Phileas Fogg, the character who went around the world in 80 days, was very fussy about his bathwater temperature. It had to be e
xactly 38.0o C. You are his butler, and one morning while checking his bath temperature, you notice that it’s 42.0oC. You plan to cool the 100.0 kg of water to the desired temperature by adding an aluminum-duckie originally at freezer temperature (-24.0oC). Of what mass should the Al-duckie be? [Specific heat of Al = 0.900 J/(goC); density of water =1 .00 g/ml]. Assume that no heat is lost to the air
Given that no heat is lost, all the internal energy that the water loses while cooling down will transfer to the duckie. So, if the duckie has ΔU = 1674 KJ and its final temperature is the desired 38 ºC, we can calculate its mass using the first law again: