Question

A blacksmith heats a 1,540 g iron horseshoe to a temperature of 1445°c before dropping it into 4,280 g of water at 23.1°c. if the specific heat of iron is 0.4494 j / g °c, and the water absorbs 947,000 j of energy from the horseshoe, what is the final temperature of the horseshoe-water system after mixing

Answer 1

Given:
m₁ = 1540 g, mass of iron horseshoe
T₁ = 1445 °C, initial temperature of horseshoe
c₁ = 0.4494 J/(g-°C), specific heat

m₂ = 4280 g, mass of water
T₂ = 23.1 C, initial temperature of water
c₂ = 4.18 J/(g-°C), specific heat of water
L = 947,000 J heat absorbed by the water.

Let the final temperature be T °C.
For energy balance,
m₁c₁(T₁ - T) = m₂c₂(T - T₂) + L
(1540 g)*(0.4494 J/(g-C))*(1445-T C) = (4280 g)*(4.18 J/(g-C))*(T-23.1 C) + 947000 J
692.076(1445 - T) = 17890(T - 23.1) + 947000
10⁶ - 692.076T = 17890T - 413259 + 947000
466259 = 18582.076T
T = 25.09 °C

Answer: 25.1 °C