Forms of Energy in Thermodynamics: Potential, Kinetic & Internal Energy

okay so in this lecture i want to go through the different forms of energy and i know you've seen all of

these before but i want to go through them so that we all think about them in the same way

and i'm thinking about them in a very deliberate context in relation to thermodynamics and

eventually for us to form the laws of thermodynamics so the first thing we have to do

no matter what is define the extent of the system uh and then think about the energy

changes within the system so what we're doing is we're going to start with

potential energy this is going to be our first form of energy so we're going to take a system that's

comprised of a mass m sitting on the ground at datum 0. we're going to define the

coordinate system as z points up we're going to define the system with this dashed line

and within the system you can think about it as a vacuum or as you know it could be air but we're not

going to worry too much about the air relative to what else is going on in it so we're going to assume a system that

is effectively isolated except for this very thin string that's attached to the mass and it

crosses the boundary now we're saying massless because we're going to do we're going to lift

the mass so in essence we're doing some work on the system and so part of the string is leaving so

if we were considering this you know in its most exact sense we would have to consider the amount of

mass that the string is taking out so we're going to consider it a massless string so that we're only

concerned about the mass and the masses relative position with respect to the ground

okay so what we're going to do in this in this experiment is we're going to raise the mass

slowly now we're saying raise the mass slowly because that way if we're thinking about it as a

vacuum it doesn't really matter because it's not disturbing but if you just want to think about

a large mass in a gas or something like that we're raising the mass very slowly so

not to disturb anything around it and we're raising it to a new position some position said

so if we write down the amount of work that we're doing on the system so the small amount of work is equal to the

force that we have to apply so the force of lifting multiplied by the the distance that we lift at dz

so the force in this case is going to be replaced by the mass times gravity okay that's the

force of lifting something up that's multiplied by dz if we integrate that to find out how much

work is actually invested to move the mass from a position at the datum 0 to some position z

we carry out the integration mg times dz and we get mgz so you'll all recognize this as

the potential energy the potential energy is in joules so newton meters is joules

and if we look at this definition so because of the new position of the mass relative to the ground

there is a potential for doing work okay so now that we've introduced work into the system

there's a potential for us to have the system do work for us so we're calling this the potential for

doing work and we're going to call this the potential energy okay so the second form of energy we're

going to look at is the kinetic energy and this is another one that you're certainly familiar with

um so what we're going to do is we're going to start where we left off with potential energy

so what we did with the potential energy is we actually had a closed system because we had a string crossing

the boundary and we were lifting the mass so we were actually doing some work on the system and the work that we did

resulted in a change in the elevation of the mass so now we're going to start with the

mass at the position where the potential where the work was done to increase the potential energy we're

going to start at that elevation we're going to cut the string and then we're going to isolate the system

so now we've got a different type of system one where we we don't allow work uh well energy or mass to cross the

boundary not in the form of work or heat or anything so we're isolating the system and now

because we've isolated the system we have to think of e as the total amount of energy inside of

the system now one of the things that we know is that e has to be conserved

energy can't be created or destroyed it can only change forms particularly when we isolate a system we

know that e must be conserved because we're not allowing any of it to escape

or be added but we also note that as the mass drops because of the definition of

potential energy pe actually drops okay pe goes down so we have to think about the energy of

the system so we can say e is equal to a constant because it's got to be conserved

and at any given instant it's comprised of potential energy and some other form of energy which

we're just going to call x for now okay so at any instant the total energy is the amount of potential

plus this other form and that sums to a constant now if we take this expression and we

differentiate it with respect to time the first thing we notice is that the constant disappears so that side is zero

we're going to replace pe by its definition mg z so we've got d of mg z dt

plus dx dt and this is the one we're looking for so we're going to solve that that expression for dx dt

so we've got negative mg dz dt now we have to think a little bit so the m is fixed in this case

g is the acceleration due to gravity it can be any kind of acceleration field you want to think about

but it's the rate of change of velocity with time that's the definition of acceleration so in this term in this

scenario it's gravity it doesn't make any difference and then dz dz dt is the rate of change of position

with respect to time which is velocity by the basic definition and in this case um

uh z is going down with respect to time so we have to write negative v and then so this part can be written as

mv dv dt and through some mathematical manipulation that i can describe in a

tutorial we can replace this by you know move this mv inside and then subtract it

away and we end up with d by dt of a half mp squared

okay so dx dt is equal to d by dt of a half mv squared which means that

this is what x is right so therefore x is equal to a half mv squared and this is called the

kinetic energy okay so this is the form that you're used to seeing

uh from your high school physics courses and from your first year university physics but the way we've

developed this is probably slightly different let's talk about our third form of

energy so in this case we're going to call it internal energy

and the rationale would come clear as we go so we're going to take where we left off

with a system so if you recall we started with potential energy so we we did some work on a system that

had a mass sitting on the ground we lifted it then we isolated the system and we let

the mass drop and we found that there was another form of energy that had to be considered and

that was the kinetic energy so then we had the total energy is kinetic and potential energy

um now interestingly if we we keep the system isolated so we're not doing anything more to the system but we're

going to do a really kind of close analysis of what happens before and after the crash

so if we consider that the total energy is simply the potential energy plus the kinetic energy

then we know that you know because of what we what we see happening just before and just after the

crash meaning that just before the crash the mass is actually traveling at the

highest velocity it reaches because it's kind of reached the end of the line and then just after the crash

the mass isn't moving anymore so the mass isn't moving and it's sitting at its original datum

so it's not moving so kinetic energy is zero and it's sitting at its original datum

so potential energy is also zero so that means that just an instant ago we had

all of this energy in the system because it's isolated um at you know through that process

the the total energy of the system had to be constant it had to be comprised of potential and kinetic energy

but we note that as soon as the mass stops moving pe and ke are both zero so this means

that the energy in the system if we relied on this

is not a constant before and after the crash well this is kind of strange and this can't happen obviously the energy

still has to be contained in the system so it means that we have to add yet another term

so what we're going to do is we're going to say now e is actually potential energy plus kinetic energy

plus this other form of energy called internal energy now what happens is that all of the

energy that is kinetic energy just before the crash so just before it crashes there's no

more potential left the kinetic's at its highest point highest velocity

and then in an instant it stops moving and all of that kinetic energy is converted into internal energy

and internal energy is kind of this it's a new form of energy for most i guess and uh

it's related to changes in the temperature so i've written down a couple of points here so

internal energy is a measure of the potential and kinetic energy of the molecular level

now if you've delved into what what temperature actually means it's kind of a measure of

kind of the subvisible molecular activity and in this process of transfer

all of that kind of macroscopic kinetic energy is converted to molecular level kinetic energy and the

molecular level kinetic and potential energies are now this new form of energy called the

internal energy so the kinetic energy is transferred to you through work

and we'll get to how this happens in later lectures the key is that at the macroscopic level

so the energy hasn't disappeared so there must be some way of us characterizing the fact that it's still

there and even if we note that you was a measure of the of the molecular level

potential in kinetic energies knowing that the molecular level kind of mechanical energies are manifest

as changes in temperature is important for us so basically we notice that a change

in the internal energy up or down in this case it would be up is manifest in a small change in

temperature or in other words delta u some small change in internal energy

is going to be characterized by some small change in the temperature and how much this

change is depends on other properties of material we'll get to that

as we start characterizing uh specific thermodynamic properties of materials