Question

At a fabrication plant, a hot metal forging has a mass of 67.2 kg and a specific heat capacity of 438 J/(kg C°). To harden it, the forging is quenched by immersion in 786 kg of oil that has a temperature of 37.1 °C and a specific heat capacity of 2950 J/(kg C°). The final temperature of the oil and forging at thermal equilibrium is 58.3 °C.

Assuming that heat flows only between the forging and the oil, determine the initial temperature in degrees Celsius of the forging.

Answer 1

Tm = 1,728.38 °C

Step-by-step explanation:

mass of metal forging (Mm) = 67.2 kg

specific heat capacity of metal forging (Cm) = 438 J/kg°C

initial temperature of metal forging (Tm) = ?

final equilibrium temperature (Te) = 58.3 °C

mass of oil (Mo) = 786 kg

specific heat capacity of oil (Co) = 2950 J/kg°C

temperature of oil (To) = 37.1 °C

Mm × Cf × (Tm - Te) = Mo × Co × (Te - To)

Tm =
`(Mo x Co x (Te - To) )/(Mm x Cf)` + Te

Tm =
`(786 x 2950 x (58.3 - 37.1) )/(67.2 x 438)` + 58.3

Tm = 1,728.38 °C