Thermodynamics: Pure Substance Properties and T-V Diagram Explained

so far what we've been looking at is different types of systems we've developed

forms of the first law by looking at all of the different types of energy and the different ways of kind of characterizing

the energies and then we've taken a good look at some some different thermodynamic principles

in arriving at what was called the state postulate which is going to become very useful

for defining properties of a substance so the first thing we have to do is we have to look at how do we define a

substance if you recall the state postulate said that the state

of a simple compressible substance is completely defined by two independent intensive properties

and we've defined what all of those terms mean now what we're going to do is we're going to look at what is the

definition of a pure substance so a pure substance as i've noted here

is a substance that is homogeneous and invariable in chemical composition in any phase or combination of phases

and a really good example of a pure substance is water now i'm not advocating that you buy bottled water in

fact i would advocate against buying disposable water bottles

and using your own water bottles anyway water is a great example and we're actually going to spend a lot of time

thinking about it in this thermodynamics course because it's one of the most useful substances but in order to really

take advantage of water we have to understand the properties and then we can exploit these properties

so for instance if i just think about water as a pure substance and what this statement means

if we look at two simple examples one where we have ice in a glass so we have a glass of ice

water and what i'm saying is that the liquid water and the solid water in the form of

ice cubes they're all h2o there's no molecule inside the system that's not h2o

in another form of this if we look at a pot of water say boiling on a stove so there's water

vapor coming off of this pot the liquid water and the water vapor are all still h2o again there's no

molecules of water in the system that aren't h2o and that's what this system what the

state means so what we're going to do now is we're going to take a really good look at

water and we're going to look at water under different pressures and then we're going

to see what happens to water when we add heat at a constant pressure and we'll just make observations for now

and then we're going to get quite a bit more detailed into how we understand what the specific properties of water

are in these different places that it goes through there's also going to be a lab

experiment in this course where you actually study the properties of water

so we're going to do a series of four experiments looking at water at different pressures to understand what

the properties look like so the first experiment we're going to do is on water

enclosed in a piston cylinder device so that it's not mixed with any other substance not air or anything it's just

pure water and we're going to start every experiment with pure water in its solid form so it's as ice and

it's at a very low temperature let's just say for argument's sake it's minus 100 degrees c

and what we're going to do is we're going to translate what we see through this experiment by adding heat

onto this diagram called a t v diagram so this axis is specific volume in

meters cube per kilogram and the vertical axis is temperature in degrees c

and i've drawn kind of a very faint sketch of this dome looking region and we're

actually through the experiments we're going to really define what the edges of this dome mean of the

different parts of the diagram so let's just start warming water that is at

negative 100 degrees c and by having the piston on top of it we're going to ensure that the pressure

inside of the cylinder is always 101.325 kpa or atmospheric pressure so we're starting somewhere down here

it's ice very low specific volume and i just want to tell you that this this part of the picture is actually way

out of scale we've actually tipped that scale in order for us to be able to see what's actually happening

the differences are subtle we're starting here and we're adding heat

and when you add heat to ice the first thing that happens is the ice warms up it doesn't change

phase it just goes from being minus 100 to a different temperature so it's warming and the temperature where it's

going to start to do something different is actually at 0 degrees c so

under atmospheric pressure 101.325 kpa as soon as the ice becomes 0 degrees c if we continue to add heat

what we're going to notice is that the temperature is going to stop changing but the ice is going to start to become

a liquid so it's going to start to change phase and i'm just showing you know we're

moving from this diagram to this diagram when ice starts to change phase to a liquid

its density actually increases the density of the liquid is slightly higher the reason we know this is because ice

floats on water so the density of the solid phase is slightly lower than the density of

the liquid phase if the density goes up of the liquid then that means that the specific volume drops

because specific volume is the inverse of density so what's going to happen is it's going to go a little bit to the

left on this diagram in a straight line because

its temperature is not changing through that phase change okay so if we have

as point a on this diagram right there we'll call that little point a to be associated with this one point b

is somewhere in the in the region where there's a phase change occurring from solid to liquid at a constant

temperature so it's somewhere on here on this little line right there let's call that b

okay now we continue to add heat at some point all of the solid phase is going to become a liquid

so the phase change will end so that the the part that's holding the temperature constant is going to end

as we continue to add heat so we've got we're going from solid liquid to pure liquid

as you continue to add heat to the liquid the liquid is going to warm up and we know that when you heat a liquid

and it warms up its density really doesn't change at atmospheric pressure

so we're going to show this as virtually a vertical line here but like i said because this is out of scale

the line is going to tip a little bit to the right but it's going to look like this

where we're going to eat it and at some point in the eating we're going to see something else happen

it's going to stop changing temperature and then another phase change is going to start to occur

okay so we're we're heating this water and the solid phase is disappearing it's become a liquid

it's rising up this curve as a liquid at a virtual constant density or constant specific volume

and then something else starts to happen it starts to change phase again and the temperature once again stops

changing and for water at atmospheric pressure we know this to be about 100 degrees c so

we'll draw that on here and then what's happening is at a constant pressure the vapor is a much

lower density or much higher specific volume than the liquid phase so we're going to

see the specific volume of the complete mixture start to increase so we're moving along

on this curve at a constant temperature with an increasing specific volume

so it goes like that and so i'm going to show i'm going to show this one where we've

got some liquid and we've got vapor i'm going to show that in this region so it's constant

temperature specific volume is increasing because this process of boiling is occurring it's a phase change

then there's going to be another point where all of the liquid has now vaporized and it's become a pure

vapor and at that point there's nothing holding the temperature from staying at

a constant which is what's pinned down by the phase change at that pressure so at that point we're going to have all

vapor and as we continue to add heat the specific volume is going to continue to go up

but also the temperature is going to go up so we're just going to show part d on this diagram as something that

looks like this okay so part d is out here and i'm going to note on this picture

that this is um p1 which is p1 atmospheric pressure

okay so just once more to iterate we start at point a very low temperature

solid phase pressure is the same through the whole thing we warm it the ice warms it gets to a

certain threshold which at atmospheric pressure is actually zero degrees c so we can

actually mark that on here as well when it starts to change phase because the liquid is slightly more dense

than the solid the we're going to first notice that the piston drops just a tiny bit

and on this diagram it means the specific volume drops at a constant temperature

once all of the ice is gone then it's just water heating so the temperature goes up at a

virtually constant specific volume when it hits this other threshold which is 100 degrees c at atmospheric pressure

it starts to change phase into vapor that temperature stays the same all the way through the phase change to vapor

and then as soon as all the liquid is depleted then the vapor continues to warm and the specific volume

continues to go up so we see this the second experiment we're going to do is at a much lower pressure

so now we're going to look at a pressure of 0.01 kpa we're going to start

at the same temperature minus 100 so i'm going to show this point right here and we're going to

start with the same type of experiment except at a lower pressure so we're going to add heat

to the solid phase so it's ice we're adding heat and the ice is going to warm up

initially so we'll just draw that happening but at this low pressure so this is

still point a right here [Music] at this very low pressure as we continue

to add heat it's actually not going to start changing phase to liquid

it's going to hit a different phase change and it's going to start to turn into vapor immediately

and then as we continue to add heat to this solid at this very very low pressure it's just

going to continue to sublimate or to vaporize from the solid

and eventually the ice is going to deplete it's all going to become vapor and then the vapor is going to warm just

as if it were at a higher pressure so we'll show this by we don't quite make it to where where

the liquid phase starts and that we go left like we did with with atmospheric pressure

it hits a different type of phase change and then as soon as vapor starts to form the specific volume goes way up

so it follows this line still at a constant constant temperature phase change all

the way across so b and c are both going to be inside of here

along this path one with just a little bit of vapor one with a lot more vapor and then once

it all of the the solid disappears lots more vapor

so higher specific volume and elevated temperature because the the solid phase is gone there's

nothing restricting the the temperature from going up so this is again going to be

point d okay so that curve is for p2 p2 0.01 kpa so at very low pressures

we we kind of um circumvent that phase change to liquid before we get to vapor at this low pressure

it goes straight from being a solid to being a vapor right so you're asking yourself now

we've gone from a from a process at a very very low pressure

that didn't go through the liquid phase change prior to going to vapor it started it we warmed the ice and then

it started to vaporize so it went underneath this this dome through a different type of phase change

for liquid we went we warmed the ice and then it turned to liquid at constant temperature and then on through the

process so you're probably asking yourself well there must be some place

in between where it does something interesting and certainly there is in fact at a pressure of 0.6117

kpa we'll call this pressure number three something else a bit unique happens so

we're going to start again down here this time it's going to be between those two lines because it's a pressure higher

than .01 lower than 101.325 so it's in between we start warming this solid phase

okay and then at some point it starts to vaporize and change phase to liquid at the same

time so it's got a kind of a double phase change happening it actually ends up in that little

corner right there on my picture once again that's point a uh point b is going to be just inside of

this this point is actually called something special but

because liquid and vapor both form the specific volume doesn't drop at that point which is the case if it

were only liquid forming it actually starts to increase immediately so it goes in this direction

it's doing kind of a double phase change all along this line so we've got places where we've got

solid liquid and vapor solid liquid and vapor at two different points it's just moving along this line

[Music] at this pretty low pressure and eventually the solid and the liquid

are going to deplete and we're going to have just vapor and once we have just vapor the specific

volume can continue to grow and the temperature can rise okay so that is

p3 now this we're going to we're going to define this a little later but this is called the triple

point and this is called the triple line for obvious reasons because we have three

different phases all occurring simultaneously starting at that point and across this

line the last case we want to consider is that of a very high pressure

so we've considered a very very low pressure another relatively low pressure atmospheric pressure and then when we go

beyond atmospheric into much higher pressures we see some similar activity but then we

see something really interesting happening so we're going to start the experiment

in the same place okay solid ice except now we're going to run at a pressure of 22.06

megapascals so a megapascal is a thousand kilopascals so this is quite a high

pressure it's going to be just a little bit left of the

very first diagram or the first line that we drew so just a little bit left of

atmospheric pressure and once again we're going to start to add heat we're going to notice that the solid

phase warms okay so it warms then it hits this line where it starts

to uh it starts to transform into liquid okay phase change so when it starts to

become a liquid the piston drops just as it did when we were dealing with atmospheric

pressure because the solid phase is a little bit uh less dense than the liquid phase so

it drops just a little bit changes phase at a constant temperature so we've got that

that's somewhere in here this is point b and then we continue to add heat and it eventually becomes all liquid right

and it uh once it becomes all liquid the temperature continues to rise so rises

like this very little change in the specific volume as the temperature is rising

now with this very very high pressure the temperature gets quite high before anything happens

in fact it just comes to the left of this curve and then it starts to turn and suddenly

the entire liquid flashes to vapor in an instant so it goes through this transition up

here and then as soon as it flashes to vapor then

the specific volume starts to grow the temperature continues to grow so point c would be somewhere on

this line and then point d would be very close to this point where it just

flashes to vapor and then it continues to go up so this is p4 very very high pressure

so now i've taken this diagram and i've actually drawn in blue it's kind of a dark blue but um i've

drawn in blue this this kind of construction line that i had before i've darkened it in

and technically if you would have done a series of experiments what you would have done

is drawn this blue line through the locus of points that you create by studying you know warming at all

different pressures so the line starts at the bottom virtually vertical then it has this

little notch that goes to the left and this is for a substance that expands upon freezing so it goes a little bit to

the left then it goes up and it would cut through all of these points that would go across

this saturation line and then at this tip it starts to turn and go down and all of the locus of

points is going this way now this is called the dome region and this is just called a tv

diagram we can also construct a pb diagram in fact we're going to show what what

uh constant temperature looks like on a pb diagram a little bit later but this just kind of summarizes

where we're at right now so we've got a tv diagram we understand what a whole bunch of processes of constant pressure

look like on this tv diagram that's an important note i want to summarize where we've gotten

to now by taking a look at the same picture except removing all the constant

pressure lines so we still have t versus v we've drawn this dome starting from the bottom so we're going

up we're showing a little notch to the left and this is what occurs for a substance that expands on freezing

of which water is an example then virtually a vertical line turns across this critical point

and then has this tail that veers off so we call this the dome and basically when we say the dome we're

usually talking about what's above the triple line but just for argument's sake this is the

complete picture for water the different regions of the diagram so we've got

to the left and below the notch we've got pure solid then in the region where the phase

change occurs between liquid and solid which is called fusion we've got solid and liquid

then once we get past the fusion region we get to a region which is all liquid and that's to the left of this dome

then once we get past this critical point it becomes all vapor on this side but underneath the dome and above the

triple line we've got liquid and vapor and this is the vaporization or evaporation region

below the triple line we have solid and vapor and this is the sublimation region and then this is called superheated

vapor okay because the vapor actually can increase its temperature increase its specific volume

now some of the important pieces of this diagram i've already used the words fusion sublimation vaporization

superheated let's talk about the different parts of the picture so we've got the triple

point that kind of defines the the corner where that notch forms

we've got the triple line because on this line starting from the triple point we can

have all three phases okay we can have solid liquid and vapor all present at the same time um

above the law of the triple line and under the dome we can have liquid and vapor

um this line that starts from the critical point and goes down to the left side of this

notch is called the saturated liquid line and what that means

is that the it's a liquid but it's about to become it's about to start its phase change to vapor so as

soon as we warm and it strikes this line it starts to change phase when we say

something is a saturated vapor then we mean that it's about to change phase

when it's underneath the dome it becomes a mixture it's no longer saturated uh starting from the critical point

going down the other way we've got what's called the saturated vapor line and in the same way as as

on this side we're defining a situation where we're a liquid but we're about to change phase to a vapor

on this side we're a mixture and once we strike that line all of the liquid is depleted and it becomes a pure vapor

so that's another place where we've got a transition occurring we call that a saturated vapor line

these two lines are very important saturated liquid saturated vapor because they define

kind of this dome region and they define where all of the phase changes above the triple line occur

uh very quickly if we if we consider a substance that actually contracts on freezing the only difference between

this picture and that one would be how the notch looks so this notch goes to the left because

uh the ice expands when it when it changes face to solid

in this case when you warm the solid it becomes a liquid it actually contracts on on uh freezing

so we have to show the substance going in the other direction so everything about it is virtually the

same except for the position of the notch and then consequently the region where

it's solid and liquid so instead of it being here it's here everything above is virtually the same