First Law of Thermodynamics: Closed & Isolated Systems Explained with Examples

so now that we have all of the different forms of energy to characterize a system in place we can

actually write the first law of thermodynamics for a couple of different systems

so the first one i've indicated here is the first law of thermodynamics for an isolated system

and this is kind of the last form of the total energy that we wrote so basically the the the first law of thermodynamics

for it for an isolated system is just that the sum of all of the energies is a constant

so e is equal to internal energy kinetic energy potential energy and that's a constant

and these are in joules or kilojoules now the other kind of system that we've looked at so let's go even a step

further so that's the isolated system i'm going to look at kind of a closed

system it's a closed system that emits work across the boundary so we're looking at a system that admits work

across the boundary and how does that change the form of the first law of thermodynamics

well basically the amount of work that you're adding to the system or being removed from the system is a

change in the energy level because you're adding or subtracting something from the system

so in this case it's the the energy of the system in its final state minus the energy of the system in

its initial state and each of these e's is just internal kinetic potential energy so

the sum of the energies of the final state minus the sum of the energies of the initial state

and the change in the energy level in this case as a result of work being done on or by

the system now to go to the next level we also have to think about

uh when we talked about a closed system it wasn't just work that would change um the energy

level of the system we said that the passage of energy is allowed in a closed system and

there's a couple of different ways of passing energy across the system so i'm gonna

in in the next slide i'm gonna look at um two different ways of adding energy that result in the same thing and we're

gonna develop an analogy between these two forms of of the passage of energy

okay so let's build on what we said in the last discussion so we had we've written the first law of

thermodynamics for an isolated system which was just a statement that the total amount of energy

is a constant whether it's comprised of you know kinetic potential and internal energies but the sum of them is a

constant then we wrote down um the form of the first law of thermodynamics where

work is being done or by the system but that wasn't completely the statement of a closed system

so i want to consider two scenarios here the first scenario uh actually in both scenarios we have the exact same

beaker or cylinder of of water let's say or some fluid and they both contain a little paddle

wheel in the first case we're going to wrap a string around that paddle wheel

and then we're going to pull on the string so we're doing work fds um we're doing work on the system and

we're going to do a very specific amount of work that's going to add up to a certain number of joules of energy

okay and if we look at you know we're doing the work and then we're going to stop so

over a period of time we've invested an amount of work uh

once the system is settled you know the fluid is spinning around at first but then as soon as you stop the paddle

the fluid is eventually going to come to rest and we're not going to allow any of the

the energy to escape we just want to quantify what we're putting into it so if we look at kind of the transfer

of that work and how it manifests itself eventually if we let the system come to rest

the work is initially inserted as kinetic energy because this paddle is spinning around

it's churning away in the fluid and then as the fluid comes to rest because of the viscosity of the fluid

it's going to eventually come to rest and that process is actually the conversion of mechanical work

into uh internal energy so some visible work the molecular level so that kinetic energy

is damped out through viscosity becomes internal energy and we know that the internal energy has

changed because we can measure a change in the temperature and that change in the temperature is

related to other properties of the fluid itself and the fact that we've added a certain amount of energy

in joules now the second scenario that i want to consider is exactly the same

beaker of fluid the same amount of water same paddle wheel except this time instead of pulling on a massless string

and spinning the paddle we're going to add exactly the same amount of energy in joules

by heating it and i'm just indicating the heat by a little candle here so we're going to

we're going to add some heat certain amount of heat and we're going to stop when it's got exactly the same amount of

heat energy as we added kinetic energy in the first case so [Music]

the important things to know are that in both scenarios whether we're adding the work mechanically

or adding the energy mechanically or we're adding the energy by a heat we're adding exactly the same amount of

joules and we're going to notice that the systems end up in exactly the same state and we know this because we

can measure the temperature at the final state so this temperature right here is going

to be exactly the same whether we add the energy using work through this conversion process

or adding heat through this very simple process so what this means is that

the work and the heat because the the systems end up in exactly the same state when we're finished

there has to be some analogy between the mechanical work that we've done versus the heating that we've done

heating is very simple uh mechanical work to result in heating depending on what

we're talking about but it's a lot more elaborate and requires a conversion process but

any in some level w and q must be equivalent so in fact the easiest way to think about

this is in the same analogy as we looked at internal energy

being subvisible kinetic and potential energies right so as soon as we couldn't see the

mechanical motion anymore the energy had to be absorbed at the subvisible level

and it manifests itself as a small change in temperature right so so we did this we said that

internal energy is basically subvisible kinetic potential energies in this exact same way

we're going to consider that heat hue should be considered as subvisible work because it's done directly

to enhance the kinetic and potential energies of the molecules without going through this whole conversion process

okay so the key here is that um in the same way as we have an analogy between internal energy and kinetic and

potential energy so subvisible versus visible we now have an analogy between the two

different ways we can add energy either by heating or by doing work on the system

right so just to summarize where we're at right now um we've now looked at the different

forms of energy so we've got potential energy we've got kinetic energy

and internal energy we've got now a form of the first law of thermodynamics for an isolated system

meaning that the total energy can't change so the sum of all of those energies has to be a constant

and we've also now got the the tools to put together a statement of the first law of

thermodynamics for a closed system before we had just looked at work now we've actually got all of the parts for

a complete closed system so just to summarize where we're at um we've got visible and subvisible

forms of energy and of work and so i've kind of you know just put

together the simple chart where you've got work energy visible sub visible so the

visible energies are kinetic and potential energies and the way we change those is by mechanical

work so the work is is w and the subvisible form of the energy is

the internal energy so that's the molecular activity molecular kinetic and potential energies

and the subvisible form of work is heat transfer so these are the things that happen at

the boundaries okay in a system if we think about a closed or or an

open system where we're admitting energy to cross the boundaries these are the way it would happen by work and by heat

transfer and one is visible one is subvisible and then the energies

collectively are kinetic potential and internal energies okay so let's finalize the first law of

thermodynamics for a closed system as i mentioned we already have it for an isolated system it just says that e is a

constant for the closed system we have to consider all ways that

that energy can be transferred through the boundaries not mass yet but just energy so i've drawn three different

scenarios that all contain the same amount of mass and some level of energy so we can

consider a system where we're adding q and we're adding w so the first law would have to say

q plus w is equal to the change in energy we can consider a system where we're

adding work subtracting uh heat so the work less the heat is equal to the change in energy

one of the most common systems is this last one where we're heating something for the purpose of doing work

so basically almost every scenario where you're where you're burning something to generate

electrical energy which is you know derived by you know you're you're burning something

to heat something to make something else spin and that's mechanical work etc etc so this is a very common

instance but you can see the connection between all of these it's just a different way of looking at the

direction of what's happening on the right hand side it's always resulting in a change in the energy

level so i like this form right here this is the one i'm going to use as kind of the

general purpose form because it's the most common one in a lot of the scenarios we look at

if we look at a short period of time we can write this statement as a small amount of heat minus a small

amount of work is equal to a change delta in the energy and remember that i write

these deltas as different from this because these deltas are a small amount of

something and this is a change in something a change in heat and a change in work

doesn't make sense a change in the level of energy resulting from an amount of heat and an

amount of work makes sense so when we differentiate this first

this expression with respect to time we have del q over dt minus del w over dt

is equal to d e dt so this delta we can write as a as a small is an infinitesimal change and what

these terms mean is it's the rate at which small amounts of heat are added

and the rate at which small amounts of work are done so we just write them as as q dot as is in the rate of heat

transfer and the rate of work or the rate that work is being done

and that is equal to d e by dt and this is now in watts because this is joules per second so it's it's work per

unit of time or heat per unit of time so this is our our generic form of the first law

for a closed system and this is the form that we're going to use this is the form we're going to build on when we look at

the open system now if you take that expression uh if this is the one we're always going to

start with because this way we can consider processes that that are transient or

processes that where we're just looking at the end point so if you think about any kind of

process so let's go back to the compression of a gas suppose we're compressing it and

heating it at the same time none of that stuff happens instantaneously it takes time for the

piston to move to do the compression to do the work on the system it takes time to add a

certain amount of heat so a process down on a closed system is done

in time so when you're looking at the change in the system you're looking at integration over time of the process

and this again brings out what what the system means so if we look at the right hand side the

change in time is manifest as a change in the level of energy

so we wrote this e2 means u plus kinetic plus potential energy at state two

minus u plus kinetic plus um potential energy at state one and this is a result

of an amount of heat and an amount of work done to or on or two or by the system

and that's why we write this as q12 not q2 minus q1 or w2 minus w1 so amounts

changes okay so this is kind of the uh where we're at now is we actually have the first law of thermodynamics for

isolated enclosed systems it's going to take a little while for us to get to open systems because it's a

little more complicated and we actually have a lot of things that we still have to do

uh in order to to study problems um so the next steps that we're going to take is we're going to start

characterizing properties of the system a little more closely so we've been able now to

characterize the levels of energy but now we have to start thinking about what the system is comprised of in terms

of the media whether it's a solid or a liquid or a gas and then we have to have very

specific properties of each of those things because otherwise it's difficult sometimes to

characterize what the changes in energy level are particularly

internal energy so that's going to be the uh the topic of the next few lectures