# Question 1dfc5

Mar 29, 2014

The Al duckie should have a mass of 75.0 kg.

There are two heats involved here:
a. the heat gained by the warming duckie.
b. the heat lost by the water as it cools down.

The fundamental equation is

heat gained by duckie + heat lost by water= 0

In symbols, q₁ + q₂ = 0

m₁c₁∆T₁ + m₂c₂ΔT₂ =0

ΔT₁ = T₂ - T₁ = (38.0 – (-24.0)) °C = 62.0 °C
ΔT₂ = T₂ - T₁ = (38.0 – 48.0) °C = -10.0 °C

m₁ × 0.900 J•g⁻¹•°C⁻¹ × 62.0 °C
+ 100 000 g × 4.184 J•g⁻¹•°C⁻¹ × (-10.0 °C) = 0

55.8 m₁ J•g⁻¹ - 4.18 × 10⁶ J = 0

m₁ = (4.18 × 10⁶)/(55.8 g⁻¹)# = 75 000 g =75.0 kg

The mass of the Al duckie should be 75.0 kg.