An aluminum saucepan with a diameter of 18 cm and a height of 6.0 cm is filled to the brim with water. The initial temperature of the pan and water is 19°C. The pan is now placed in a refrigerator and cooled to 9°C.
Calculate the drop in water level in the pan.
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To calculate the drop in water level in the pan, we first need to determine the change in volume of the water when it is cooled from 19°C to 9°C.
To do this, we can use the formula:
△V = βV₀(△T)
Where:
△V is the change in volume
β is the volume expansion coefficient of water (approximately 0.00021/°C)
V₀ is the initial volume of water
△T is the change in temperature
The initial volume of water is equal to the volume of the pan, which can be calculated using the formula for the volume of a cylinder:
V₀ = πr²h
Given that the diameter of the pan is 18 cm, the radius (r) will be half the diameter, so r = 9 cm = 0.09 m. The height (h) of the pan is 6.0 cm = 0.06 m. Plugging these values into the formula, we get:
V₀ = π(0.09)²(0.06)
Next, we can calculate the change in volume:
△V = (0.00021/°C) * V₀ * (19°C - 9°C)
Now we can substitute the calculated values into the equation to find △V.
Finally, the drop in water level in the pan can be determined by dividing the change in volume (△V) by the area of the base of the pan.
Drop in water level = △V / (πr²)
Substitute the values to calculate the drop in water level in the pan.