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Problem 2: Work and Heat (10 pts) In a sealed container 2 moles of an ideal gas are slowly compressed at constant pressure as shown in the diagram: A total work of ...

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Problem 2: Work and Heat (10 pts) In a sealed container 2 moles of an ideal gas are slowly compressed at constant pressure as shown in the diagram: A total work of 400 J is done o the gas during the compression that takes the gas from an initial temperature TA 60 Kto a temperature TB 30 K (5 pts:) Determine the change in the internal energy of the gas B. (5 pts) Calculate the amount of heat Q involved in the process_ State if heat flows tQ or from the gas during the process.

Problem 2: Work and Heat (10 pts) In a sealed container 2 moles of an ideal gas are slowly compressed at constant pressure as shown in the diagram: A total work of 400 J is done o the gas during the compression that takes the gas from an initial temperature TA 60 Kto a temperature TB 30 K (5 pts:) Determine the change in the internal energy of the gas B. (5 pts) Calculate the amount of heat Q involved in the process_ State if heat flows tQ or from the gas during the process.



Answers

A gas is suddenly heated from A to B from a pressure of 2.0 atm and temperature $300 \mathrm{K}$ to a pressure of 5.0 atm. The volume stays constant at $2.0 \mathrm{L}$. From $\mathrm{B}$ the gas expands isothermally to a volume of $5.0 \mathrm{L}$ at $\mathrm{C}$. The gas then returns to its original state at A by an isobaric compression at a pressure of $2.0 \mathrm{atm}$ (a) Sketch these changes on a pressurevolume diagram. (b) Find the temperature of the gas at $B$. (c) Find the internal energy change and the thermal energy given to or taken from the gas from A to B. (d) For the leg from $C$ to A find (i) the work done, (ii) the change in internal energy and (iii) the thermal energy given to or taken from the gas.

Hello and welcome to this video solution of new Madrid. This question is based on the principles of thermodynamics. Here we are given with two moles of ideal gas. So let me quickly down the variables. So n equal to two moles and equal to to multiply ideal gas are there and the specific heat. See physical too. I tried specific eight CV specifically that comes constant volume, which is equal to fight by two. Are the temperature T is 300 kelvin. It's given this is the initial temperature T called 300 kelvin pressure is 100 kilobytes. Mhm free. Now we have to determine the final temperature and the walk down off the gas went 1.5 kill a jewel of heat is added. So the amount of heat added is Q. Which is 1.5 killer jubilee when five kg june. And we can write it as one factories ritual. First of all, it's a party. So the heat is added at is a thermal condition is a thermal. Okay, for is a thermal we know that the temperature immense constant. Okay, so it is implied that the temperature will be equal to 300 kelvin. So we have the temperature after the size of thermal process. Now we need to calculate the work done by the guests also, we know that. Okay, so first of all, let us write the equation first law of town enemies, that is Q. The heat transfer by tour gas is equal to the change in internal energy. That is tell you plus the external wartime. W Now for a suitable process for no change in temperature we have delta equal to zero. So this will be called to zero. So we have got worked on is equal to Q. Thus we can see the water by the gas is equal to 1.5 killer too. So we have got both this temperature as 300 kelvin and walk down as 1.5 color tube for this ice thermal conditions. Now we move on to part B, which tells us that uh he deserted at constant volume. Right? So the L. V. Is equal to a constant right? Or 0 12 equal to the volume is concerned about. The change in volume is actually okay. So here we have four delve equal to zero. The walk down by the gas which is given by us P L. V. This is equal to zero. Thus we again, does we can say that Q equal to only tell you right? Because what penny zero. Thus we can say Q as 1500 And then we call to end C. V thirsty. No, 1500 equal to two times five by two. This is given rate cp The value of this value. Three way to see a five by two times. Are are is the universal gas constant which is equal to 8.314 All right times delta P. So we have caught healthy equal to Mhm. Mhm. 36 degrees. Okay. 36 killed when you can write thus, we have the final temperature T. F. Equal to T plus healthy. Which is equal to P. S. 300 kelvin which is given. And the history 36. So we have 3 36 Calvin So we have got the final temperatures to 36 Calvin four uh for this constant volume process and the work done is also zero. We got here right now let us move on to the time when we have a constant pressure. So to help equal to zero. So here we need to find out the specifically that constant pressure cp. And the relation between C. P and C. V. Is equal to C. V. Plus our so we have got five by two. R plus R will be seven by two are cbs five paid to our that when added to our we get seven wait one. So the value of cp seven way to our fine. Now we know kiwi equal to the heat added or he transfers equal to end cpt. Tell that. So cue again we have one pipe double zero and equal to two. Cp will be seven by two. Seven by two. Are will be equal to eight point 314 And we have got delta T. This gives us delta equal to 25.8 Calvin. Okay so again we have this final temperature T. S equal to T F. Equal to 300 plus 25.8. Right, so 3 25 28 Calvin, which is to President lee. Right, So here we have the final temperature. Great. And now we need to calculate the work done. Yeah. So for that we need to calculate tell you the change in internal energy which is in C. V. Healthy. They So here we have two times CVS three, sorry, five by two. This is five by two times eight point 314 And delta is from here 25.8 jules, which is nothing but 10 seven 2.5 choose. Right now we have Q plus equal to tell you plus W. From first lifetime of thermodynamics. So Q. We have 15 double zero which is equal to tell you with already. We got 1072.5 plus W. From here we have got we get the Washington equal to yeah. 4 27 0.5 june's. So we have got three things first. We have considered. I saw thermal case where we have the temperature is constant and we have a value equal to zero. So Washington will be equal to the heat which is added. So 1.5 kg tune. Now we have caught constant volume process where we have the work done equal to zero and Q equal to delta. You and delta. We call too insipid. Lt Cv. You plotted. See, you know that. I bet you are. And you will get delta equal to 36 Calvin. So initial temperature T was 300 300 plus jelly which gives you 3 36. Now here in this case it's a bit tricky. Delpy called zero from that. You need to find out the specific heat at constant pressure. So the relation between constant volume and constant pressure. The specific it is C. P. Called the city plus R. C. V. We know that. Fight by to R plus R. If you add in seven by to the similar process you have to opt to find out this temperature. DLT. So the final competitive D plus D which is 300 initially. Now it will come through 25. From here. You have to calculate the delta, you the change in internal energy. You have to plug in all the same equation the values. And you will get this 1072.5 from here to apply the first law of thermodynamics and you get the work done. I hope this is clear to you and have a very good day ahead. Thank you.

But a off the problem is Mmm. In first step, the William is constant or you miss a constant. So a constant. Therefore no work is done. So work is it zero in first step? Because the William Off Monster in second step and the work is a cool thio pressure times till we changing Warning. So your pressure off 141.4 times 1.1 times 10 to the power of strife Paschal Moscow Times changing the war You are changing more. Liam is a 9.3 minus 5.9 litres and converting these values interesting units in the world. Then we get here is a four individuals for individuals. This is for you to Jules in part B. Since there is no order all changing the temperature so change into preacher um zero. Therefore, the changing internal energy changing internal energy is recalled to zero zero in part. See, we can write Ah, the jianjun Intel Energy using the first law of thermodynamics That is a call to change in energy is good heat given into the system minus the work done since the changes Internal energy is little that our cue is equal to work on where work is equal to. We already found these. And for you too, Jules. So this work is aided into the guests. This whole warhead is ending into the guests. Yes. This is the end off the problem. Thank you.

So here we have a gas with specific number of moles in the saner on, we should chemist that he's the guest first by having the given quantity of kids this. And so this is the first process. The economic process and the second there with dynamic process, is when she allows the guest expend and gas gains twice off his initial wallet. So for the part A. We need to solve for the temperature that comes after the first part of the process of the heating part. In order to do so, we know that the Q equals and in this case, cause it's morning his capacity on the change in temperature, which is equal to wear. Siri the V minus d A. From here, we can derive the formula only for TV by moving this part left in sight and then adding these parts this term to both sides. So this way we derive that take me equals que over and c lost the Since we know where the body is here, we consent. It is equals to one point 52 times tended. Afford. This is jaws over 2.5 most times 20.76 drools, promote Calvin, and this is all going to be in killings at the end of Plus 290 Treat Kelvin's, which therefore equals Davey Evils 585. Kevin's also in relationship to wall you. We can say that for for after the heating process for the expansion process, which is capturing at the cost of pressure we know that did the ratio formula will be true? So the racial formalize a t c o r t being since we have from point A to point B. This is the heating part when the chemist kids to guess from the point being to that. But see, this is expression part when the gas is left out. Expend, Really? So here we are doing for the big to see Part two the grosses and this is equal to racy over be May. And from here we can derive that TC eagles. And here we have to Levy, since we see is twice of the baby volume over. Maybe this cancel out times TV when we substitute the no bodies we obtain that this is equal to doing times 585 killed ins and therefore the same equal. Still, 1170 killed. These therefore, we should depart a off the probe, not for the part b of the problem. We were asked to find a thought work done for both processes. So we know immediately the work down. But with the addition between work from A to B plus work from me to see, observe dead. Since the problem is constant from for divorce crowed grosses from A to B this part or the work will be with zero and therefore there are only we are going to calculate for the V B for the world memory B C part and we can express the world down here from the formula work from the C equals B times Delta view. But from the little gas equation we know that speed times that the week was an times are times delta teats. So all these peoples and times are times delta deep and this is also equal to a man. Times are and then we subtract the C minus. Stevie Nicks is it is from being to see change, begin knows directly, substitute values and find that that it is 2.5 Morse Times ain't going 314 juice spurred. More Sheldon times The difference between the temperatures. Andi by In doing this, we obtain that value for the B C were keys 11.5. I'm standing third rituals are just time and didn't quite kill the jewels. I shouldn't be 12 to to up to the fire 12.5 to 10 to return. So the final result is that w equals W B C, which equals well point 15 killed Jules, which is also intimate development 0.15 year. So this is the answer for the part to be for the part C we need to find were you to find the internal energy change? Uh, we need to find the how many how much heat is added for the birthday. We need to find the internal energy change. So the additional heat in this case but for the part of the process where the gas expands. So it is from from me to see, since we know how much heat is added in the first part of the process from A to B. So for the guard, see, we can stay that Q weebles and now the pressure is constant. So CV dealt of the B C on. In this case, this is ableto 2.5 more times doing denying when 07 Jules burnt Oh, Kelly. And this is corresponding to the Given. Yes, and the difference in the temperatures. So for being from the known values Childrens. And finally, when we put this father's into calculator and bothering them, you attended chemicals for to do point five killer jewels for the part d. We need to find the total change in internal energy. So we know that the total changing internal energy similar to the work done is the ignition off the total change Internal energy from A to B and glass. The change thrown who need to see change view from me to see in the process a bases. The volume is constant. The work down zero. We can say from the first law of thermodynamics that Q A B equals belt you a b thus World Commission zero. So this can be the director substituted since we know the you may be right now, for the part may see part of the process is we will need a different kind off of elevation. But also, we should actually calculate there you a b using standard formula where the process is captain and under cross and for him. So, until the from from this, we can use these for you and I'm see me times Delta t remain to be and this is equal to 2.5 moves times 20.76 draws bird oh, times that did the difference in the temperatures. So my guest tonight tree killed ins and when we put this body center calculated you obtain that that the U A. B actually equals two 15 points 15 killing girls for the part That thing being seen also from the first loved Herman economics we can say that you may see equals Q B C minus work done, which will be seen here. We should substitute the corresponding foreign yours that goes as follows And CBC is the pressure is constant The change in temperature, B C minus, and are and build a d they see so we can write this down as end times Delta T B. C. This is the common common parts for others. And then we will have C b. My eyes are we can substituting nobody. This is the this attraction between They see empty beats, so we can immediately say that the U B C equals. And now for all of the known bodies we have 2.5 most and the brackets different with temperatures. And in these brackets the Constance. This will all be enjoys. But they will express this in kill drills because it is more comedians. This is equal to 13 point trade. Pillage ALS. Therefore, finally they offer you equals to 15 0.15 for Jules 30 point tree killer jewels. And the final value is Delta U equals 45.45 killer jewels. This ends the parks the last part of this problem. And we have evaluated everything at the problem. Asked us to evaluate. I hope you find it's helpful and they hope to see you in another less

It's all the first part of this pussy. Yeah. According to first lock thermo, next weekend that eat is equals to change in internal energy. Yes, you work them. No. The increased temperature of ideal gas in the two different process are equal. The temperature difference is equal. The change in internal energy is that you proposed on to change in temperature. Hence the two different process that changing interment energy is also equal. So the more work will be done when the more it is added to the system. The heat added in process A. Since you in process A. Is less than you in process be and more work is done in process be and the blue B. Is greater than the blue things. Delta you A. Is equal to delta. You the sure the work done in process be is more than work than in process Option two is correct. Hobson who is correct. No. Now let us move to part B first. Let us calculate the change in internal energy of the system. We can write it as three D. whatever too. And artie minority for energy will be changing temperatures. We can write it for the three developer to nr. The f minus th E final when ste in his hip. 40 finally is given He finally is equals two 1 50° integrate. We can write it has 150. This 2 73 Kelvin, It will be 4 23 Calvin. Similarly, Initial temperature is given to 50° integrated. You can write it as 250. There's 2 73 The Greek 11. It will come out to 523 11. No. Now we can find the change in internal energy is equal to three divided. Where two multiplied by the number of moles is to mold multiply the value of our is eight even for multiplied by the training temperature 5 23 minus 4 20. After calculating you will get it as two point warning. The multiple were 10 to the power of the julie. Hence the training. Internal energy of the system. After rounding of weekend date it is 2.5 multiplied way went to the party. We do. This is the changing internal energy for this system. No, we will calculate the wagon in the first process. So you one is equals two delta U. One. Let's W. One here. The change in internal energy here the change in internal energy of the system. This constant that is 2.5. Multiplied by 10 to develop three. And from here we can I W one is equal to you were minus delta U. One. But The Cuban heat artisan has given us 2500 jule w minus When it's delta even we have calculated there's 2.5 multi caliber tend to be part of the jewels. From here we get it as Bergman W. one is equal to zero during. So this is this is the wagon. In the first process. No work done in process. The second process. Now we can write you two is equals two delta U. Two. Yes. W. Two. But we can further right. W. Two equals 22 to minus delta youtube. Thank you to is given us 3000 June. My name is Jintao. You do. We have calculated 2.5 multiple. Where And for three jewels after subtracting we get W. two equals 2 500 years. So this is the bargaining process. Second, thank you very much.


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