Answer:
<em>The initial temperature of the metal is = 938.63 °C</em>
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.
<em>Given: c₁ = 430 J/kg.°C, m₁ = 75 kg, c₂ = 2700 J/kg.°C, m₂ = 710 kg, T₂ = 32°C, T₃ = 47 °C</em>
<em>Substituting These values into equation 2,</em>
<em>T₁ = [2700×710×(47-32) + 430×75×47]/(430×75)</em>
<em>T₁ = (28755000+1515750)/32250</em>
<em>T₁ = 30270750/32250</em>
<em>T₁ = 938.63 °C</em>
<em>Thus the initial temperature of the metal is = 938.63 °C</em>
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