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Fhe 2xcess Vilume iN #tank uhen Al Syseen 15 Coeled_-o 12 % _You use 4 JAH to shre heat from 2 Soler process _ -3 84244 Zs Zdded_- &_rate e€ 8.6m W 2 8,8...

Question

Fhe 2xcess Vilume iN #tank uhen Al Syseen 15 Coeled_-o 12 % _You use 4 JAH to shre heat from 2 Soler process _ -3 84244 Zs Zdded_- &_rate e€ 8.6m W 2 8,8x12 7/ Assuacnelbss 2_heat _ Dtecmz n EL_inccease in Frerae Per Second Lzl #sah have 3 ~ectAiz_ hest st Ge Jla k

Fhe 2xcess Vilume iN #tank uhen Al Syseen 15 Coeled_-o 12 % _ You use 4 JAH to shre heat from 2 Soler process _ -3 84244 Zs Zdded_- &_rate e€ 8.6m W 2 8,8x12 7/ Assuacnelbss 2_heat _ Dtecmz n EL_inccease in Frerae Per Second Lzl #sah have 3 ~ectAiz_ hest st Ge Jla k



Answers

Answer Problem 30.17 for the thermal and photochemical cyclizations of $(2 E, 4 Z, 6 Z, 8 Z)-2,4,6,8-$ decatetraene.

The amount of heat generated in the loop during a small time interval Ditty can be given by the Q. Is equal to e square by our DT. It's been also, I can write the value but the value of is well known as minor defy by DT, which is equal to 80 -8 hour. So I can write the value of D. Q is equal to 80 -8 hour minus eight doll. Holy Square by our DT, solving it further, the amount of heat generated in the group during the time interval zero to tao is given by Q is equal to integration of 0 to 10, How To AT -8 hour. Holy Square by our DT, Which is equal to one x 3, is where doc you buy are as the final answer.

Well, in this problem, we have a mantra. Tomic Gas on a as are working substance and we have a thermodynamic cycle. Um, where we go from 1 to 2 in a process where the pressure and the volume are linearly related. And then from 2 to 3 with the constant volume process and from three back toe, one in a constant pressure process again, we're going to use our ideal gas laws and the definitions of work he transferred and changing thermal energy to figure out what did they want here? Well, when they want the temperatures at all three states and a table of all the energies and the thermal efficiency Okay, we're also told that we have two moles of this Mon atomic gas. The pressures, the pressures and volumes are given at all the states. So one and 21 and 3 400 killer past girls. At two, it's 600 killer past guys and the volumes are 0.5 keeping meters at two and three and 0.25 keeping meters at one. So since we know that the number of moles, the pressure and the volume it every state we can figure out just from the ideal gas law. What? The temperature is that every state. And so at one it is 601 Calvin. At two. It's 1810 Calvin. And that three, it is to 1200 Calvin. So now, now, we actually know all the thermal dynamic properties at each of these appoints. So then we can look, turn our attention to energies. The work done in going from 3 to 1 is the pressure at from 3 to 1 times the change in volume from going from 3 to 1. So we get minus 1.0 times center, the fourth jewels or minus 10 killer jewels of work here and again because we're going from a higher volume to a lower volume, we're putting work into the system, which is a negative sign. Now, the work from 1 to 2 is actually the negative of, um is this area here, which is the negative of the work of 3 to 1, plus the area under this of this triangle here. Um, and in fact, the total network is just gonna be the area of this triangle because it is Theo area enclosed in this cycle in a pressure volume chart. So we have the negative of the work from 3 to 1, and then this is the triangle here, and you can think of it as the average pressure 500 killer pass cows over the change in, because again, it's just, you know, it's basically, um, you know, well, it would be this right? So the triangle, it's just basically looks like in the average, um so that's like the average and this gives us about Let's see here. That's 12.5 killer jewels now from 2 to 3, we have, uh, constant volume process. So there is no mechanical work or electrical work done along eso Then we Since we know the temperatures everywhere, we can figure out what the change in thermal energy is from every state transition. And so, let's see, That's the number of moles times the heat capacity, constant volume, times the change in temperature and again because it's Amon Atomic. Guess you know that that is, uh, three halves are so plugging in all our values we get 30 killer jewels. Yeah, eso Now, since we know the change in thermal energy and we know the work. We can get the heat transfer, and that is 42.5 killed. Jewels. The change in thermal energy from 12 to 3 is again the heat capacity council volume times the number of modes of material times a change in temperature. And that gives us minus 15 killer jewels. So we actually getting heat out here, Here, we're getting ah, heat in, um, from 2 to 3, we know that the the thermal energy or the heat, I think e think I got ahead of myself here. We know the change in thermal energy from 2 to 3. We know the work done is zero. So we know that they keep transfer is the change in thermal energy, which is minus 15 killed jewels. So we're getting heat coming out of here from 3 to 1. We know the heat changing thermal energy is also minus 15. Kill of jewels. And let's see, here we have again. That's basically because we have, you know, 600 Calvin kind of changes in all of these. So again, these air rounded. But no, it's not that this is exactly this. Um, eso don't confuse that. These are actually equal. They are. I mean, to this and a couple of significant digits. They are, but not not if we kept it. Not because of any thermodynamic properties. There's no relationship there. So we can then find we know the work. And we know that change in thermal energy so we can find the heat transfer. And that winds up being minus 25. Kelly jewels. So, um, made a table like they asked, Um, let's see here. Yeah, they for a table of all these energies. And these are all in killing jewels. Uh, so the work, um, we have from 1 to 2 is 12.5 from 3 to 1 is minus 10. So we get a total work of 2.5 killer jewels out of this cycle. He transferred again. We get total nut. He transfer of 2.5 killer jewels again should be equal to this. Um, and the teeth that we put in is 42.5 killer jewels. And again, the change in thermal energy. We should be at all these up when we should get zero, which we dio. So the efficiency is the network that come out plus my divided by the heat that we put in and that winds up being 5.9% so a very inefficient cycle here.

The heat dissipated in a heater H is given as I square are delta T. This can also be written as as equal to P delta T. Where delta T. Is the time interval. P. We know can be written as ice square are so we have replaced by square are by P. So as will be equal to in the crash. In the value of P is given as 100 watt and delta T. Is given as seven minutes. We can we can Change the seven minute in two seconds. Seven multiply 60. That comes out to be 4-00 jewel. This is the value in jewel and in the answers, the value is in calories. So heat in calorie hit in calorie will be equal to will be equal to four to triple zero, divide four point. We need to divide by 4.2 and it comes 10 to the power four calories. So the option will be correct.

As we know debt as we know that in this problem the value of W is equal to zero. The value of dairy W is equal to By multiplication 10 square. So I'll bring it further. I can write a test family square by june. So according to the option in this problem, obstinacy. The correct answer here, option C, each correct pencil or this problem, I hope you understand the solution of this problem.


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