)Linear expansionChange in length depends on three factors:- Change in temperature (DT)- Initial length (L0)- Material of the object (?)? is called the “linear expansion coefficient” and isdifferent for each material. Consider a thin long steel rod. Thelinear expansion coefficient is defined as the fractional change in length (L) perunit temperature change (DT). Thus, Hence, the change in length is given by And the new length of the rod will be Or b)Area ExpansionConsider a thin, flat piece of metal. Suppose the area of theobject increases from A0 to Af astemperature increases from T0 to Tf. As usual,temperature change is DT=Tf – T0 and area change is DA= Af – A0.
The dependence of area change on temperature change is given by: Because for each dimension the linear expansion coefficient is , and as we have 2 dimensions involved here, we mustwrite 2? instead of . The inthe formula is the same as in the linear expansion formula. c)Volume ExpansionFollowing the same line of thought, we can draw that for a 3dimensional object, expansion, the formula becomes: 1.9Molecular Interpretation of TemperatureWe haddefined temperature as degree of hotness.
What is the physical difference betweena hot object and a cold object aside from feeling hot or cold? In other words,which property of a substance determines its temperature?Molecular – kinetic theory tellsus that temperature of a substance is related to the motion of moleculesforming the substance. Remember from previous chapter that all matter (solid,liquid, gas) consist of unthinkably small molecules, and these molecules are incontinuous random motion which is called thermal motion. The form of thermalmotion depends on the phase of the substance. In a solid, molecules oscillatearound fixed positions. In a gas, they fly around freely continuously collidingwith each other.
Temperatureof a substance is related to thermal motion of molecules. In general terms, highertemperature means faster moving molecules.Forsolids and liquids the relation between molecular speeds and temperature of substanceis complicated because of the bonds between the molecules. In case of an idealgas this relation is quite simple. For an ideal gas, temperature isa measure of average kinetic energy of molecules of the gas. Averagekinetic energy means sum of kinetic energies of molecules divided by number ofmolecules.
Actually average kinetic energy of gas molecules is a very smallnumber since the mass of a molecule is so small. At 20 °C for example an oxygenmolecule in the air has about 10-20 J of kinetic energy.As we know,molecules of a gas can have a wide range of velocities, and speed of a moleculechanges millions of times in a second due to the collisions with other molecules.At a given instant one molecule of a gas sample may nearly be at rest whileanother molecule moves with almost speed of light. Consequently kinetic energiesof molecules of a gas are quite different. But average kinetic energy of moleculesgives us an idea about the behavior of the gas sample.
An analogy to averagekinetic energy of gas molecules could be the national income per capita of anation. As we know, national income per capita means total value of all incomeof a country in one year, divided by the population of the country. Considertwo countries X and Y. National income per capita of country X is higher thanthat of Y. This means average citizen of X country is richer than average citizenof Y country. But naturally in both countries we can find very rich and verypoor people. Higher income per person does not mean that every single person inX country has much money, but still it gives us an idea about the average richnesslevel in the country.Similarlya gas sample with higher temperature has molecules with higher kinetic energyon average than a colder sample.
But it is always possible to find very fast andvery slow molecules in both samples. Later in this book we will be able to showthatAverage KE of gas molecules = (aconstant) x (temperature) 2. Gas lawsGaslaws are relations between the macroscopic parameters of a gas. Macroscopic parametersof a gas are pressure, volume, and temperature. These are called macroscopicbecause we can either see them or directly measure them with devices such asthermometer or manometer. On the other hand, a quantity like speed of a singlemolecule is microscopic by definition.
Beforestarting to deal with gas laws, we should get to know something called “cylinder- piston system” better. We will be using this device throughout all our thermodynamicsstudies.Considera cylinder – piston system as described below:Thepiston is tight fitting enough not to allow any gas to escape, but in the same timemoves up and down without friction. Naturally this is a difficult apparatus toproduce.
But it will be useful to get a grip on the basics of gasWe can adjust the pressureapplied on the inside by the piston, by changing the weight of the piston asshown below. In acylinder – piston system: Movablepiston implies constant pressure.Historicallythe relations among the temperature pressure and volume of a gas wereestablished in 17th century by different scientists.
Now we remember therelations by the names of these scientists. We will investigate three gas lawshere, at constant temperature, at constant pressure, and at constant volume.Pressurevolume relation of a gas sample at constant temperature is established nearlyat the same time by the English physicist Boyle and French scientist Mariotte. Nowwe name the relation as Boyle-Mariotte law.
a.Boyle-Mariotte LawPressure – volume relation of a gas sample at constanttemperature.Changing volume and pressure of a gas sample at constanttemperature is called isothermal process. “Isothermal” means happeningat “constant temperature”. When a fixed amount of gas is compressed,decreasing its volume, we expect its pressure to increase. You can easilyobserve this effect by trying to squeeze the air in a syringe with its nozzleclosed.
Pushing the piston will require more and more force as the volume ofthe air trapped inside decreases. But this “syringe experiment” isnot a good example for isothermal process. As the air in the syringe is compressed,not only the pressure but also the temperature increases. To overcome thisdifficulty and keep the temperature constant we must work carefully. To achieve isothermal process we can make such an arrangement. Weplace the cylinder in figure in a lake to keep the temperature constant. Thento increase the pressure slowly, we start to drop grains of sand on the pistonone by one.
Impact of each grain pushes the piston down a little andtemperature tries to increase by – say – 0.01 °C, but since we cannot heat thewhole lake, and the process is slow enough, the gas inside the cylinder willhave time to cool down, until its temperature equals the temperature of lake water.We can say the temperature of the gas is kept constant.The lake in the process described above is acting as a heatreservoir.
This means it is cooling down (or heating up) another object withoutchanging its own temperature.