An aluminum vessel with a volume capacity of 530 cm3 is filled with water to the brim at 20.0°C. The vessel and contents are heated heated to 42.5°C. During the heating process, will the water spill over the top (in this case the answer would be positive), will there be more room for water to be added (the answer would be negative), or will the water level remain the same? Calculate the volume of water that will spill over or that could be added.
To determine whether the water will spill over, remain the same, or allow more room for water to be added, we need to consider the expansion of water due to heating.
To calculate the volume of water that will spill over or that could be added, we need to calculate the change in volume of water when it is heated from 20.0°C to 42.5°C.
Water has a coefficient of volume expansion of approximately 0.00021/°C. This means that for every degree Celsius increase in temperature, the water expands by approximately 0.00021 times its original volume.
First, let's calculate the change in temperature:
Change in temperature = Final temperature - Initial temperature
= 42.5°C - 20.0°C
= 22.5°C
Now, let's calculate the change in volume of water:
Change in volume = Coefficient of volume expansion * Original volume * Change in temperature
= 0.00021/°C * 530 cm3 * 22.5°C
Simplifying,
Change in volume = 0.00021 * 530 * 22.5 cm3
= 249.225 cm3
Since the volume of the vessel was already filled to the brim, any increase in the volume of water due to expansion will cause the water to spill over.
Therefore, the water will spill over, and the volume of water that will spill over is approximately 249.225 cm3.