For more information, please see full course syllabus of Physical Chemistry

For more information, please see full course syllabus of Physical Chemistry

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### Joule's Experiment

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Joule's Experiment 0:09
- Joule's Experiment
- Interpretation of the Result 4:42
- The Gas Expands Against No External Pressure
- Temperature of the Surrounding Does Not Change
- System & Surrounding
- Joule's Law
- More on Joule's Experiment
- Later Experiment
- Dealing with the 2nd Law & Its Mathematical Consequences

### Physical Chemistry Online Course

### Transcription: Joule's Experiment

*Hello, welcome back to www.educator.com and welcome back to Physical Chemistry.*0000

*Today, we are going to talk about Joules experiment.*0004

*Let us just jump right on in.*0007

*Recall in the last lesson what we did is we said that energy was a function of both temperature and volume.*0010

*We created this total differential expression we had which was du = du dt sub VDT + du DV sub TDV.*0021

*In that lesson, we associated this particular thing with the constant volume with a heat capacity under constant volume.*0041

*Now, the question is, we took care of this, we associated with some easily measurable quantity.*0052

*What can we do about this?*0059

*That is the question here.*0061

*We are just going to deal with the other partial derivative in this total differential expression.*0063

*What can we do with that?*0066

*As it turns out, the answer is not much.*0068

*A little bit disappointing but we will be able to say a couple of things about it.*0073

*But the truth is we cannot really do much about it right now.*0077

*Let us talk about this Joules experiment.*0080

*Let us go ahead and draw out what is that he did.*0090

*He came up with something very ingenious.*0097

*This is going to be water and of course the water has a thermometer in it.*0100

*Its measures change in temperature, things like that.*0106

*There is a little stir in here to make sure that the water is stirring up well.*0110

*Let me go ahead and draw this apparatus in here.*0115

*This is A and this is B and I will go ahead and shade this one in.*0135

*Basically, the idea is this.*0145

*We want to find out, remember du DV, we want to find out if there is a change in volume, what is going to be a change in energy?*0148

*Because that is what this derivative says.*0160

*It is the rate of change of energy with respect to volume per unit change in volume, how much does the energy change?*0161

*Basically, what he did was this.*0174

*He took his apparatus which consisted of two balls separated by a stop cock.*0176

*He evacuated this chamber altogether, this B, and A is filled with his gas.*0182

*Basically, what we do is we take this thing and we drop it into this tub of water and we allow this to come to thermal equilibrium.*0188

*The system to come to thermal equilibrium with its surroundings.*0198

*When that happens, what we do is we open up the stop cock because of the evacuated his gas is going to expand.*0202

*It does experience a change of volume.*0209

*And then upon this change of volume, we allow the system to become the thermal equilibrium again.*0212

*What we do is we measure the temperature change of the water.*0221

*If that is what we are doing, we are seeing if there is going to be some energy change based on a change in volume.*0225

*We are trying to measure this, what is the relationship between a change in volume and a change in temperature which is a change in energy?*0232

*Here is what actually happened.*0242

*Here is the result, no change in temperature.*0248

*Is it surprising, the expectation was that you open this up, the system would undergo volume change,*0261

*there would be a temperature drop or temperature rise and then heat would either flow in or out and that heat flow in or out will be measured by this.*0268

*That would give us a change in energy vs. A change in volume.*0277

*Here is the interpretation of the results.*0283

*We have the interpretation, the gas expands against no external pressure.*0290

*Remember, we said that B is completely evacuated, there is a vacuum in there.*0300

*There is no external pressure against which this gas would expand is pushing.*0305

*It expands against no external pressure.*0310

*In a situation where that is the case, it is called a free expansion.*0317

*If a gas expands against 0 external pressure, it is called a free expansion.*0322

*No work is done, P external is 0.*0335

*Work = P external × the change in volume.*0340

*If there is a change in volume if the external pressure is 0 the work is 0.*0343

*No work is done.*0349

*In other words, DW is equal to 0.*0355

*Du = DQ – dw, DW= 0 so du = dq.*0361

*Therefore, this particular case, the change in energy is just a change in heat.*0372

*So far, so good.*0377

*Since T of the surroundings which is the water, does not change, the temperature of water does not change so no heat is transferred.*0382

*Dq = 0, dq = Du = 0.*0407

*The energy change is 0.*0416

*The system and the surroundings are in thermal equilibrium.*0426

*The change in temperature is equal to 0.*0443

*The system DT, the temperature of the water does not change which means the temperature of the system does not change.*0448

*That is this DT.*0457

*Du=DUDT sub V × DT +du dv sub T × DV or it becomes du is equal is 0.*0463

*Therefore, this goes to 0.*0486

*What we are all left with the terms of that equation, this total differential equation is du DV sub T × Dv is equal to 0.*0488

*Because we know from the previous part of this that the du is equal to 0.*0501

*For this equation that DT is equal to 0, that goes to 0.*0507

*All we are left with is, du = du dv sub t dv.*0510

*We know that = 0.*0516

*But you know the change in volume does not equal 0.*0520

*There is a change in volume, the system change this volume.*0524

*If dv is not equal to 0, basic property of mathematics A × B.*0527

*If B is in 0 and A has to be 0, therefore, du Dv sub T is equal to 0.*0532

*That is the interpretation.*0544

*That is what this is, we just found that this derivative is not some property, it is actually equal to 0.*0553

*Nothing is happening.*0560

*In other words, the rate of change of energy with volume is equal to 0.*0564

*The change in energy is not associated with a change in volume.*0577

*The volume can change, the energy of the system does not change.*0584

*That is what this is saying.*0587

*The previous lesson, we found out that if the temperature changes, the energy changes.*0589

*That was this thing right here.*0594

*Now, we are working with this one.*0595

*This experiment says that this is actually equal to 0.*0597

*Energy does not depend on volume.*0601

*Energy only depends on temperature.*0603

*Since the rate of change of energy with volume = 0, that is that thing, energy is independent of volume.*0605

*Our initial U is equal to TV becomes U is just a function of T, not a function of V.*0630

*That is what this is.*0642

*That is Joules experiment says, this is Joules law.*0644

*This is what Joules law says, that the energy is a function of temperature not a function of temperature and volume.*0651

*That is what Joules law is.*0657

*Here is what is interesting, Joules law is not exactly true.*0661

*That is pretty close to being true.*0674

*As it turns out, the large heat capacity of the water and the small heat capacity of the gas in that apparatus,*0678

*it caused the temperature effect caused the effect to be too small to be observed.*0714

*As it turns out, there was a temperature difference.*0738

*If the difference was so tiny, that the difference in the capacity of a water and small heat capacity of that gas itself, it is as if the water did notice.*0742

*It is like dropping a teaspoon of water into the ocean.*0751

*The ocean is not going to notice.*0754

*Later experiments, with much more sophisticated sense instrumentation showed that du DV under constant temperature for a real gas does not equal 0.*0761

*It is very small though.*0792

*For all practical purposes, we can take DU DV T equal 0, even under for real gases.*0794

*For ideal gases it is always true.*0799

*For real gas it is not, it is very small though.*0801

*For an ideal gas, for the most part we would be dealing with ideal gases unless told otherwise.*0808

*From ideal gas, du/ dv sub T = 0, definitely something that you want to remember.*0819

*When we start doing problems, we will go over all this again.*0828

*When we get to the second law of thermodynamics, when we deal with the second law and*0838

*its mathematical consequences, then we will identify this derivative, this du/ dv sub T with an easily measurable quantity.*0850

*Remember, that other derivative, that DUDT in the last lesson, we associate it with a very easily measurable quantity, the heat capacity of the system.*0888

*In this particular case is 0.*0898

*Later on, when we deal with the second law, we will actually be able to identify this with an actual measurable quantity.*0900

*Even though, we now have a U, the energy is just a function of T, to be as precise as possible*0917

*both qualitatively and mathematically, for the purposes of derivation and working with the mathematics of equations,*0942

*we will continue to write that the differential change in energy is equal to the heat capacity × DT.*0962

*We will replace the derivative of what we know what to be the heat capacity + du/ DV sub TDV.*0974

*We are dealing with an ideal guess, we can just go ahead and take this equal to 0 and it just drops out, it just vanishes.*0983

*For mathematical purposes and to be as precise as possible, we will go ahead and keep it this way.*0989

*That is it, that is what the Joules experiment was.*0996

*We just want to associate and we want to find out what this partial derivative represent and can we measure it.*0998

*What it is associated with.*1005

*Thank you so much for joining us here at www.educator.com.*1007

*We will see you next time, bye.*1009

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