Question

At a fabrication plant, a hot metal forging has a mass of 75 kg and a specific heat

capacity of 430 J/(kg?C°). To harden it, the forging is immersed in 710 kg of oil that has
a temperature of 32 °C and a specific heat capacity of 2700 J/(kg?C°). The final
temperature of the oil and forging at thermal equilibrium is 47 °C. Assuming that heat
flows only between the forging and the oil, determine the initial temperature of the
forging.
(5)

Answer 1

The initial temperature of the forging is 34.23 °C.

Step-by-step explanation:

To find the initial temperature of the forging, we can use the principle of heat transfer. The heat gained by the oil is equal to the heat lost by the forging. The equation for heat transfer is Q = m * c * ΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Let's calculate:

Q gained by oil = Q lost by forging

moil * coil * ΔToil = mforging * cforging * ΔTforging

Where moil is the mass of oil, coil is the specific heat capacity of oil, ΔToil is the change in temperature of the oil, mforging is the mass of the forging, cforging is the specific heat capacity of the forging, and ΔTforging is the change in temperature of the forging.

Substituting the given values:

(710 kg) * (2700 J/(kg•°C)) * (47 °C - 32 °C) = (75 kg) * (430 J/(kg•°C)) * (47 °C - x)

Solving for x, the initial temperature of the forging:

x = 34.23 °C

Answer 2

940°C

Step-by-step explanation:

Heat lost by the forging = heat gained by the oil

-mCΔT = mCΔT

-(75 kg) (430 J/kg/°C) (47°C − T) = (710 kg) (2700 J/kg/°C) (47°C − 32°C)

-32250 (47°C − T) = 1917000 (15°C)

47°C − T = -892°C

T = 939°C

Rounded to two significant figures, the initial temperature is 940°C.