Answer:
T = 40.08 °C
Step-by-step explanation:
Given:
m₁ = 0.33 kg, mass of iron horseshoe
T₁ = 693°C, initial temperature of horseshoe
c₁ = 448 J/(g-°C), specific heat
m₂ = 24 kg, mass of water
T₂ = 39°C, initial temperature of water
c₂ = 4186 J/(g-°C), specific heat of water
let T be the equilibrium temperature.
For energy balance,
m₁c₁(T₁ - T) = m₂c₂(T - T₂)
(0.330) * (448) * (693 - T) = (24) * (4186) * (T - 39)
147.84 * (693 - T) = 100,464 * (T - 39)
102,453.12 - 147.84T = 100,464T - 3,918,096
102,453.12 + 3,918,096 = 100,464T - 147.84T
4020549.12 = 100316.16T
T = 40.08 °C