Hmwk Problem 8.91

[Nasir_Ahmed]

I understand in this problem when you assume it took 10 hrs for the ice to melt, but in the solutions manual it says to divide 10 hrs by the half hour it took for the water to reach 5 degrees Celsius and then multiply it by the 3135 J it took to get it there...my question is, why do we divide the 10 hrs by the half hour? I feel like there's an easy explanation but I can't think of it. Thanks.

[Jessica Huang 1M]

Well, the water took 0.5 hours and 3135 J. The problem is saying that the ice took 10 hours to melt.

There are 20 half hours in the period of 10 hours. In 1 hour, there are 2 half hours. (10 hours)*(2 half hours/1 hour)= (10 hours/ 0.5 hours) = 20 half hours.

Water took 3135 J in half an hour. Ice would need 20 half hours. 10 hours/ 0.5 hours = 20 half hours.
3135 J * 20