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0.145 kg of water at 86.0°C is poured into an insulated cupcontaining 0.510 kg of ice initially at 0°C. How many kg of liquidwill there be when the system rea...

Question

0.145 kg of water at 86.0°C is poured into an insulated cupcontaining 0.510 kg of ice initially at 0°C. How many kg of liquidwill there be when the system reaches thermal equilibrium?

0.145 kg of water at 86.0°C is poured into an insulated cup containing 0.510 kg of ice initially at 0°C. How many kg of liquid will there be when the system reaches thermal equilibrium?



Answers

A $0.60 \mathrm{~kg}$ piece of ice at $14^{\circ} \mathrm{F}$ is placed in $0.30 \mathrm{~kg}$ of water at $323 \mathrm{~K}$. How much liquid is left when the system reaches thermal equilibrium?

So we can say that the amount of thermal energy lost would be equal to the mass of the water times a specific heat of water, times of change in temperature of the water and this would be equal to 0.25 kilograms times 4,190 Jules per kilogram per kelvin, and then this would be times 40 minus 75 degree Celsius, and we find that Q lost. It is going to be equal to negative 41,825 jewels and this is in cooling the water. That's almost there. Most. That's how much thermal energy must be extracted In order. Teo, bring down the water temperature. We know that the temperature the thermal energy gained from the ice is going to be equal to the negative. The thermal energy lost. So essentially, we can say that the mass of the ice initially is called the mass of the ice times thie specific heat of the ice. Time to change in temperature of the ice, plus the latest he of formation plus the specific heat of the water time. The change in temperature of the water would be equal to again Negative. Que los? So we would have the mass initial Ah, equaling negative Q lost. So 40 positive, 41,825 jewels. And then this would be divided by this entire term here. So we would have 21 100 for the specific heat of ice 21 100 jewels per kilogram per kelvin times 20 degrees Celsius because it started from at negative 20 degrees Celsius that I started at negative 20 degrees Celsius plus the latent heat of formation. So 334,000 and then plus 4,190 the specific e of water times again, that 40 degree, um, the 40 degree temperature increase and this is going to equal 6.74 times 10 to the negative two kilogram. Or we can simply say, um, rather this one. This is already sa units. So yeah, we would essentially keeping us kilograms. So that would be how much ice is needed in order to cool the water from 75 degrees Celsius to 40 degrees Celsius. That is the end of the solution. Thank you for watching

Everyone. This is question number 48 from Chapter 14. So this problem says that we have. We're given 0.25 kilograms of water. It's 75 degrees Celsius and then we have ice at minus 20 degrees Celsius. Ice is dropped into the water, the final temperature is 30 degree Celsius and we need to find the kilograms of ice that needs to be added in order to reach this 30 degrees Celsius mark. Okay, so tempter change. Once again, temperature change masses. He which means or he'd equation emcee Delta team. But we're also going to have a phase change here because the ice is melting. We know the boiling point. Excuse me. The melting point of freezing point of water is zero degrees Celsius and the ice is starting at minus 20. Gets to thirties. That means we're gonna have a face change. And that we know is Q equals he effusion because it's melting times mass and keep that equation in mind as well. So now we can write equations for our water in our eyes. So Q water master, your 0.25 kilograms, see for water for 0.19 times 10 to the third Jules for kilogram kay. And then temperature change. We're going. Our final is 30 degrees. Our initial 75 30 minus 75 is minus 45 and that equals minus 4.17 times 10 to the fourth, Jules. Okay, so now we go onto our eyes. So cute eyes. This is where it gets a little bit trickier. So we have three steps to this. We have the ice from minus 20 to 0 degrees, and then we have the melting process where the temperature doesn't change, and then we have zero degrees, 30 degrees. So we're gonna have three terms in this ice. We're going to take out mass because it's the same for everything. So then we have sea delta T for the first part, see, for water Mercy for I excuse me is 2.1 times 10 to the third Jules per kilogram. Kay, Our delta t for this one final is your degree. Celsius initials minus 20 0 Minus negative. 20 is going to give us 20 degrees Celsius. That's our first part. And then we have Plus, we took out em. So all that's left is the lf so heat of fusion for ice is 3.34 times 10 to the fifth Jules per kilogram. And then we have plus our last M Delta psi, which is, um, sea of water. Because at this point, we've melted. So 4.19 times 10 to the third Jules per kilogram Kay Oh, and then our delta t where are finalised 30 degrees our initial zero degrees. So it's 30 degrees Celsius. If you multiply the sell out and put it in the correct terms, you get m times massive the eyes times five times 10 to the fifth Jules per kilogram. Okay, so now we have our two terms. We have kyu vice. We have cubed water were told No heat lost. We can assume that. So the summation of this is going to be zero. So summation of cue of the system zero. So we can just set everything equal to zero that's going to give us I am I sw five times 10 to the fifth chills per kilogram minus four point 71 times 10 to the fourth. Jules equals zero. Add this over to the other side. Divide by this and we get massive ice needed equals 0.9 42 kilograms will supply that by 1,000 you get 94 point two grams.

So here we have heat throwing out of the water and into the ice. The minute he felt for the entire system is zero. The ice wants to zero degrees Celsius melts, and then the water from the mouth of haste warms from zero db Celtic's to the final temperature. First, we'll calculate queue for each component system and we neglect the mass off the beaker. So we use the equation Q Musical to emcee down to t Firstly for the water. So zero point 25 off water and this water cools from 75 degrees. Lt's 30 degrees Celsius. This water does not change face, so you never you do. You water is equal to em. See got to teach where m is the mass of the water. See in specific heat capacity and out TV change of temperature. So we have zero point 25 G's off water times specific heat capacity for 190 Jules Cagey Caliban multiplied by a change in temperature. Oh, 30 degrees Celsius minus its initial temperature of 75 defeat Celsius. Hence we get the heat loss by the water since the watch is now being cooled is for 0.71 four I'm standing before Jules. The negative sign implies the water flows out of the heat flows out of the water and into the ice. Next we'll calculate the heat gained by the ice as it warms to zero degrees Celsius melts, and then the water from amount of ice warms to 30 degrees Celsius. So here we have a slightly different equation. He came by the ice. Que is it too? The mass of ice will call it him. This is known times specific heat capacity off the ice, time out cheap. Thus the mass of ice him. I'm the latent heat a fusion in turning the ice into water, so we're going from a solid to a liquid phase. Thus this mess off ice which not turns to water that was the heat capacity of waters. He w times change in temperature to get to the final temperature over 30 degrees Celsius. So putting all of us to get that you get that this is M, which is the unknown. Massive ice to the specific keep propensity flies is 2000 100 Jules, her cagey Calvin times about T, which is zero minus minus, trying to decrease Celsius, which is anti southeast, Agrees. Fascinating effusion going from ice water is 334 instant be jurors. Okay, G plus specifically it off Water C W which is for And I know fuels, can't you, Calvin? Quantified by temperature change off 30 degrees Celsius minus eroding case lt's so the water that is melted goes from zero degrees Celsius. Been to the result is that temperature change off that Celtics degrees Doing this calculation without one are known We get the heat gained by the ice in terms of its mess is five when 01 seven by 0.17 Hence into the fire Jules K G multiplied by its mass in So now we have the heat game by the ice and the heat lost by the water there was actually in system. So what we do know is that you with the system is equal to zero NGS quotes out for this implies bet heat We don't want a close by the water and game by the ice must equal to zero. And so we put our values in here we get you w just minus four 0.71 full instant before Jules Best The answer for energy gained by the Ice with you, calculated five 0.17 I'm still the fire Jules changing I was mess him is equal to zero and hence we have an equation would not known. This is the mess we reached a soulful and therefore a mess of ice that needs to add into the system in order to achieve everything explained above is 0.0 94 jeez, So since the final temperatures 30 degree Celsius, we know that all the ice melts in the final systems. All liquid water, the mess of ice and it is much less than the mess off the 75 degrees Celsius water, and hence the ice acquires in large heat input for the face change.

So fast, every vehicle plate he lost. Why water when it's cooled from Or did you sell shares? Toe generally searches by using their relation cume equal toe mass time specific. You get arrested times. Gen. Jim from Britain. You're a mess of water is Do you know why? 33 kilogram in tow Specifications APIs Tear water is 41 and six. Do what are glued on or did. He says she is in tow. Genting Temperature water when interpreted of water is zero ready? Search Yes, minus initiative. Britain of Water is 14 degree sexual. This use us he released while water. When it goes equal, do minus 1.90 time 10 to the power for do now. In the second stuff, we will calculate required toe melt on the eyes air zero degree Celsius By using the relation que y is equal to mass times letting it a fusion here myself ices Zubair little 75 it all in tow Let it heat up food and for ices that it see point five times 10 to the power for doom What we grow. So excuse us. Here we go after meant all the eyes equals Do blue quite five times 10 to the power for do IHS magnitude off heat lost by water. Very cools Using listen magnitude off heat required to melt on eyes. So under what so on the eyes will not be converted into water so some part of ice will be convert into water. There's little big researches and other part of eyes. Other border of eyes. Windham in it. So did absolute beauty. So she is so the order. The richer off the system will be zero degree Celsius. Now here we want to complete Mais off the belt it eyes again by using the relation he released by water. But let us he absorbed by I meant it. Eyes is equal to zero. According Toa Laugh conversation off energy he released by water that is equal toe messa water time specific. It gave Mr Water into changing the brittle water unless he absorbed by advantage eyes as they really sections is equal to miss off. Many dies times letting you go Good. Yeah, disabuse us a little disc. Use us mess up magnetize equal toe minus into a mess off water Specifically give Mr Water into attended the ritual of water upon letter Udo who get no by police Defend release Here, Mr Water is zero point 33 kilogram suppressive. Give a still water is 41 Air six June parking ground party usages Genting temperature water is hear what is going from 14. Did researches toe really searches So financial prejudice The big associates man in Egypt and Pretty is fortunately searches upon letting it a fusion for water is 33.5 times 10 to the power for dual but it could go down. This gives us mess off. Mental ties equal to did acquire little five Double seven You never know. So this is a mess up made it. Why melted eyes began calculated Miss off unmilled it eyes that is equal to total mess of eyes minus miso melted eyes Yes, totally yourself. Vices zero point. They're 75 kilogram minus Mess up. Mend it Ices little pine 05 The wall seven Katie, this gives us mess off. Unwanted eyes Equal toe zero point 01 73 Gonna grow now in the second part of this problem. If our eyes new stupid meant then maybe you Defeat released by water should be able to He require Drew meant on the eyes so we can write. He released by order for less heat Require you meant on eyes. Is it going toe? Do you know? So here we want Oh, Google it initially on greater of water so that the ice meant zero degree Celsius He released by water. There is equal to messa water into suppressive PKK Mr Water into changing the original water. But let's he required Meant all the guys There is a photo makes off ice times. Let any doubt fusion he called potato. But I mean the friend with this here mess a water is zero point 23 Get a gram. The best we could give a still water is 4186. June. What is wrong? Bardi said she has here what it is called. Those interviews sections from initial temperature T I. A year final temperate. It is really such as minus initiative. Ritual of water is t I. And here we want to calculate the value off de I plus mess off ices zero point 075 kilograms in tow. Let any tax wiggin far Isis that it's you buy it five times into the power for do parking ground equal to zero. This gives us minus little fire Country Kilogram in tow. 41 Air six dune particle groom for release issues. Is he going toe minus? Do you know if I do a 75 kilogram in tow? That it's you? Point five times dented the power for dune butter. I did a little mistake here. Here, in the left hand side, there is a drunk day. All right. I mean, the next. Still we have You should come pretty. The water equal to minus 0.75 kilograms in tow. Started. See, Fine. 5 10 10 To the power four. June. But it on. Do I buy minus little point Gentry, Get it wrong. Into 416 Do part wrong. Barghouti said she is so here. Minus and minus. You can sell from new murder. Really matter. Disc, Use us. Initial completed off water equal to 18 duty. So she is so that imprinted off the initiative. Britain Water must be 18. The decision is to melt on the eyes


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