Engineering MAE 91. Intro to Thermodynamics. Lecture 02.

I will keep giving you some in concepts that you need to understand the material alright so so that's where we were the last item we were discussing was the concept of equilibrium and I said then that a simple way to describe what equilibrium is in thermodynamics is essentially to say that nothing is happening that nothing is happening in the system that's a very plain way to express it but if you want to be a little bit more formal then you say what is written there it's a condition of balance characterized by the absence of driving potentials and at the very end of the lecture we were talking about driving potentials and what's the driving potential and you give me an example of a driving potential you can even give me the one from the end of the lecture somebody else how about you you have no idea where you here okay what about you anybody raise your hand if you have an example of a driving potential a temperature difference right we have another one the same one yes well you're making it a little bit maybe a variation in distribution of a catalyst but at this point really it's a variation in something so a variation in temperature will produce heat transfer it's a temperature in one part of the system is higher than another part of the system then heat transfer will occur and you think of another one another difference that would make something happen pressure difference what happens if I have a pressure difference within a system what will what will be moving fluid or you know part of it be a substance that is in the system so if it's liquid or a gas you have a pressure difference within the system then fluid flow will occur and just like that you can think of many others but for the time being so equilibrium would be that would mean that yes sir does he pay you he's so far back there yes I'm sorry this microphone is not for you guys this microphone is for the video over there so that's why and you guys need to be quiet because I don't want to have to carry another microphone if I don't have to so that's why I checked last time make sure you hear me in the back if you don't and raise your hand and I'll try to speak a little louder or you're welcome to move down you're going to come down speak into you yeah there are there's plenty of seats there is one here front row so so that's what equilibrium is so it typically you would have no temperature difference within the system no pressure difference within the system in fact if you pick any property of that system then you would find that that property is the same everywhere within that system and that would define a condition of equilibrium now the next concept is the concept of a process in thermodynamics what is a process and it says there is a transition from one state to another state we already define state last time so you know what the state is in fact this is such a few lines above that the state was a certain condition that the system is in and is characterized by whatever properties it has so if I go from one state to another state then that variation in the state of the system occurs by means of a process so our process takes the system from one state to another state so I could you know right that in a simple schematic I have the system here in state one on the left something happens to that system and then it goes to state two and that is the process and of course what we call the process path is really a succession of states as you go from the original state from the initial state to the final state so you have certain initial State certain final state as you go from the initial to the final state you go through a series an infinite series of many other states that are all intermediate states so typically we would do this in a in a by plotting you know two or more properties so one way you could you could think of this is if I take I pick two properties for example I could say let's plot for example pressure versus volume two properties of a of a system and then initially say that we are at this volumes I call it v1 and this pressure p1 that define our initial state and then a process takes place and it takes me on a certain path to the final statement so here is v2 and here is p2 and let's say that I am going that way I'm wanted to so that's my process but what I am saying is that all along that process path I have infinitely many intermediate States so I can stop anywhere and that would of course be a different intermediate state so in terms of the definition of equilibrium what needs to happen for a process to take place what is the connection between that process taking place and equilibrium can you connect the concept of equilibrium to the concept of a process no not exactly no no I mean can a process step take place if I'm in equilibrium no so the connection is actually then a disconnection because for a process to take place you have to be away from equilibrium if you're in equilibrium and remember I said nothing happens so if a process takes place that means that the system is not in equilibrium because otherwise nothing would happen so in general in a typical engineering system something has to happen otherwise there is nothing to study so suppose you're looking at the internal combustion engine you're trying to find out what's happening inside the cylinder with the air and the fuel that came in obviously for things to be happening you must not have equilibrium isn't it much better up here in the front yeah so so we need to be away from equilibrium for a process to take place and that actually makes things very complicated so we come up with another concept to help us out and that concept is this one a quasi-equilibrium so a process takes place it cannot take place in equilibrium because that's contradictory but we can say that a process takes place in quasi equilibrium and what do you think that is what's quasi equilibrium no no it's not an equilibrium let me ask you right there you just blew a nice chewing gum bubble what is quasi equilibrium some sort of fake equilibrium ok there is a better word than fake for quasi anybody knows what quasi means a synonym for quasi nobody yes yeah what about almost right so quasi equilibrium is really almost equilibrium and so when we say that a process takes place in equilibrium in an asari in quasi equilibrium what we are meaning is that it takes place in quasi equilibrium what do you think has to happen for a process to take to take place in quasi equilibrium whose it that it has to be very slow and those two concepts are really parallel so quasi equilibrium process has to be a very slow process because the idea is that you only allow the system to deviate from equilibrium a little bit so you make a little variation a small variation occurs then the process the system goes to the next step so if you go back to this plot say you started here then you allow for a small variation to take place and then the system maybe moves there and so it's like it's almost in equilibrium it's just a small departure from equilibrium every time and it keeps going until it makes it to the final state the problem of course is that in reality if you were to do that it would take forever however is still a very convenient tool for us to study processes at least at the very beginning to consider them to take place in quasi equilibrium and we will do that very often make the assumption that things are occurring in quasi equilibrium alright so so if for example when here is that a more formal definition a process in which each intermediate state is only infinitesimally removed from equilibrium it's sort of putting together all the ideas that I just gave you in some nice text a process in which each intermediate state is only infinitesimally removed from equilibrium so let's say that we look at a very simple system like this that we have been looking at I have a gas in a cylinder it is fitted with a piston and suppose that I'm interested in compressing this guy so I want to push that piston down by applying a force if I do it very fast as I would do it normally then I would be significantly away from equilibrium because imagine that I start pushing that piston down what happens the initial is let's say that that's air in that in that cylinder so when I start pushing what part of the air gets compressed near the very top so you might expect that they might be a compression near the top but not really near the bottom because it'll take a while for that information to travel down so you'll have a deviation from equilibrium there'll be a high maybe a higher density a higher pressure near the top maybe that's gonna drive some of the gas even down because as we said if there is a pressure difference the gas might move so we'll be away from equilibrium so but I don't want that I want this to happen in quasi equilibrium so one way I could do it would be for example by adding infinitesimal weights rather than try to push the piston down with a finite force so I think about it you know instead of putting a large weight on top of the piston to push it down you're just gonna add infinitesimal amounts so you put a little piece of weight the piston goes down and if any decimal amount and then you keep doing that you keep adding eventually you accomplish the same thing the volume will go down pressure will go up perhaps but it will happen in a very gradual manner and that's what we mean when we talk about a quasi equilibrium process any questions all right now we talked about properties let me flash this back again of the very top thermodynamic properties I remember we agreed that it was a properties a characteristic that helps me describe the state of a system so we talked yes we'll do it for calculations actually yeah when we do our car when we do our calculations in introduction to thermodynamics will most of the time if not all of the time assume that processes are taking place in quasi equilibrium we will learn a little bit about the departure from that approach near the end when we go to the second law of thermodynamics but at least for the very for the first part of the course the first few weeks we're really going to assume when we're doing our calculations that the processes are taking place in quasi equilibrium all right so let's talk a little bit more about properties and let's classify them so we'd have properties mm-hmm let's talk about types of properties one way we can classify properties is by calling some of them extensive and some of them intensive and the difference between the two is actually very simple extensive property is very directly with the mass of the system whereas intensive properties are independent of the mass another way to look at is able to look at this is an extensive property will depend on how much mass you are taking into account when you are evaluating that property whereas an intensive property you don't it doesn't matter what sample you use or the size of the sample of that system that property will be the same with the assumption that the system is in equilibrium so with that in mind can you think of a an extensive property a very simple one that depends hold on let me ask mr. other people I don't want to give you all the floor and I'm happy that you're participating a lot but yes huh and how do you find inertia well mass times something okay I want something even simpler than that it's part of what you said though yes now I want a simpler one who said that yeah mass itself okay mass itself is the most obvious extensive property because I told you the this property the value of this property will depend on the amount of mass that you're using to sample so obviously the first one is mass mass itself as a property will depend on how much mass I used to sample that property so here's here's a fear what about an intensive one give me an example of an intensive property temperature somebody said pressure back there those are intensive always think of a when you're trying to answer the question about whether something is extensive or intensive you can always go back to looking at a system like that where the process is taking place in equilibrium so if I look at these guys down here it doesn't really matter what sample I used to measure the temperature I could use some gas from near the piston some gas near the bottom as long as it is in equilibrium that temperature is the same everywhere and the temperature will be independent of how much mass or if I take a small sample or a larger sample it'll be the same temperature same for the pressure and and the opposite of course for mass or any other extensive properties another extensive one volume right okay so let's come back to this one density in extensive or intensive so what do you think huh well suppose I go back to this and I said this system is in equilibrium this gas samples the density will you get different values depending on how much gas you sample you look at the same so in that sense is really intensive and what is making it intensive is that you're dividing by the volume so it's mass but it's divided by the volume and that's gonna be if the system is in equilibrium is going to be proportional so you'll have the same density no matter how big of a sample you take because the system is in equilibrium but here's a few more so mass volume energy will depend on the amount of mass temperature and pressure you gave me those I added two others on the right inside and you can see that they are the same one on the Left I have volume and energy but here I have specific energy and specific volume anybody know what those are what is a specific volume no good good good try though it is the inverse of density which means that what am I doing with volume making it too complicated what am i doing with the volume to take to get specific volume divided by the mass right is the inverse of the density he said which is correct so density is mass over volume specific volume is volume over density I'm sorry volume over mass so by dividing it by the mass it becomes specific in what we call specific internal dynamics so specific energies then energy divided by what mass again so precisely same ideas we're doing with the density by dividing by something that is proportional to the mass in this case the mass we make it intensive so we will use a lot of specific properties as as we go along you start doing calculations you'll find out that when you're using data you will typically use specific property specific volume specific energy specific enthalpy when we talk about enthalpy and so on we are just the same extensive properties but divided by the mass you have your hand up if you take a next epic Li if you if you take an extensive property and divided by the mass you get an intensive property so you can do it with any of those will it make sense of course to divide temperature by the mass you could do it but doesn't really help us in any way so there it is specific means per unit mass how do we tell them apart how do we know if a property's extensive or intensive by the case in which we write it so that's why I say here use lowercase so if I write capital e for energy then lowercase e would be specific energy if I write capital V for volume like I was doing in this plot a little while ago so if this is the actual volume capital b sub 1 and capital V sub 2 then if I want this specific volume I will write it as a lowercase so lowercase denotes a specific property capital denotes an extensive property so for example specific volume which we're just talking about a moment ago take the volume divided by the mass the units in in SI units is of course cubic meters per kilogram or as I said energy specific energy lowercase e would be capital e or total energy divided by mass joules per kilogram if I'm using SI units alright okay let's see so we talked about processes so I for example I put an arbitrary process in this plot but I could have for example thought of another process so let's let's leave that one there but put another one somewhere here doesn't matter that this lines will cross where I maybe start here and I go straight up to there what is particular about this process with a black dashed line it occurs at constant volume so this process is like that are important to us I could also do another one where I just do it like this so I go from 1 to 2 along a horizontal line and now this process is taking place at constant pressure so we will often encounter processes like that so we give them names so there's three of them right there some types of processes an isothermal process takes place at constant temperature an isobaric process takes place takes place at constant pressure and an isochoric or isometric process takes place at constant volume mmm so I used in my graph here I gave you examples of a isobaric the blue one and isometric the black one so like unless I give you a little bit of more information I could not put a an isothermal process here because this is pressure versus volume so it's not clear where the temperature is but it will be clear later so there is another type of process that would be very important for us and I already told you a little bit about them about this process is in the first lecture when we look for example at the power plant or the internal combustion engine so everybody remember what type of processes were occurring there there was something particular about those processes he's got it a cycle all right so that's not important well so how do i define a cycle or a cyclic process with your own words comes back to the beginning so in a cycle the system returns to the initial state so if the red dot there denotes the initial state then of course I go around in one or more processes I can divide a process into sub processes so I can do that and but as long as I come back to where I started from then that's a cycle it's a cyclic process we saw the a very complicated one when we looked at at this write the indicator diagram for an internal combustion engine I said well if we start at our you know we go on a series of processes from R to a C prime C Z B back to R so going from R to R defines the cycle okay let's see what else I'm sure you all know these things but I'll flash it here just to make sure I will only give you problems in SI units so most of it maybe once in a while I might give you a problem where you have to use English units so most of the problems you're gonna have to deal with SI units it's a lot easier to convert back and forth because it's all decimal so make sure you remember all those things all the units for the important quantities and all the conversions and so on little review about units we already talked about density but let's flash it here again density mass over volume or the inverse of specific volume so you have it right there one over lowercase V remember lowercase V was volume over mass so the units of density in Si kilograms over cubic meter what about pressure this is a more or less formal definition of pressure all right what am I doing there when I say the limit when da goes to 0 of D F and over da that's how you define pressure really so it's a force normal to a surface take a force normal to the surface divide the force by the area but take it to the limit as the area gets smaller that defines pressure at a point units of pressure Newton's over meter square right and what is that what is the Newton over meter square it's a Pascal all right so a Pascal Newton over meter square what about one atmosphere how many Pascal's yeah 101 kiloPascals or 0.1 zero 1 mega Pascal's or 14.7 pounds per square inch and the only other one that you'll see a lot is the bar 1 bar 10 to the 5 Pascal's or 100 kilo Pascal's just you're going to be doing a lot of calculations with pressure and so on so it's to make sure that that you have that okay now let's talk a little bit about the difference between absolute pressure and gauge pressure what is the difference what is gauge pressure right it's usually the the pressure referred to the atmosphere so when you take the tire pressure in your car what is that absolute the number that you get 32 psi or so is that absolute or gauge that's gauge because it's measuring against the atmosphere so this diagram is useful to see the difference is not that complicated so this is just pressure the horizontal is nothing we just care about pressure measurements so we're going from 0 to some value this is absolute zero at the bottom so that would be of course vacuum absolute vacuum nothing zero pressure and then the other important entries here at atmospheric pressure is right there P atm so that's whatever units you're using to the node atmospheric pressure you'll be there and so here is a system for example that is at this absolute pressure one and here's another system that is at absolute pressure too so those would be the absolute values read from zero the gauge pressure of course would just be the difference between the absolute value of the pressure and the atmospheric value so this is ordinary pressure ordinary great pressure this Delta P from atmosphere to the absolute one and this one because it's below I'm a spheric pressure we call it a vacuum pressure so vacuum pressure would be a pressure that is under atmospheric value but real real vacuum would only be if you have zero pressure all right any questions okay couple of things a couple of other things that I want to review with you and this is all review as you can probably tell whoops let's make that a little smaller so this is a simple calculation of course of the pressure at the bottom of this tank so I have a tank that has a certain area cross sectional area I have for example a liquid to a certain depth capital H the volume in the tank is of course area times the depth how much does that water way is of course density times gravity times volume so if I want to come up with the pressure at the bottom of course is the weight of the water the way of the water divided by the area so Rho gh it's a handy expression to determine the pressure at a certain depth and this is really fluid statics which you have probably seen before and that you will see more of in fluids but this is a handy expression that everybody should know right the pressure a certain depth is just Rho G times in depth and you can use that principle in a simple manometer if you're using a very simple manometer to find the pressure for example in this tank so here you have a tank that has a gas and this gas is at some pressure PT and I want to determine what that pressure is by using this very simple manometer so I used that principle that I described a bob that the pressure are certain that this just Rho gh I can use that here to arrive at this expression and this is fairly simple let me go through it very quickly first of all we agree that the pressure at a is equal to the pressure at B so that statement that's ten minutes right there these two pressures are the same because they are the same depth these two points a and B now I also say that the pressure in the tank is equal to the pressure at a how accurate is that how good or how bad is that what is the error that I am making if I say that that the pressure in the tank is the same as the pressure at a which is the interface between the gas and the liquid how good or how bad is that nobody that's a very good point that's a very good point if it's if this is an equilibrium it should be equal right now to think about the following is this is in mechanical equilibrium but there is something external that is affecting this system which is gravity right so what what gravity is doing for us is of course this this is not moving because if I just said that there and I don't disturb that it will not move so it is in equilibrium is mechanical equilibrium but gravity which is an external agent is making some other things change right so if I think of the pressure right if I think of the pressure in fact if I go back to the first diagram if I think about the pressure here we're actually saying that the pressure is not the same everywhere but that's all because of gravity that's what it's throwing off the equilibrium because we have a pressure difference between the top and the bottom say that here at the top this is open to the atmosphere so I have atmospheric pressure above but we just said that the pressure at the bottom is is this value this is this is a gauge value Rho gh so there is a pressure difference but it's due to the gravity so you gotta keep that in mind when you're looking at this that there is gravity that is disturbing the pressure so so it's not in equilibrium because it is in mechanical equilibrium but the pressure is not the same but the error that I am making here if I take gravity into account is what what will be the difference in pressure between here and there it would only be whatever weight this column has on top of a but that will be negligible because this is a gas and the density of the gas will be a lot smaller than the density of the liquid that I drew in red so that's the error that you would be making the error of the weight of a very small column of gas that error I mean that pressure is not always negligible give me a simple exam where the pressure at the bottom of a certain column of gas is not negligible atmosphere pressure here is due to the weight of the atmosphere above us that's a of course a very large depth in that case is not negligible but in a simple experiment in a lab for example that's irrelevant that's why I'm saying that pressure at a is the same as pressure in the tank that's the statement right here and of course the the pressure at B I can determine from the column of the red liquid that is sitting above B so that's this depth H capital H from the interface here with the atmosphere and B so the pressure at B is atmospheric pressure plus Rho G H and I put the row in red because it's the density of the liquid of the red liquid so in the end I come up with an expression that tells me the pressure in the tank is atmospheric pressure plus this the weight of this column that is denoted by H that's a simple very simple manometer okay so with this in mind we're doing here we can look at an example so let's look at this one which actually is one of your this is one of your homework problems this problem has two parts I'm just gonna tell you a little bit about the first part and then the TA probably we'll go over some of the second part so this is chapter one purl and a tea it has this arrangement there are two tanks they're both open to the atmosphere but they're connected by a line it's a pipe connecting the tanks and there is a valve that is in that line but that valve is closed so with this valve closed the first part of the problem is simply asking you to determine the pressure on on both sides of the valve what is the pressure on the left side of the valve what is the pressure on the right side of the valve that is easy because it's a straight application of what we were just doing so what is the pressure so this one I'm calling a the one on the right and B the one on the left you can see that I have the note that this height of the liquid in the right tank in the a tank as H sub a and here on the left side I actually divided it up into a lowercase H which is from the valve to the bottom of the tank labeled B and then there is an H sub B which is the actual depth of the liquid in the in the tank label B so finding the pressure at the bottom is the core very easy this is what we know so we know how much mass there is in each tank we know M sub a M sub B we know the area of each tank a sub capital a sub a capital a sub B we know the heights and we know the density so that without that the problem is very simple so to find the pressure on either side of the valve you can of course express this H is H sub a and H sub B as the ratio of volume over area and if you bring in the mass for the volume then you can find an expression for a sub a and H sub B that's very straightforward and then on the a side then of course the pressure at the bottom which is the pressure that we're looking at that would be the pressure on the right side of the valve P sub a is atmospheric pressure plus this column which is Rho G H sub a that's that's easy and then the pressure on the left side of the valve is of course atmospheric pressure plus the total height which is now H sub B plus h times Rho G so that's easy that part of the problem is easy what you have to think about now let the TA talk a little bit about it on Friday tomorrow is what happens if I now open the bulb so if I open the valve what now of course if I opened about the system will be away from equilibrium so because the fluid will try to flow to balance the pressures again and in the end I have to have the same pressure across the valve because I will reach a new condition of equilibrium so once I reach that new condition of a pelear and the question is what is going to be that pressure and of course the problem has to do with determining what the heights will be in the tanks when everything is done but I'll let you think about that and if you go to discussion you can see a little bit more any questions about this okay let's talk about something else actually let me do this first actually let me do this right now here is a problem that you will see once in a while the same cylinder that we have been looking at so I have a cylinder there is a piston on top but to make the problem more complicated we add a spring so there is a spring there at the top of the piston that can be compressed if the piston moves up or stretch if the piston moves down now in this particular case you can see that I have chosen and this was my choice to set the equilibrium position for the piston I'm sorry for the spring to be when the piston is at the very bottom I allowed therefore the thickness of the piston so when the piston is sitting at the bottom that spring is in equilibrium so it's neither stretch or compress now as the piston moves up because there is a presumably fluid in here or a gas or something if the volume inside increases then the spring gets compressed but I make it a linear spring so I say this spring has a constant K which is a linear constant meaning that the force is going to be proportional to the the amount of compression or extension of that spring so that's simple so how do I determine for example what I really want to get in an in a problem like this I want to get a relationship between pressure and volume let me go back to that to this plot precisely in this example I use pressure and volume to describe certain processes so it is very important for us to be able in many problems to obtain a relationship between the pressure and the volume in a system and we can do that in this problem how do we do this by simply doing a force balance on that piston and assume that it is in equilibrium so if this piston which by the way has a certain mass M if this piston is in equilibrium what should happen some of the forces is zero so that's all you need to do so if I do the forces which forces do I have act in there okay so pretty much weight due to gravity the spring you said and the gas or I should say perhaps the gases right because there you guys on both sides this is open here presumably to the atmosphere so that is also a pressure there so you have four things to worry about so all you have to do is you do that force balance and that's a very simple force balance PA is the force due to the gas inside the cylinder and I made that positive so I'm making forces pointing out positive so PA is positive it's in the upward direction but then I have minus P naught a which is due to the pressure outside that's negative is pointing down the way this negative is pointing down minus mg and the force that the spring is producing on the piston which is as we said linear and it's minus KX so those have to be zero the piston is in equilibrium does that mean is not moving it could be moving how a constant velocity so the piston could be moving at constant velocity so that's important for us because if there is a process taking place you know we want the piston to move but it will still be in equilibrium if we make the assumption that is in equilibrium and it's moving at some constant velocity and it doesn't matter how fast or how slow we want to make it very slow we want to make it in quasi equilibrium so we say it's moving very slowly with some constant velocity so you got all of that in there the volume of course inside the cylinder is the area times the displacement I'm the only reason I'm putting that down there is because I want to get rid of that X because I'm typically not measuring X I'm gonna be measuring volume but I can make that substitution and I end up with this if I solve for the pressure inside the cylinder I find that the pressure inside the cylinder is P naught plus mg over a plus kV over a squared and now I have obtained a relationship between the pressure and the volume in the cylinder what type of our relationship is that in this problem what type of our relationship is here between pressure and volume inverse or inverse linear right it's a linear between pressure and volume right it's linear would you agree with me that I can write that whole expression like this right P naught is a constant atmospheric pressure the mass of the piston is constant gravity is constant the area is constant so the first two terms of that equation are constantly I'm just calling them C 1 and of course K over a square is another constant calling it C 2 so that's just to show that in this problem in this problem as represented by that drawing there is a linear relationship so if I now go back to my plot here and I want to draw that process in this plot what do I draw hmm a straight line okay I would need to draw a straight line this is getting a little cluttered but let's say let's pick for example the first the same two points so I'm just gonna go and put a straight line right there that would be the process that takes place in this cylinder it would look like this in a PV diagram because it's a straight line all right you will see problems involving this geometry once in a while and he does anybody have any questions okay so what if I don't have the spring what changes take the spring away what is the relationship between pressure and volume same I think I'm taking the spring away take the spring away and get a new equation and put it on this diagram which one it would be isobaric if I take the spring away I take the spring away I'm taking the c2 away so pressure is constant right c2 becomes zero pressure is constant so without the spring the process the process would be the one denoted by the horizontal blue line right without the spring okay took a little bit about temperature so enough about pressure for now let's talk about temperature how many temperature scales are you familiar with one how many yeah that's that's fair enough four centigrade Fahrenheit Kelvin and Rankine again because we're going to be working mostly on s with SI units really centigrade some Kelvin will be important there are some problems in which you must work with absolute temperatures and we'll see those later there are some other problems in which it doesn't matter typically if all you need is a temperature difference then it doesn't matter well if you need an absolute temperature then you have to work with with Kelvin so of course Kelvin and Rankine are absolute scales they start from absolute zero you already know that and then you have your conversions from Kelvin for example to centigrade to Kelvin Fahrenheit to ranking those you have somewhere in your database and of course centigrade to Fahrenheit and Kelvin to ranking in case you need to do that conversion so I'm sure you're familiar with those so on Tuesday I told you that this course essentially deals with two laws which were first law of thermodynamics and second law of thermodynamics however there is something that is called the zeroth law of thermodynamics so let's quickly talk about it so anybody know what the zeroth law is you do yeah it's very it's a very it's a very trivial low it has to do your AUB and your see our temperatures that's all but but that's exactly what you said that if I have three systems three systems a B and C and I know that the temperature of system a is equal to the temperature of system C and the temperature of system B is equal to the temperature of system C then the conclusion that I reach right away is that even though I didn't make a direct measurement of or direct comparison between a and B that the temperatures of a and B must be the same so if a is the temperature of a is equal to the temperature of C and the temperature B is equal to the temperature of C then ta equals T be that simple statement the that is obvious to us is called the zeroth law okay we talked about energy on Tuesday and in particular I talked about internal energy remember I told you when we talk about energy there are many forms of energy you know about kinetic energy you know about potential energy chemical energy in thermodynamics we try to make our life simple by defining something that we call internal energy and I mention it to you on Tuesday what is internal energy what is internal energy associated with molecules so they mark the microscopic nature of our system the microscopic natural system says that there are molecules in there those molecules have energy and usually you can talk about those energies there is potential energy associated with the distance si between molecules there is kinetic and kinetic energy associated with velocities of those molecules or atoms in those molecules and of course there are vibrational energies associated with molecular structure remember we're looking at thermodynamics from what we call a macroscopic approach so we don't deal with the molecules but we have the information about what that energy is because people make measurements determinations about difference in energy systems in different states and all of that energy that is associated with all that molecular activity we call internal energy that would be by far the most important form of energy that we will have in our systems I told you enthused a that on occasion we will add kinetic energy which is macroscopic kinetic energy because of macroscopic motion or that we could have potential energy with respect to a gravitational system but for the most part it is internal energy that we're going to be dealing with so we use remember we use capital e for total energy all of the energy modes together make up capital e the internal energy we call capital u so just internal energy is capital u that is of course an extensive property because the amount of energy contained in a system will depend on the size of that system and then of course what we do is we usually work in terms of specific internal energy which is now lowercase U and that is as we have seen earlier today the extensive internal energy divided by the mass units of course for energy our jewels for master kilogram jewel turns out to be a little bit of too small of a unit for most problems so we typically Express internal energies in kilojoules per kilogram and you will work with with those units okay let me let me see if there are any questions I'm going to switch gears a little bit this is more or less the introductory at the end of the introductory review and what we're going to do next is the following and see how much time I got here I don't have time we're going to do an experiment and not surprisingly we're going to be looking at a system like the ones we have been looking at the typical thermodynamic system cylinder piston and a substance in here in this case as you can see that substance is liquid water so I'm going to have liquid water in a cylinder filled with the piston exposed to some pressure outside let's say that I can control this pressure out here to be whatever I want it to be and for the for simplicity let's ignore the weight of the piston so let's say that the weight of the piston is insignificant compared to that pressure that is outside if I say those things then what is the pressure in the liquid water huh what is it what is the pressure in the liquid water well I'm using mice notation peanut alright so the pressure is peanut remember I think I'm neglecting the pressure I mean the weight of the piston you can just go back to the previous derivation and see what happens nope no spring no mass for the piston is just peanut and the experiment that we're going to conduct is very simple I am going to add heat to this liquid and I want to do it very slowly so this process is going to be a quasi equilibrium process so I have the liquid in there I'm gonna start adding heat to it and I'm going to make a plot and the plot that I want to make as I do the experiment is a plot of two properties so I'll do we were doing pressure a while ago but now let's do let's do temperature so I'll put temperature here on the vertical axis and I'll put volume here extensive volume and I'll start somewhere so let's say that that liquid water if I go back to my you know I could measure the temperature measure the volume and then put it on this diagram so let's say that that's there this called that v1 t1 all right and I'm going to start adding heat so add he'd slowly what happens a process takes place with direction with that process go on this plot you can see how easy would have been if I have put pressure versus volume because if I have put pressure versus volume what direction do we go pressure versus volume what direction would we go well not in this plot but in the pressure versus volume now we were looking at a while ago on this plot where would I go huh I'm sorry the volume will expand if I start hitting this thing up that pace then didn't tell you but is unrestrained so I like that piston is not stuck in a position but piston can move up and down so I'm adding heat if I plot it on this diagram where do I go down the correct answer is horizontal right the correct answer is horizontal because we just concluded a moment ago that that would be a constant pressure process alright so but but not in this plot because I put temperature so maybe now whoever was talking about temperature where do we go now that's the best answer right we could get a little picky it's your same diagonally up right because you're saying temperature will go up I'm adding heat right you can think about doing this in the kitchen for the water in the pan in the kitchen turn on the stove right put it on simmer so it's very slow right there's a difference well and there has to be covered but with a lid that can move so you be so ash a little harder to do at home but so but you get the idea it has to heat up the volume will increase so it's diagonal but do you think it'll be steep or shallow steep or shallow see this is when the iclicker would be good right so it's gonna be steep right because that's liquid right how much will the liquid volume change if I heat it up not a lot so it should be steep so I'm going to presumably be going something like that the temperature will increase the volume will increase but probably very little it will be probably going to be very hard to measure that volume change piston will move up a little bit okay but that's not going to be happening forever something will happen at some point what will happen okay but that's that because the process is in quasi-equilibrium it's gonna be very slowly so if I am paying attention and looking at my cylinder at some point I might see that some gas begins to appear hmm so maybe I see a first a small spot somewhere turns into vapor now this could get complicated if you're doing it say in in the kitchen and you're putting it on the stove where will the first bubbles appear at the bottom right you cannot see them you put this stuff you put the water in the pan put it on the stove you see the little bubbles appearing at the bottom because that's where the heat is coming from so gravity is playing a role the location of the heat source is playing a role those are realistic conditions that we're trying to avoid here but we know that there's gonna be a bubble somewhere and then more bubbles and more bubbles and more bubbles right so what's going to happen to the volume now can I increase a lot more so this will be a steep anymore does anybody know how it will be it'll actually be the most shallow you can think of it's gonna be horizontal because what's happening to the heat so let's put a mark here that the notes when I first saw gas right I first saw gas there and now we're gonna be going this way the volume will increase why is the temperature not increasing if I'm still adding Heat where is the energy going from the heat to break the bonds of the liquid and turned into vapor so that happens at constant temperature right so as I go as I keep going here from the first appearance of gas and more and more and more and more gas the volume will change considerably in fact now we will be very noticeable that the volume is changing and I in fact we wouldn't be able to put it on the scale if I make this plot the scale I you know this is gonna go way to the right but I'm not gonna do that of course I'm gonna pretend that at some point I see what situation no more liquid I saw at some point here I'm gonna put in another another open circle no more liquid all the way all the way all the liquid is gone in all turn into vapor now what's going on inside the system again it depends because if there's gravity what would happen if there is gravity wouldn't we see something like this right if there is gravity the liquid will behave it will sink to the bottom will we stay at the bottom the vapor will be on top but if there is no gravity it isn't clear exactly where the vapor is gonna be could be anywhere right so let's not be too worried about where the vapor is we know that as we are going from the first open circle to the second upper circle I go from a situation where everything is liquid to a situation where everything is vapor right so when I reach this open circle all I have is vapor what happens if I keep adding Heat so now I have something like that what I have is very poor and I keep adding heat what happens volume will increase a temperature will increase is it gonna be steep like before yeah it won't be as steep as this one it will be a lot less because the vapor can expand right a lot more than the liquid so it'll be something like that and that'll be my experiment and whenever I want to end things are getting pretty hot so at some point we ended so that we don't burn the place down and that's our experiment so now I say all right very good let's repeat the experiment let's repeat the experiment but change the pressure remember I told you that we could control this pressure so let's repeat this experiment two more times there's two more experiments one at a higher pressure than we did the original experiment and another time at a lower pressure we're always gonna start with water let's say that we start at the same temperature start the same temperature but one time we're gonna crank up the pressure second time we're going to drop the pressure so let's do for example the one where we crank up the pressure same temperature but now I crank up the pressure what happens to the volume at the initial state it's gonna be smaller because I'm compressing that liquid as hard as it is I'm compressing it a little bit so if I repeat if I start with the same temperature but at a higher pressure you all agree with me that we're gonna start perhaps somewhere over here again it's gonna be a very insignificant or very hard to the tag variation in volume because it's liquid I'm cranking of the property will compress a little bit so I'll probably start somewhere here now qualitatively speaking is the experiment going to be different in a qualitative sense the same thing will happen so I'm gonna still be going like that right when will I see the vapor for the first time at a higher temperature and so I'm going to see the vapor perhaps there it will be at a higher temperature because if you boil a liquid at a higher pressure it will take a higher temp that's why you have this pressure cookers yes it won't be the same but it doesn't really matter whether it's deeper or less tape it doesn't matter is this there will be a little difference there but it's not important to us right now it'll be steep alright in fact you can see how I made it a little less steep here because I have to get to a place that I wanted to get to so so that's what will happen and if I do the experiment at the lower pressure where do I start well now it'll be a little bit to the right right because I have less pressure qualitatively it will be the same so I'll be going up all right but now when will I see vapor at a lower temperature right you all have gone camping right in the mountains or some of you have right you boil water say in Big Bear it will start boiling at a lower temperature if you're high enough you can actually stick your finger in there won't be a hundred degrees Celsius will be a lot less so hmm so these are the three scenarios the original experiment the experiment conducted at a much higher pressure and now the experiment at a lower pressure and again my open circles here denote when I first see vapor so of course what happens after that is the same as before liquid turning into vapor and then I'll find out that at some point all the liquid is gone look like that and at the low pressure I'll be going like that and then at some point all the liquid will be gone it'll look something like that and the continuation after everything is vapor will be qualitatively similar so when everything is vapor then it'll go that way and that's the end over there and then here everything has turned into vapor I keep going and I stop somewhere so they're qualitatively speak in the three experiments look the same there are some quantitative differences due to the fact that we're doing the experiments at three different pressures so I do all of that and suppose now that I asked you well now do the experiment many more times right do the experiment so that you fill in the entire plot what would happen if we do that so clearly if I you know do more and more lines I'm going to just fill in the gaps in between and suppose I tell you well let's join with a line all the points that the note when vapor first appeared all right so I'm gonna do that in red I'm going to join these points with a red line those are all the points where I first saw vapor and of course if I do it down here I'll see even more that's what that line is and then I say well do the same thing at the other side when you see leak the last drop of liquid disappear which is the open circles here on the right hand side join all those with a line and this is right again so say well I'm gonna join that and dad and some more over here and what question is what's going on up there right so it look like that I'm just joining the dots of the first vapor and the last liquid if I keep doing this at a higher and higher pressure what will happen with those two red lines they will eventually meet each other as is obvious from the way I'm drawing this so if I keep doing this I might find that this looks like that I will find that it looks like that so the line that denotes the first appearance of vapor merges with the line that denotes the last particle of liquid right and they meet at a higher point here and we give this point a name what do you want to call it hmm what should we call this point how about laid it right there why should we call that point at the very top I'm sorry okay hat nobody knows does anybody know the name of this point nope not that one we call this point the critical point the critical point and then we also give these lines names right we call this line here on the left hand side remember that's when the liquid the vapor first appeared we call this line saturated liquid line saturated liquid line and obviously what do we call this one on this other side saturated vapor line so we have a saturated liquid line saturated vapor line they meet at the top of the critical point think about what happens if I do the experiment at a pressure that is sufficiently high that the blue dashed line goes above the critical point think about what happens in that scenario I do the experiment at a sufficiently high pressure right so that you are above the critical point you start with liquid you end up with vapor but what happens in the middle all right think about that and then we'll talk some more next week

Channel: UCI Open

Views: 72,252

Rating: 4.9313726 out of 5

Keywords: UCI, UC Irvine, OCW, OpenCourseWare, Engineering, Thermodynamics, Mechanical and Aerospace Engineering, Thermodynamic Properties, driving potentials, equilibrium, Quasi equilibrium process, specific energy and volume, Isothermal process, Isobaric Process, Isochoric Process, Isometric, absolute pressure, Gage pressure, Zeroth Law of Thermodynamics, Internal Energy

Id: ws5nd-9EE8w

Length: 78min 46sec (4726 seconds)

Published: Fri Apr 05 2013