How to Calculate the Pressure Necessary to Lower the Freezing Temperature of Water to -10.000°C?
Understanding the Pressure and Freezing Temperature Relationship
The freezing temperature of water is typically 0°C at atmospheric pressure. To lower the freezing temperature, pressure must be applied. The relationship between pressure and freezing temperature is governed by the Clausius-Clapeyron equation. This equation states that the pressure change is proportional to the change in temperature divided by the enthalpy of fusion.
Assuming the enthalpy of fusion is constant, we can set up a proportion to solve for the necessary pressure needed to lower the freezing temperature to -10.000°C.
Given the densities of water (0.917 g/cm³) and ice (1.000 g/cm³), we can convert the pressure to approximately 1,121 atmospheres (atm) for the desired temperature decrease.
Calculation Steps for Determining the Pressure
1. Convert the densities of water and ice to kg/m³:
ρwater = 0.917 * 1000 = 917 kg/m³
ρice = 1.000 * 1000 = 1000 kg/m³
2. Convert the calculated pressure to atmospheres (atm) using the formula:
∆P = (∆Hfusion * ∆T) / 10.000
3. Substitute the known values into the equation:
∆P = (∆Hfusion * (-10.000)) / (10.000 * 1.013 * 105 Pa)
4. Calculate the pressure (∆P) in atmospheres:
∆P ≈ 1,121 atm