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(III) Suppose a gas is taken clockwise around therectangular cycle shown in Fig. $32,$ starting at b, then to a, tod, to $c,$ and returning to b. Using the values given in Problem$39,(a)$ describe each leg of the process, and then calculate(b) the net work done during the cycle, $(c)$ the total internalenergy change during the cycle, and $(d)$ the net heat flowduring the cycle. (e) What percentage of the intake heat wasturned into usable work: i.e., how efficient is this "rectan-gular" cycle (give as a percentage)?

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(a) Leg ba is an isobaric expansion, and so the work done is positive. Leg ad is an isovolumetric reduction in pressure, and so the work done on that leg is 0 Leg de is an isobaric compression, and so the work done is negative. Leg cb is an isovolumetric expansion in pressure, and so the work done on that leg is 0(b) $46 \mathrm{J}$(c) 0(d) $46 \mathrm{J}$(e) $40 \%$ (2 sig. fig.)

Physics 101 Mechanics

Chapter 19

Heat and the First Law of Thermodynamics

Kinetic Energy

Potential Energy

Energy Conservation

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

The Second Law of Thermodynamics

University of Michigan - Ann Arbor

University of Washington

University of Sheffield

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In physics, mechanical energy is the sum of the kinetic and potential energies of a system.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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So the information we're giving is all on the screen right now for body simply to describe the process. Be to a is an I saw barbaric expansion where the pressure is constant. It's called this. You see all this, sweetie? Okay. On a treaty is an isil volumetric competition. I'm sorry. I saw you might pick afraid of change pressure. So in process be too, eh? The volume volume increases and the pressure is constant. Betweens work. It's positive, whereas Trudy, because the volume is constant work in zero now. Did you see The pressure is constant and volume decreases. So what is make you do? I'm from sea to foresee to be the It's another I saw volumetric increase in pressure where the work is zero Because the volume remains constant for part B. We want to find out the total world in by the gas during the cycle. So that so obviously in a Trudy and be to see the work is zero. So the total work done you simply world and you will be too, eh? On world enduring. Did you see? No. We used the same trick asses we used in the last two problems number 38 39. So world enduring B A is Q B A minus e b a using the first law of thermodynamics and you're in D. C. It is you, d c minus e d c No, no, that we have this. We know that work. Enduring the process CD A is 30 a Jules, but notice that developed enduring d A must be zero, which means this is simply world enduring CD, which means word. Then during the process, D. C is negative minus of that. So that's minus 30. A. Jules. Now that we have this notice that word enduring B a is Tzeitel double that is region at B times we am I a sweetie on from the graph. It's obvious that PB I mean, we know that two p b is two point opd and we know that he is the same as greedy. On V. B is the same as we see. It's accusing that we can write well, you might as well be us. We d minus. We see if you notice this is Peter Darbee for the process D to C. So that's work done during the process D. C so using this, we can see that work enduring for process be a is 84 jewels. Therefore, the total work done is work done doing here, less world enduring D. C. So that's 84 minus 38 which is 46 dudes for Part B. You want to find the total change in internal edge inside for Potsie on Because total internal energy the internal energy depends only on state of system. For a circular loop, the system comes back to its original position, which means the change in energy is zero for Part B. We want to find out the total heat you're in. The process of this gets a tricky This gets a little tricky here, but it's very straightforward. The total heat is simply the total sentimentality, plus the total work there, I told Internal energy changes zero on. We saw that the total working is for six year olds. So which means the total heat supplied to the system is 46 years now. For Part E, they need to find the efficiency. Efficiency is a little trickier. Efficiency is work done by the system, divided by the heat supply to the system that is the heat that was expended in doing this whole cycle Times 100. So in our skates, he it is subjective system only during D. C on C b. So you supply the heat supply to the system is simply you d c less I'm sorry. Uh, he did supply doing B C on B A so q b c less. I'm so C B and B so that you'll see be plus Q B. He did supply to the system on DDE. Now we know that Q C b is u C B less W c v on q b is a beer. Let's w here. No, because B C in the process bc The workman is zero w c b zero So we have W p a less. You see people's e B a is you see it now from the if you remember what we found. We found that W B was 84 tools, so we have 84 jewels less we need to find you. See you now for easier. We used these tow this information easier. He's use a year minus WC year were given QC and appreciate directly, So that's minus 85 minus minus 55. This minus 30. Jules, I'm sorry. Uh, this would be this is easy and QC and Q W c. Notice that kid, this is Q. Is he? And this is W A C. So what we insert phone was e S E E s is equal to Q A C minus WSC, which were found to be minus 30. Jules, which means you see you is minus year. See, which is 30 Jules. Therefore you see it is 30 Jules giving us 114. Jules, we already know that the work done by the system is W. D. C. I'm sorry. The world number system was 46 year olds. Therefore, efficiency is 46 years divided by 140 in jewels in 200 which turns out to be 40% after two significant digits.

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