At a fabrication plant, a hot metal forging has a mass of 74 kg and a specific heat capacity of 430 J/(kg·C°). To harden it, the forging is quenched by immersion in 710 kg of oil that has a temperature of 32°C and a specific heat capacity of 3000 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.
To determine the initial temperature of the forging, we need to use the principle of conservation of energy, which states that the total energy of an isolated system remains constant.
The equation we will use is:
Energy gained by the forging = Energy lost by the oil
The energy gained by the forging can be calculated using the equation:
Energy gained = mass of the forging * specific heat capacity of the forging * change in temperature
Similarly, the energy lost by the oil can be calculated using the equation:
Energy lost = mass of the oil * specific heat capacity of the oil * change in temperature
At thermal equilibrium, the final temperature of the oil and the forging is the same. Therefore, the change in temperature for both is the same.
We are given the following values:
Mass of the forging (m1) = 74 kg
Specific heat capacity of the forging (c1) = 430 J/(kg·C°)
Mass of the oil (m2) = 710 kg
Specific heat capacity of the oil (c2) = 3000 J/(kg·C°)
Change in temperature (ΔT) = 47°C - initial temperature of the forging (T1)
Applying the conservation of energy principle, we can set up the equation:
m1 * c1 * ΔT = m2 * c2 * ΔT
Now we can rearrange the equation to solve for the initial temperature of the forging (T1):
T1 = (m2 * c2 * ΔT) / (m1 * c1)
Plugging in the given values, we can find the initial temperature of the forging.