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An experimental power plant at the Natural Energy Labo-ratory of Hawaii generates electricity from the temperaturegradient of the ocean. The surface and deep-water tempera-tures are $27^{\circ} \mathrm{C}$ and $6^{\circ} \mathrm{C}$ , respectively. (a) What is the maximum theoretical efficiency of this power plant? (b) If the powerplant is to produce 210 $\mathrm{kW}$ of power, at what rate must heat beextracted from the warm water? At what rate must heat beabsorbed by the cold water? Assume the maximum theoretical efficiency. (c) The cold water that enters the plant leaves it at atemperature of $10^{\circ} \mathrm{C}$ . What must be the flow rate of cold waterthrough the system? Give your answer in $\mathrm{kg} / \mathrm{h}$ and $\mathrm{L} / \mathrm{h}$ .

(a) $c=7.0 \%$(b) $\left(\frac{Q_{H}}{t}\right)=3.0 \mathrm{MW}$ and $\left(\frac{Q_{C}}{t}\right)=2.78 \mathrm{MW}$(c) Flow rate $=60.0 \times 10^{4} \mathrm{L} / \mathrm{h}=60.0 \times 10^{4} \mathrm{kg} / \mathrm{h}$

Physics 101 Mechanics

Chapter 16

The Second Law of Thermodynamics

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

Cornell University

Rutgers, The State University of New Jersey

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So this is a question on experimental power plant in Hawaii, which works due to the temporary green of the ocean. No excuses there. The surface off the temperature on the surface that is the edge off for the ocean is 27 degrees Celsius. If we write this in Kelvin, this comes out to be 300 together. Similarly, the temperatures air off the cool. Deep inside the surface is equal to six digger seances. And if it turns out in killed in to be 279 killed in right? No, What we have to find out is in question here. Where did the maximum efficiency off this part? So for the first question we find noted that maximum efficiency that can be obtained is one minus D c right Deitsch come. But that is a culture you substituted back in the values off D. C and tears you this you get Mr B 0.7 and I, besides seven persons, is okay. So there's no one with second part B. It says the department has to produce 210 kilowatts of power of power that it has. The Paris is 210 kilowatts. So it asks us what writ must he'd be expected from the one water. So it asks us the hit extracted is from the one would risk us, right? So Q et vie time, right? It rate is going to What isn't it? Now you find this out. What we do is that the word done by this engine? Actually, the work done by this engine he's appreciation C times 0.7 times the heat. That is a job from the ocean, right from the hot reservoir. So this work, then you can write this in terms off power and time soapy into T is equal to 0.7 year itch. So cue edge by T physical took power upon 0.7 So this gives me if you substitute the value of power to be in work in 210 thousands. You're beautiful and you're a seven. This gives well, three mingle. What? So this is the raid It which the hit must be extracted from the warm water. Now how much it want? Rid the cool water absorbs the heat. Now the cool water hit that is released by this engine. Now this Indian takes in three megawatts off takes in three megawatts off. It does 7% off this hideous convert. It converted into electricity and the remaining 93% person days off heat is released to the core water which is absorbed by the corps water. Right. So working what we can right in expressing his dad, Lynch, it is that 97 persons is so 93% is off. Three will be equal to the heat. I have job by the radar feed observed by water. So just you can simply right. You see, by T is equal to 0.93 into three, which is easy called who? Point slave in line. You got juice so you can just ride this to be what? You know what? Maybe just for a second is this to me Go water. So this gives us the answer for the second part in B. Okay, so this goes like this Desolation? No, for wishing the mercy. The cool water that interest the plant leaves it it our temperature of change agree. So the cool water is initially or 62 senses. But when it leaves the plant its stem present. It's tenuous. Senses sued. The heat at job by the water you see is equal to mass off it mass of water that adopts it specifically, tapestry of water in the difference in temperature that is equal to obtain minus six. Now the question is asking us it. What rate? The cool water should flow into the system. So what we can do is that the rate? It was the cool waters before in the system. Just let us divide these both by time. So we are interested in finding mass or time that goes into the system. So m bitey he is simply qc fighting into one open So 10 minutes sixes for so I read. This is for us. Now we know the value of a QC ready. This is equal to two point 79 into 10 to the power six. Divide by four s so four into value up, as is 42 hundreds of sport Kinsey for second place for water. So if you can believe this, this comes out to be 1 66 0.7 busy for a second. So this must gives you off water. Sued, entered the blood for a second. Right? So we want our answer in, comes off kilogram per hour. So just multiplied. This with 3600 because of one hour is equal to 600. Right? Leave it at this year, one hour is equal to a practice. 600 seconds. So if you want this import our somebody like a greater 600 you get 59 saving age. Hi. Seven Keesey for our no. Since the density of water is one getting per liter 1000 get sabermetric You So the density one kids easy called a one liter. So you can just write in the same answer If you want that in kilogram as in leaders as well. So this must liters per hour. So it is. I concluded the solution for this problem. Thank you for watching.

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