Calculate the freezing point of water at a depth of 10.0 cm below the surface of the water. The density of the water is 0.9998 g/cm3.
To calculate the freezing point at a particular depth below the surface of water, you need to take into account the effect of pressure on the freezing point of water. The pressure increases with depth due to the weight of the water above.
Here's how you can calculate the freezing point at a depth of 10.0 cm:
Step 1: Convert the depth from centimeters to meters.
To convert from centimeters to meters, divide the depth by 100.
10.0 cm ÷ 100 = 0.10 meters
Step 2: Calculate the increase in pressure.
The increase in pressure is given by the density of water multiplied by the acceleration due to gravity (9.8 m/s^2) and the depth.
Pressure increase = density × acceleration due to gravity × depth.
Pressure increase = 0.9998 g/cm^3 × 9.8 m/s^2 × 0.10 m
Step 3: Convert the pressure increase to pascals.
To convert from grams per cubic centimeter (g/cm^3) to kilograms per cubic meter (kg/m^3), divide by 1000.
Pressure increase (in kg/m^3) = 0.9998 g/cm^3 ÷ 1000 = 0.9998 kg/m^3
Now, we can calculate the freezing point depression using the formula:
Freezing point depression = Pressure increase ÷ (density of water × heat of fusion)
Step 4: Determine the heat of fusion of water.
The heat of fusion of water is 334,000 J/kg
Step 5: Calculate the freezing point depression.
Freezing point depression = 0.9998 kg/m^3 ÷ (0.9998 g/cm^3 × 334,000 J/kg)
Now, we can calculate the freezing point at a depth of 10.0 cm below the surface of water.
Step 6: Add the freezing point depression to the normal freezing point of water.
Normal freezing point of water = 0°C (273.15 K)
Freezing point at a depth of 10.0 cm below the surface of water = 0°C - Freezing point depression
After performing the calculations, you will have the freezing point at a depth of 10.0 cm below the surface of water.