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Assume that 91% of the energy stored in the prey animals is lost to heat when they are eaten by the Owi Further assume that the prey animals eat grass and seeds,; b...

Question

Assume that 91% of the energy stored in the prey animals is lost to heat when they are eaten by the Owi Further assume that the prey animals eat grass and seeds,; but that only 8% of the energy in the grass and seeds is transferred to the prey animals (which the owls in turn consume). Given the number of prey animals you found and using your answer from question #2 how many kilocalories of grass and seeds does it take to make all the prey species consumed the size that they are? How many kilocal

Assume that 91% of the energy stored in the prey animals is lost to heat when they are eaten by the Owi Further assume that the prey animals eat grass and seeds,; but that only 8% of the energy in the grass and seeds is transferred to the prey animals (which the owls in turn consume). Given the number of prey animals you found and using your answer from question #2 how many kilocalories of grass and seeds does it take to make all the prey species consumed the size that they are? How many kilocalories from the prey species are lost to heat in one day when the owl eats them? In your answers show the formulae (simple addition or subtraction or division or multiplication) that you would use to answer these questions There are equations from class that you will find useful to use for this question. (5 marks) Epred Eprey wnere Epred is the energy of the predator Eprey is the energy of the prey E is the efficiency factor (a number between 0 and 1) This tip is helpful for questions 3-4



Answers

The energy output of an animal engaged in an activity is called the basal metabolic rate (BMR) and is a measure of the conversion of food energy into other forms of energy. A simple calorimeter to measure the BMR consists of an insulated box with a thermometer to measure the temperature of the air. The air has a density of $1.29 \mathrm{~kg} / \mathrm{m}^{3}$ and a specific heat of $1020 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K}) . \mathrm{A} 50.0 \mathrm{~g}$ hamster is placed in a calorimeter that contains $0.0500 \mathrm{~m}^{3}$ of air at room temperature. (a) When the hamster is running in a wheel, the temperature of the air in the calorimeter rises $1.8 \mathrm{C}^{\circ}$ per hour. How much heat does the running hamster generate in an hour? (Assume that all this heat goes into the air in the calorimeter. Ignore the heat that goes into the walls of the box and into the thermometer, and assume that no heat is lost to the surroundings.) (b) Assuming that the hamster converts seed into heat with an efficiency of $10 \%$ and that hamster seed has a food energy value of $24 \mathrm{~J} / \mathrm{g},$ how many grams of seed must the hamster eat per hour to supply the energy found in part (a)?

Everyone. This is question number 86 from Chapter 14. In this problem, we're talking about a hamster in a kalorama ter basil mint of metabolic rate and stuff. But so we have this hamster in Kalorama ter, and he's running on a wheel were told, were given the air density, the heat capacity of the air. The were given the mass of the Hampshire 50 grams, and we're told that the crown barometer contains your 500.5 Weiner's cubed ofher at room temperature, or then given that while the hamsters running on a wheel, the air temperature increases 1.8 degrees Celsius per hour. The Hampshire converts seed to heat a 10 degrees, 10% efficiency, and the seed has an energy value of 24 Jules program. So part a asked, asked us to find the heat generated in in an hour, so he generated in an hour. We don't have a face change or anything. We're just dealing with a change in temperature so we can use our basic equation. Q E equals M C. Delta team Kalorama Tree specifically should also remind you of this so we don't have the mass of the air but we have. We have density and volume and density equals mass over volume. So then mass equals Roe V, so then we can replace them with Robie. So then we have Q equals ro V C, which we have Delta T, which we have, so we can just plug these numbers in. So this gives us 1.29 kilograms per meter. Cute times. What's your point? 05 meters cubed times, one out tio tools per kilogram k times our delta teams 1.8 degrees Celsius and that gives us Q is equal. Tio 118 Jules. So if the heat produced by the hamster So now we move on to Part B, which says, which asks us to find how many grams of seed the hamster needs per hour. So for part B, normally, in order to find how much energy something produces, we would do the mass times, the energy times, the efficiency, which in this case is your point is 10% 0.1. And that would equal R Q eve for efficiency here or energy. Excuse me, energy value. But in this case, we're actually solving for mass. We don't have mass is what we're looking for. So this becomes mass. Times 24 Jules per kilogram. Time 0.1 equals our 118 Jules. And then we rearrange that equation and we get Sol for mass. M equals 118. Jules over 0.1 times 24. Jules, her Graham. And that gives us a value of 49 grams. So is our hamsters. Wait at 50 grams. This doesn't really seem reasonable that he will able to eat his equal body weight every hour, but who knows?

In this problem, we are asked to consider a unit of energy called the quad and World energy. A few other things related to energy were given the following information. World energy supplies are often measured in units of quadrillion british thermal units And a quad is one times 10 to the 12 british thermal units. Be to use world energy consumption. And keep in mind that this was written prior to this time. This book. World energy consumption is predicted to be 5.81 Times 10 to the 17th, killer jewels by 2015 I realize it's much later than that, but that's what the prediction was referencing question they asked us to reference question 5 17 and that one was actually answered in the back of the book. So I just looked it up and in that question, we find out that to see if I can find this year and I think I'm on the wrong page can be upset to find this a 1 54 We find out that 1,054 jewels Is equal to one Btu. Any question A We are asked to convert killer jewels two quads. This is just a simple conversion. First step will be to convert killer jewels to jules. The second step will be to convert jewels to be to us. And our last step will be to convert BTUs two quads. Sure, I got everything there. I believe I do Do the math on this. You will get 5.51 Times 10 to the 5th quads. I'm going to go to the next page for B. I should have erase that. Let me clear that. So for B what Were given 99 0.5 quads is the energy consumption in the United States per year. We're going to assume that all the energy is generated by burning methane CH four in the form of natural gas were asked to assumed that the reaction is 100% division and we are to calculate the number of moles of methane needed to be combusted in order to meet this demand. We are going to solve this by applying Hess's law to the combustion of methane And I'm going to use the H 20 product as a liquid. Remember if my answer is different, it might be because they used a gas and my standard heats of formation are mhm -74.8 killer joules per mole for the methane zero for standard here, -3 93.5 killed jules from all as well. And water is negative 285.83 has. This law tells us that we're going to take the products minus reactant times of coefficients, so let me balance my chemical equation. Delta H. For the reaction is One times negative. 3 93.5. These aren't killed joules per mole Plus two times negative. 2 85 .83. Also killed joules per mole subtract. I'll put the one in there even though I don't need to Do the math here. And I got 890 0.4 kg jewels per mole of methane and were asked to convert to moles again. So we're going to take it's pretty easy little thing here, We're going to convert our 99 .5 Quads. I'm gonna abbreviate that Q but that's not official. And I've got one times 10 to the 12th. BTUs british thermal units per quad And one Bt. U. is equal to 1,054 jewels. And there's 1000 joules per kilogram all. Which gives us 1.05 times 10 to the 14th. Last but not least, we're going to take our 1.05 Times 10 to the 14th killer jewels. In terms of value we calculated above which was 8 90 0.4 kg jewels per mole. Easy peasy. 1.18 Times 10 to the 11th moles of methane. How many kg is co two would be generated. Um and were referenced to question 11 and we were told that the earth fixes 5.5 Times 10 to 13 kilograms of CO. Two per year. So we need to convert Our moles of Ch four which we just had. Mhm. Which was 1.18 trump. Okay, Times 10 to the 11th malls And this was co two. Yes, I don't think I have to do. Oh that's CH four. And we have a 1-1 more ratio here, Molar mass was 44.01 grams per mole. And let's go ahead and do kg divided by 1000 g. I got 5.19. Let's write this over here. 5.19 Times 10 to the 9th kg of co two. And then we're going to compare our answer with part C, compare 5.19 times 10 to the 9th kg of CO two. With the information given in earlier where we said We had 5.5 times 10 to the 13 kg is how much Co two is fixed by the Landmass. And we see that we have um we do have sufficient yeah photosynthesis going on to handle us needs slash consumption. Now is photosynthesis adequate to maintain a stable of CO two in the atmosphere? Well, if we start looking at the world, let me see where I've got this written down here. Mhm. Yeah. Okay. so in the world we have 551 Times 10 to the 5th quads. And if I multiply that by what I just got for the United States here was 5.1, Maybe I should have written 5.18, but now I've got 5.19, I'll just keep that Times 10 to the 9th kg Per 99 5 quads. We'll see that worldwide we get 2.87 Times 10 to the 13 kilograms. And that number, when I compare these two numbers, it's still sufficient. But since this is a parent per year, it's not sustainable. Mr I believe that's it.

For this problem of the hand stuff we'll call the vein p debated which he heat energy is generated by the gemstone. So he the heat energy generated and keynote called Great in which food energy is consumed. So we have variables for the heat energy produced any food energy consumed. And we know that the official sees 10% So that means only 10%. Or think food energy is used to convert heat energy. So P is equal to 0.1 he not so for part a calculate the heat generated in the books. We need to know that he generated by the hamster as that heat is the heat Add it to the books So power that the hamster generates heat Hey is equal to make it do you for your time But we know that he too is good and seed out t I am is the mess it see your specific He could best your a I doubt it to you The change in temperature Oh my time t The mass of the isn't density times its value identity of it is 1.2 Hagi's cubic meter and occupies a volume in McAllen limiter. Oh, zero points, you know, five cubic Brutus. Dr. T is equal to 1000 20. Well, doesn t actually but see this person keep capacity for its 1000 and 20 jewels. K g tell her and finally got a t over tea is one or in six south use degrees every hour. So that's a faint and what's The temperature is changing 1.6 degrees Celsius for every hour. And if we computers, we get that the power generated by the hamster which the heat added to the box, is happening at a rate off 97 0.9. Jules, our that's the heat energy at into the books in the hour. So no party. We want to calculate the mess off seed that must be consumed by the hamster in order to provide this poor. So the massive see that needs to be beaten him. Are you in a time T is equal to he, not the rate at which food energy is consumed, divided by no see. So I'll see is the rate at which is the conversion energy converting the food energy into heat energy, the latent heat of consumption. So this is simply P over 0.1 device by sea, so P recalculated to be 9 97.9. So 97 point 9/0 97.0.1 979. Jules Our and 20 juco jewels. Grandma food is converted into heat energy, and so the total amount off food at the hamster must eat every hour is 40 0.8 grams. So if they hamster consumes 20.8 g off seed every hour, it will be able to provide 97.9 joules of energy every hour.

Well, Hello again, we are here in this physics problem talking about tomatoes. So first part, we need to look up the calorie content of tomatoes. I saw something that said it was about 20-35 calories per tomato. So I opted to just say 30 kilocalories for tomato. Now, for part B. He made the mistake of trying to google what the typical plant outside, what the typical leaf area was on a tomato plant and ended up finding a lot of scholarly articles. So after some failed searching, I just decided to assume that the area was a quarter of a meter. I really don't have a good feel for tomato plants. So I went with a quarter of a square meter now, part C. So in this case, if we've got a quarter of a meter of area and our light intensity is 800 watts, then we're looking at a power of 200 watts because it's one quarter of 800 eighth here, We assume that really only 5% of the total energy here is useful. And so that means we're really only getting 5% of 200 5% of 200 There's just 10 watts. So we've got 10 watts or 10 jewels per second. I'm gonna write it that way because then we have to work with it in terms of jones. Now, part E. We need to figure out how many photons per tomato per second we're getting. So actually a little bit more ranks is kind of little bit of meth that I've got to do a little bit of calculation to show party. So the energy contained in a photon right this way East of New is given by plank's constant times the frequency. But frequency can also be written as speed of light divided by wavelength. And so when we do this, we plug all these values in Planck's constant. 6626 Times 10 to the negative 34th Time Speed of Light which is three times 10 to the positive 8th. And then we got to divide that by the wavelength which is very very small. 600 Times 10 to the -9. Is that the same? The others? And when we actually punch that into a calculator we get 3.313 times 10 to the negative 19 jewels 19. So that's how many jewels we have per photon. That's jules. Her photon not very much and that's kind of what we should expect. So now if we've got 10 jewels per second coming in then the number of photons which alright ends up news, it's going to be equal to 10 divided by the number we just found 3313 Times 10 to the -19. When you do that, you get 3.18 times tend to be What did I find? 10 to the 19th? Photons per second. That's photons per second. It's not fun. We're not having Vietnamese noodle soup here. Photons per second. Okay. Yeah, I guess if that was to be a little bit too much noodle soup for anyone. Three times 10 to the 19th. All right. So assuming that is than the total number of photons that are hitting this plant. Now, we we need to assume that only about half of those are actually going into uh actually making tomatoes. So we cut that in half right away. So the number we're interested in, We cut that in half and we get about 1.5 Times 10 to the 19th per second. Going to um Making tomatoes, but then there's 10 tomatoes. So that gets cut in half And we get one side doesn't get cut in half. We drop a power of 10. We divide that by 10 And we have 1.5 times 10 to the 18th photons per second per tomato, the middle one. Right? So that is that. So now part F. We need to figure out how many photons it takes total just to make a tomato. And the answer is a lot. I mean a lot, a lot calculated this earlier kind of a big number. Oh come on now, just trying to shrink all of this work down. If it will let me select it. There we go. Oh okay, whatever. We'll just move it up. All right, saddle away. Now, sometimes that's all you can ask for. What? S we are assuming We've got 30 killer cows, Which is 30 times 4,186 jewels. You get 125,580 jewels for a tomato. It's a lot of rules now, we need to take that and we need to divide it. So the number of photons down here, it's going to be given by this total amount of energy divided by the number of jules per photon. Because we want to get jules per tomato. I'm sorry, photons per tomato. So we're gonna take this big number, 125,580. We're going to divide it by the energy of a single photon. 3313 Ties down the neck of 19th. And so this number down below is jules per photon. A number of top is jules total. So when we do this, we're going to get a number of photons and we get 3.79 Times 10 to the 23rd photons. That's a lot of photons. So for part G. Now we want to know how long it takes to grow a tomato. So we're going to take that total number of photons found in part F. And we're going to divide it by the number of photons that we had per second per tomato. And we're going to find how many seconds it takes to grow tomato, then we can turn that into a number of days, weeks, whatever. So part G. We're really just taking the answer and F. And dividing it by the answer. Andy and then doing some unit conversions. So this turns into 3 7, 9 times 10 to the 23rd. That was photons per tomato divided by 1.5 times 10 to the 18th photons per tomato per second, That gives us 2.53 Times 10 to the 5th seconds. Yeah. Now if you want to convert that two hours, you simply take that number and divide it by 3600. And I find I found when I did this earlier that this is about 70 hours per tomato. And if the sun shining 12 hours a day, that's roughly six days to grow a tomato, I think that's a little bit faster than it happens. I have never grown tomatoes, never been on a farm of any kind. Um But six days sounds a little fast. If I had to guess the real problem was that my estimate of the area at a quarter metre squared was probably too big. It was probably too much area. I can't say by how much, but if the area where even just a quarter of that in actuality, then that would mean it would take four times as long to grow tomato, and I don't know about you. But 20, days to grow a tomato sounds more reasonable than six, so that's my feedback on that. But the rest of the problem is fine. The math itself works out. It's just that quarter square meter was probably too much, and that should complete it for you. Have a good one.


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