At a fabrication plant, a hot metal forging has a mass of 84.5 kg and a specific

Question

At a fabrication plant, a hot metal forging has a mass of 84.5 kg and a specific heat capacity of 442 J/(kg C°). To harden it, the forging is quenched by immersion in 751 kg of oil that has a temperature of 26.5 °C and a specific heat capacity of 2810 J/(kg C°). The final temperature of the oil and forging at thermal equilibrium is 51.0 °C. Assuming that heat flows only between the forging and the oil, determine the initial temperature in degrees Celsius of the forging. Please show all steps!!!!

Explanation / Answer

Assuming that heat flows only between the forging and the oil, the initial temperature in degrees Celsius of the forging which is given as ::

Heat from metal forging = Heat absorbed by an oil

mf Cf (T0 - Tf) = mo Co (Tf - Ti)

where, mf = mass of the metal forging = 84.5 kg

Cf = specific heat capacity of forging = 442 J/kg 0C

mo = mass of the oil = 751 kg

Co = specific heat capacity of an oil = 2810 J/kg 0C

initial temperature of the oil, Ti = 26.5 0C

final temperature of the oil and forging at thermal equilibrium, Tf = 51 0C

inserting all these values in above eq.

(84.5 kg) (442 J/kg 0C) (T0 - 51 0C) = (751 kg) (2810 J/kg 0C) [(51 0C) - (26.5 0C)]

(37349 J /0C) (T0 - 51 0C) = (51702595 J)

(37349 J /0C) T0 - (1904799 J) = (51702595 J)

(37349 J /0C) T0 = (53607394 J)

T0 = 1435.3 0C

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