At a fabrication plant, a hot metal forging has a mass of 75kg and a specific heat capacity of 430 J / (kg. C°). Toharden it, the forging is immersed in 710 kg of oil that has atemperature of 32 °C and a specific heat capacity of 2700J / (kg. C°). The final temperature of the oil and forgingat thermal equilibrium is 47 °C. Assuming that heat flowsonly between the forging and the oil, determine the initialtemperature of the forging.

The initial temperature of the metal is = 938.63 °C

Explanation:

Heat lost by the metal = heat gained by the oil.

c₁m₁ (T₁-T₃) = c₂m₂ (T₃-T₂) ... equation 1

making T₁ the subject of the equation.

T₁ = [c₂m₂ (T₃-T₂) + c₁m₁T₃]/c₁m₁ ... Equation 2

Where c₁ = specific heat capacity of the metal, m₁ = mass of the metal, c₂ = specific heat capacity of oil, m₂ = mass of oil, T₁ = initial temperature of the metal, T₂ = initial temperature of the oil, T₃ = Equilibrium temperature.

Given: c₁ = 430 J/kg.°C, m₁ = 75 kg, c₂ = 2700 J/kg.°C, m₂ = 710 kg, T₂ = 32°C, T₃ = 47 °C

Substituting These values into equation 2,

T₁ = [2700*710 * (47-32) + 430*75*47] / (430*75)

T₁ = (28755000+1515750) / 32250

T₁ = 30270750/32250

T₁ = 938.63 °C

Thus the initial temperature of the metal is = 938.63 °C