A rod made from a particular alloy is heated from 22.0°C to the boiling point of water. Its length increases by 8.15 10-4m. The rod is then cooled from 22.0°C to the freezing point of water. By how much does the rod shrink?
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 find out how much the rod shrinks when cooled from 22.0°C to the freezing point of water, we need to know the coefficient of linear expansion (α) of the alloy.
The equation for thermal expansion is given by:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L0 is the initial length of the rod
ΔT is the change in temperature
Since we are interested in the change in length when cooled, the change in temperature would be the difference between the initial temperature (22.0°C) and the freezing point of water (0°C).
Let's assume we have the value of α for the alloy, we can proceed with the calculation.
1. Calculate the change in length when heated:
ΔL1 = α * L0 * ΔT1
Where ΔT1 is the change in temperature from 22.0°C to the boiling point of water.
2. Calculate the change in length when cooled:
ΔL2 = α * L0 * ΔT2
Where ΔT2 is the change in temperature from 22.0°C to 0°C (freezing point of water).
3. The rod's shrinkage when cooled would be the difference between the two changes in length:
Shrinkage = ΔL2 - ΔL1
To find the value of α for the alloy, you would need to refer to a material properties table or consult the specifications of the particular alloy.