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