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Basketball player does 45x105 J of work during her time in the game and evaporates 0.120 kg of water: Assume latent heat of 2.26 x 106 J/kg for the perspiration (th...

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Basketball player does 45x105 J of work during her time in the game and evaporates 0.120 kg of water: Assume latent heat of 2.26 x 106 J/kg for the perspiration (the same as for water) .Part ADetermine the change in the player's internal energy:AZdBSubmitRequest AnswerPart BDetermine the number of nutritional calories the player has converted to work and heat:AEdAUIkcalSubmitRequest AnswerAU

basketball player does 45x105 J of work during her time in the game and evaporates 0.120 kg of water: Assume latent heat of 2.26 x 106 J/kg for the perspiration (the same as for water) . Part A Determine the change in the player's internal energy: AZd B Submit Request Answer Part B Determine the number of nutritional calories the player has converted to work and heat: AEd AUI kcal Submit Request Answer AU



Answers

A basketball player does $2.43 \times 10^{5}$ J of work during her time in the game, and evaporates $0.110 \mathrm{kg}$ of water. Assuming a latent heat of $2.26 \times 10^{6} \mathrm{J} / \mathrm{kg}$ for the perspiration (the same as for water), determine (a) the change in the player's internal energy and (b) the number of nutritional calories the player has converted to work and heat.

I guess I'm doing problem seven from Chapter 18 and it tells us the basketball player is doing a certain amount of work during her time in the game. And she's evaporating a certain amount of perspiration and were asked to determine the change in the players, internal energy and the number of nutritional calories the player has converted to work in heat. OK, so using our equation for internal energy changing internal injury, tell Tus Cumin w right. There are two parts of this is the cue, the heat from evaporating water. And there's the work just done by the player in the game. Okay, so the signs on both of these are going to be negative because it's it's all energy flowing out of the system. Okay, so it's important to remember that. So, delta, you should be a big negative number. So using the the numbers were given, we can compute this. So we put in 0.151 kilograms for em and 2.26 times 10 to the sixth Jules per kilogram for LV, the latent heat of vaporization. We should get something like, uh, negative 822 killer Jules. Okay, So this is the answer for part A, and it should be negative because all both both the heat and the work are going away from the system. And so this leads to a large negative change in internal energy. So then, for Part B were asked to compute the the number of nutritional calories the player has converted to work in heat. In other words, the number of calories of the players burned. So in order to do that, we take 100 20 to kill Jules. I mean, this is just a simple conversion. So you just need to know the conversion from calories to kill Jules and their 4.186 killed Jules per calorie. So did then just divide 196 calories, and that's your final answer.

Hello and welcome to digital tea with mystery, where we will see what's brewing in the world of physics solutions. So in this particular problem, we have a basketball player who is running around playing basketball for a full hour, and in that hour they have an average of, um, a power exertion of 30 watts. So, um, this is a very active person as they average, you know, 30 jewels per second used each hour. Um, so in the diagram, I have the person dribbling a basketball and a bunch of blue dots. If you're running with the blue dots is, it's what naturally happens to basketball players. When they put out a lot of exertion, they sweat. In fact, basketball players sweat a lot. So at any rate, this person is perspiring. You may wonder, why does somebody sweat when they do a lot of work? Well, the answer is simply this. The body puts out the water onto the surface of the skin. Then the heat that is being generated by the body and doing all that work is utilized to Vape arise that water and then put it off into the atmosphere. So, as a result, you can think of the human body as a heat engine and it's using, um uh, it's heat to evaporate the water, thus carrying heat away from the body, hence making the body, uh, stay cooler. So the sweat itself doesn't cool you down. It's the evaporation of that sweat that cools down. So what are we trying to find in this problem? Well, uh, probably the most disgusting thing we confined. How much mass of sweat will be vaporised by this person as they play basketball for an hour? So let's start off first with a time of being one hour, Um, change at the 3600 seconds. How you do that, You might ask. You simply multiply 60 seconds in a minute. Time. 60 minutes in an hour together and you get 60 times 60 or 3600. And then I have the latent ah, heat of vaporization for water listed there, a 2.26 times ended the six jewels per kilogram. So let's figure out how much work this person does this start. Um so power is equal to work overtime, so the work will equal the power multiplied by the time so if we take our power of 30 wants and we multiply it by 3600 seconds to get a total of 108 fouls and jewels of work is done in playing basketball for an hour now, over into determining how much masses of sweat that's going to be evaporated are evaporated off, you'd want to say that that work causes the body to heat up, so W is going to equal cute and it's being vaporized. Therefore, the work is going to equal to the latent heat equation of M. L. So solving for mass is simply a case of taking the work, dividing it by the latent heat of fusion are vaporization. The mass of the water mass of water will be equal to We'll take that 108,000 jewels of work that we figured out and divided by the latent heat of vaporization of 2.26 times ended 26 jewels per kilogram, and it gives us a total of 0.5 kilograms. So about 50 grams s, so to speak of water ah will be evaporated in that hour. You know, you shouldn't have to wonder anymore. Why? One needs to drink plenty of fluids in the time outs and basketball is. What you're doing is you're replacing the water and some other chemicals as well, um, into the body so that they can continue to sweat out sweat. Hey, thanks for learning with me. I certainly enjoyed learning with you.

When we lift her, does he work off 1.4 times 10 to the power, five jewels in lifting wears. Then it loses 0.15 kilogram a water through your operation. So the u masa water equal to 0.15 Get it on. We're done by way. When Lifter is 1.4 times standard of our five, you'll little hit off the opposition off perspiration is Duke. My photo. Diane's tended a bower. Six you'll, but a kilogram. Now in the first part, we want to calculate standing internal energy off the weird lifter by using the relation. No, Didn't veto position equal to total heat upon mess from here. Reveal hit equal toe mass times leading youto position Here, Ms of last Water is a little quiet 15 Laurent times letterhead off opposition is two by 42 times ended up our six dual bar Katie So v hell hit the choir for reposition a water equal to three point 63 dimes. Tended a power five. You're nobody using fossil off term dynamics. We helped you equal to W. Poulos Delta You now, by putting different values in the relation ISS he do? So lost. Bye lifter doing position. Ah, water. So you will be in negative that this man its report 63 dimes tended a bow or five You are Is it called Tau Wagon by lifter is 1.4 times Kendra Power five dune plus judging internal energy. So we have 20 internal energy equal to minus 3.63 I am standing up our 5 June minus 1.4 times 10 to the power five. You're so the hill Genting Internal Energy equal to minus 5.3 dimes tender power five You begin right. It is minus five Little tree Diame's tended upon what tree, Jule? Which is it called? Toe minus 5 to 3 Gilou. Yo. So this is the judging internal energy off the lifter. Hear Negative sign shows there Intelligent energy off The lifter is decreasing. No, in the second, but we want to calculate number of minimum nutritional galleries s one a nutritional Guillory, physical toe. 14 head six. You're by using the relation number off and your additional calories. Equal toe. Total loss off internal energy upon upon number. Abdul's inn one nutritional Hillary s the magnitude off total loss of internal energies. 55 dilip three times ended up our five. You upon your scene one nutritional calories, 41 air six you're so after dividing these two numbers, we have answer equal to 1.2 times tended a power two. So this is ah, minimum number. Off nutritional calories are food that must be consumed to replace the last off internal energy.

So here we're going to do an interesting back the envelope calculation. Um So let's suppose that a professional basketball player generates 300 watts as power. Okay, so that is a power that's doing useful work during the game. And we're going to ask how much it heat gets exhausted from their body. And furthermore, a more interesting question is how much perspiration could they vapor eyes? Uh How much perspiration could they vaporize? So, sort of an interesting calculation, which, well, let us know why you have to drink a lot of fluids while you're doing such an activity. So we are told that this power is generated at 15% capacity, Um 15% efficiency. Um and we want to know how much perspiration is vaporized in one hour. So let's say that this person could keep up their activity Fully for one hour. So, we want to start with the definition of efficiency of a heat engine is the amount of work produced divided by the amount of heat absorbed and to conserve energy. That work is the difference between the heat absorbed minus the heat exhausted. And these are of course absolute values. Um Okay, so we can start off and let's assume we're thinking about um Just the power of course everything could have time dependence on top of it. So what I mean by that dot is take a a jewel and turned it into a jewel per second or a lot. Okay, so we can do the same with our efficiency And using are 15% efficiency. Um We can Use our work of 300 lots and solve for the amount of heat absorbed. And we find that to be 1700, That's it. 2000. Let me take this one step at a time. My napkin is getting a little cd. Looking here, we go back at the envelope here. Um let's see it. So that is 2000 watts. And then now we know that that amount of wattage minus the exhaust wattage is equal to the useful work done power in the work anyway. And so we can solve for the time rate of change that of energy that's going into the exhaust. Okay, so look at this. Um it means that most of the energy that this person is using is going into exhaust heat. And we probably realize that as to be true um from our own personal experience. So in one hour, what we want to do is take this power in watts. That news power equals A Q. Over delta T. He'd expelled unit time and delta T. In this case is one hour or 60 squared seconds. And we can solve for the exact amount of heat exhausted 1700 What's Times 3600 seconds. So yeah, an enormous amount of exhaust heat. Okay, now, to figure out the amount of um, perspired, we're going to make a very big assumption that all of that exhausted heat goes into, uh, evaporating perspiration. And that's not quite true. There are other ways for the body to dissipate that heat through radiation and conviction, assuming there's fans blowing in the gym, et cetera. Um, but we're gonna go ahead and assume that that q exhaust all of it goes to paper eyes, your sweat. That's sort of a weird phrase right there vapor I sweat. Um, So we're going to use, uh, that the heat goes into the massive sweat times. Elite latent heat of vaporization of sweat. And will make the further assumption that that latent heat is the same as for water, sweat is mostly water. Yeah, yeah, there's some salts in there. Um, but we'll go ahead and make that assumption and then we can solve for the mass. Yeah. And it's a very surprising amount. It's close to three kg Or close to £6. So that may help explain why people who are doing lots of physical activity need to drink a lot of water um And you actually can lose water weight when they're doing physical activity.


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