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Gasoline-powered water pump 7.5 x 10*kg of water from flooded basement floor the ground outside the house in an hour while consuming 0.8 gallon of gasoline: Assume ...

Question

Gasoline-powered water pump 7.5 x 10*kg of water from flooded basement floor the ground outside the house in an hour while consuming 0.8 gallon of gasoline: Assume the energy content of gasoline is 1.3 x 106 /gal and the basement floor 3.0 m below the ground. (a) Calculate the work done by the water pump (Wemgh): (b) What is the thermal efficiency of the water pump? (c) How much heat is wasted the environment in one hour?(a) W =(b) Efficiency(c) Q =

gasoline-powered water pump 7.5 x 10*kg of water from flooded basement floor the ground outside the house in an hour while consuming 0.8 gallon of gasoline: Assume the energy content of gasoline is 1.3 x 106 /gal and the basement floor 3.0 m below the ground. (a) Calculate the work done by the water pump (Wemgh): (b) What is the thermal efficiency of the water pump? (c) How much heat is wasted the environment in one hour? (a) W = (b) Efficiency (c) Q =



Answers

A pump on the ground floor of a building can pump water to fill a tank of volume $30 \mathrm{~m}^{3}$ in 15 min. If 9 the tank is $40 \mathrm{~m}$ above the ground, and the efficiency of the pump is $30 \%$, how much electric power is consumed by the pump? (Take $\left.g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$ (a) $36.5 \mathrm{~kW}$ (b) $44.4 \mathrm{~kW}$ (c) $52.5 \mathrm{~kW}$ (d) $60.5 \mathrm{~kW}$

We have water entering a pump, which I have to know. Um, schematically here is a circle. Um, so we have. It's entering at 100 till Pascal's and it's excelling at four bigger Pascal's coming in at 30 degrees C and we'll assume that it's just saturated, uh, saturated liquid. And we have a nice and topic efficiency for the pump of 70% and a mass flow rate of and 1.35 kg per second. So we can ah, get the property is we need at the inlet because we know the temperature and the pressure. And again we'll just assume that it's ah saturated liquid. Um, so then we have Let's see, here the power the, um, reversible or the ice and Tropic power out. Um, is then just let's see, Here we have, um, I am My notes should follow along here. Uh uh. Let me football here. Yeah, so we have. So we know the ice and tropic efficiency. So we need we can get the ice and Tropic Power. Eso if if the process was ice a tropic, we just have, um the you know, the volumetric lower, You know, times the pressure difference. So we would just be moving. Um, there would be no entropy change. Eso we'd have nothing. Um, e thing toe worry about here. So just the ec Sergi. Um and that is 5.288 killer watts. Now we have to figure out we once we have the Eisen Tropic Power, you can get the actual power by dividing it by the efficiency again. This is, um, stuff going into the pump. So this would be the least amount. So what we actually need to put in is 7.554 kilowatts. Um, now the heat transfer. Um, they say that there's ah, what did they say about this pump? There's, ah, the rate of frictional heating eso. So we have, um, heating that we from friction in the pump. And we have obviously some heat coming out of here so we can take the rate of frictional heating is just the It's just the work that we basically the losses here. Andi, that's 2.266 kilowatts. Um, is the rate of frictional heating the actual onder The difference between the action on the ice and tropic work. Now the entropy of the exit of the pump. Um, we have we know then that the actual work done is Thea. Entropy flow out, finance the entropy follow in. And we know everything in here, but h two so we can figure out what h two is. And then we can use that with this pressure to figure out what the actual entropy is at the exit and we can see that it is slightly higher, actually than, um so it's not ice and trap it here now. So whenever you can find the reversible workout So this was the ice and Tropic work. Now, this is the reversible work, and that is the mass flow rate times the well. It's the, you know, the entropy difference. And then the kind of the temperature times that, um, entropy difference. We have all of these values now so we can figure out that, um are reversible work that we, um would could put into here would be, Let's see here 5.3, 5.362 kilowatts. So, interestingly, we can see that we would need way analyze the system as reversible. Uh, we would need mawr than if We just said it was ice and tropic, because in the ice and Tropic case here, we basically assumed that there was no heat transfer either. S so that was kind of Ah, you know, um, yeah, we assume that basically, yeah, um, so I sent Tropic. Wasn't is not the same as reversible, because we have he transferring this problem. So we have then this reversible work. And so the exit, the rate of expertise, destruction is just the actual work we did power. We put in minus the reversible power that we would need if it was a reversible process that winds up being 2.93 2.193 kilowatts. And so we can get the second law efficiency, and we can see that it is 71% which is slightly higher than the the ice entropic efficiency, which was which was ah, 70% again because we were assuming now that, you know, there is, um, this heat loss, basically, we're basically saying that we're gonna have some heat loss here, so we'd actually really need some. This would not be the minimum. This would be the minimum movie. Didn't have any heat laws. But if we have some heat laws, then that is the minimum. And so that's why this percentage is bigger than this percentage. Because here we basically we assume that it was, uh, the end. There was no entropy generated. That means so there is no entropy change. Um, here, because we had heat going out. We have actually had some entropy differences. Um, yeah. Anyway, that's Ah, it's about about all there can be said about this problem, I guess.

So we're giving a heat pump that's extracting groundwater, and the first thing we're trying to do is find the coefficient of production. So we know the equation for this is equal to the hot temperature over hot temperature minus the cold temperature. And we can see these values are given with the hot jumped or being 70 degrees Celsius in the cold being 10 degrees Celsius. And then we have to add 273 in order to get these two. Kelvin. So you get that, too. 343 Calvin over 343 minus 283 and this gives us a c o. P. Value of 5.7. It's this answer to partner and then for B were asked to find the electric power consumption if it supplies it a certain right. So since we're given well, we're not given. But we have just figured out seop we confined. The power consumption is equal to the produce power. Just 20 kilowatts, divided by R. C. O. P. Just 5.7, and this means get a value of about 3.5 kilowatts is the amount of electric power supplied the system I've never seen. We're told you compare two different operating costs of oil and of electricity. So we're given the cost for oil or for electricity and for oil were given the price. And then how much with burns. So we can figure out the cost for the oil, which is $3.60 per gallon, divided by 30 kill hours per gallon and since per gallon and we can see our units cancel out here. So we get true sentence per kilowatt hour and then we can compare this to the value for electricity, which is 15.5 cents. Write that down here per kilowatt hour and here we can see that it would be cheaper to go with oil, which is what we just calculated in this scenario.

Let's solve the first part of this problem as we know that the efficiency he's equals to the work done divided by the heat transfer for the heating. So from here we can write 18 ft U. is equal to well done. You were a little bit efficiency. No, the work done even in our question is 900 megawatt Divided by the efficiency of the engine is 25%. That is 0.25. So from here we get 18 ft Q. Is equal to 3600. Make our This is a required eight input in part B. We need to calculate the rate of it starts from the plant, acute poverty is equals two. We were too divided right B minus the balloon it very well So it will come out to be 3600 minus 900 meg award. So it will be equals two. 2.7 Multiple hardware tend to report of the make a word this much amount of it will be discharged or rejected. Now in part C we need to find the mass of the water per second. So as we know that he deserves is equal to M. C. DLT so that he deserves. We have found in previous party as 2.7 multiplied by a 10 to 43 megawatts. So let us convert it into a world where multi language tend to be about six. It is, it is in the world. This will be equal to the mass. Multiply the value of cps or one 8 6 jewel parquet de already disintegrate, multiplied by the change in temperature. That is 40° integrate minus depending recent period. So from here you get masses equals two masters calls through 25,800. Is he purse again? Is your question. So this is this is the amount of water clue per second. Now the volume of the water required to cool the discharge. The volume we can be written as must divided by the density. So must we have already calculated as 25,800, Divided by the density of water is 10,000 1000. From here we get the volume is 25 it meter cubed per second. So we can convert the volume into literal per meter cubed by multiplying with 25.8. multiplied wear, 60 multiplied by 1000. So this will be later permanent. So we will get volume flow rate V. Z equals two. He's equals two 1.58. 1.548. 1.548 multiplied by 1034 of six. Later per minute. Mm Let's convert this into a gallon. Permanent by dividing with 3.75785. So this will be equals two, one point 548 Multiplied by 10-4 of six, divided by three point 785 Yellen. Permanent, for the final value will come out to be 4.1 multiplied were 10 to the power of bye gallon per minute is the volume fluid. Hope you like this solution. This is the final answer.

In the first case of this problem we have to calculate the current drug by the water from that is represented by I let's calculate the power input to the appliance. For that case we define the efficiency which is written as it is, equals two power output divide by power input. So from here we can ride this question for power input is equals two power output divide by this efficiency. Now this can be written as power input is equals to power output which is equals two 2.0 kilowatt divide by the efficiency which is equals two uh 84%. That is written as 84 divide by 100. So from here we will get the value for this power input as 2.3 at one clot. So this is a bar input. We can wait. The electrical power as p input is equals two. We multiply way I. Well this week is the potential difference supplied by the source and eyes that current drawn from the what's the pump formula? We can watch the screen for I. S. I. Z. Equals two. Power input defied by fee. And we call it the question number one. So I can be written as icicles to 2.3. Each one multiply waiter is power three ward divide by this week which is equals to 240 vote. So from here we will get the value for this. I as I. Z equals two. My point 9 to 1 compare let's move to the part of this problem. So in this case we have to calculate the resistance of the water pump. That is our we can write the home slide as well as equals to IR So formula we can white out as ours equals to be divided by I so we can write areas are as equals to 240 wall divide by nine point 981 I'm fair from here we will get the value for this areas. 24 point 05 Oh thank you.


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