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Numerade Educator

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Problem 40 Hard Difficulty

In a container of negligible mass, 0.200 kg of ice at an initial temperature of -40.0$^\circ$C is mixed with a mass m of water that has an initial temperature of 80.0$^\circ$C. No heat is lost to the surroundings. If the final temperature of the system is 28.0$\circ$C, what is the mass m of the water that was initially at 80.0$^\circ$C?

Answer

$0.491 \mathrm{kg}$

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Video Transcript

since there is no hit loss from the system. Therefore, uh, Kim Total pure toto is equal to, uh, Kim for ice plus Q. For water is equal to zero. No, let's calculate pew for ice UH, which is equal to muscle fais times. Specifications capacity off ice Multiply delta T So moss off ice times our specifications Capacity of ice times Delta T Delta T for ice less must suffice times lightened heat of fusion, which is l Yeah, A laugh is the Latin T to fusion plus must suffice. Multiply by multiply by, Ah, spastic heat off water Multiply by down toe t doubt a T. It's for melted, so it's important down titty for melted All right, not bloodied values we get fuel for eyes is equal to ah zero point two. Multiply by ah specifications. Capacity for honesty's, uh, 1100 jewels. Particular Graham or decree sent a great that's 2100 Multiply by Delta T. Change in temperature is ah plus 40 Decrease Santa. Great, since it's changing temperature zero minus into minus 40 which is equal to bless 40 40 degree centigrade, so change in temperature is 40 degrees centigrade. bliss began 0.2 witches Marcel Vice multiplied by, um 33.4 multiplied Return to the bower four. Multiply by 33 point four, multiplied by 10 to the power for 10 to the power four. Right plus no Marcel vice is again 0.2. Is that your point? Two. Multiply by, ah, spastic. Eat off water, which is 4192 per kilogram per degree centigrade. It's for one mind. Zero Multiply by and delta T it's Ah, 20. Do It's Andy Reid 10 which is torture. So solving this weekend kun for eyes is equal to at one point 004 Multiply by 10 to the power flying Jules. All right. No, let's calculate Q for the water date, which is a mosque m and it's camp rate. Your drops from 80% agreed 20 degrees centigrade. So queuing for water is equal to Marcel. Water multiplied by specific Ito water multiplied by Delta T and Delta T is changing temperature. The delta T is change in temperature. So putting the values we have, uh, you for water is a cold too. Okay, Well, um, first of all, let's would value of specific You could best you off water which is equal to 4190 So am multiply by 4119 multiply by delta t So here, del titties. 20 degree centigrade, minus 80 degree sandy graves. Therefore, your W is equal to minus do by phone. Sorry, that's my gas minus two 514 Double zero Jule part kilogram Multiply by moss No, to get the mosque and substitute for killing water and kill ice. So doing so we get one point 004 multiplied by monk 1004 multiplied by 10 to the power five. Fine. Bless into minus 251400 Multiply thy and is equal to zero and solving for m we have m is equal to, um one point 004004 multiplied by 10 to the power five divided by 251 double four double zero. And this is a cool too 0.399 kilograms. Zero point tree nine mine kilograms. Which is our answer. End of the problem. Thank you for Ji