Question

Phileas Fogg, the character who went around the world in 80 days, was very fussy about his bathwater temperature. It had to be exactly 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

Answer 1

The mass of the Al-duckie should be 30 kg.

Step-by-step explanation:

We will use the first law of thermodynamics:

ΔU = m·Cv·ΔT

Since the specific heat of water is 4.185 J(gºC), the change in the water's internal energy would be:

ΔU = 100 kg · 4.185 J(gºC) · (42ºC - 38ºC) = 1674 KJ

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:

`m=\frac{\Delta{U}}{Cv{\Delta{T}}}=(1674)/(0.9*[38-(-24)])=30Kg`