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Numerade Educator

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Problem 58 Hard Difficulty

One end of an insulated metal rod is maintained at 100.0$^\circ$C, and the other end is maintained at 0.00$^\circ$C by an ice-water mixture. The rod is 60.0 cm long and has a cross-sectional area of 1.25 cm$^2$. The heat conducted by the rod melts 8.50 g of ice in 10.0 min. Find the thermal conductivity $k$ of the metal.

Answer

$227 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$

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Video Transcript

we know that heat current floor etch uh ohh is equal to Delta Q. Divided by del titty. And this is a cool, too kid times, which is a thermal conductive ity. Time's A, which is 80 off cross section dimes P H, which is high temperature minus two cold, divided by limp. Oh, all right. And we also know from the table they l f now, which is the light and heat is equal to 334. Multiply by tend to the power free Jules per kilogram and, uh, we have each for ice is equal to kun for eyes divided by time on this is a call to soaking for ice can be written these Marce off ice times l f divided by teeth on. After plugging the values, we get inch for ice. Yeah, four Eyes is equal to 8.5 1st awful mass, which is 8.5 multiplied by 10 to the power minus three minus AA minus tree into, uh, we have so and it's equal to tree 34 multiplied by 10 to the power tree. It's train divided by derided by land on DDE link. It's not length Rather, it's, uh t sorry, it's Steve, which is equal to can Multiply by Ah, 60 seconds since physical to 10 minutes Phone. We have 10 multiply every 60 seconds and this is equal to sold. This we have itch for Eyes is equal to 4.732 wars. Four. Find 732 what and what is also Jules per second. So at four eyes is 4.732 boats on duh! Again, we have actually equal to actually cool, too. Delta kun divided with Delta t and this is equal to key times eight times d h minus t c divided by how limp I know sold ing for key. We have Kay's equal to, um, and resold for Can we have? Oh, kid tour is equal to etch divided by 80 off prosection times D h minus d. C divided by now, and this is equal to h times l divided by hey into two at minus D. C. Let's put the values. Therefore, K is equal to much, which is four point 732732 Jew per second length is equal to 0.6 meters, uh, divided by any off cross section A, which is 1.2 fine. Multiply by 10 to the power minus before major square into 100 minus zero Cowan And this is Nicole. To simplify this, we get to do seven point 136 Watch launch far meter, but accounting. End of the problem. Thank you for watching.