Theoretical max. pressure of a given quantity of water freezing to ice

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SUMMARY

The maximum pressure exerted by freezing water can be calculated using the relationship between force and area, specifically applying the equation P = F/A. At a temperature of 263.15 K, the density of ice is 0.9 g/cm³ and the density of water is 1.0 g/cm³. Assuming 1 mole of water, the volume of ice formed is 20 cm³, leading to a change in volume (ΔV) of 2 cm³. To determine the pressure, one must relate the change in volume to the force exerted by the expanding ice, which requires knowledge of the area over which this force acts.

PREREQUISITES
  • Understanding of basic thermodynamics, specifically phase changes of water.
  • Familiarity with the concepts of pressure, force, and area in physics.
  • Knowledge of the ideal gas law and molar volume calculations.
  • Basic algebra for manipulating equations related to pressure and volume.
NEXT STEPS
  • Study the relationship between pressure and volume in phase changes of water.
  • Learn about the physical properties of ice and water at various temperatures.
  • Explore the concept of pressure in fluids and its applications in geological processes.
  • Investigate the mathematical derivation of pressure equations in thermodynamic systems.
USEFUL FOR

Students in physics or environmental science, geologists studying erosion processes, and anyone interested in the physical properties of water and ice.

anisotropic
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Homework Statement



Water in rock crevices often causes erosion when it freezes, given it expands and exerts pressure on the rock. What is the maximum pressure that water can exert when it freezes?

T = 263.15 K
dice @ 263.15 K = 0.9 g cm3
dwater @ 263.15 K = 1.0 g cm3

Homework Equations



Force = Pressure x Area

Perhaps?...

The Attempt at a Solution



Assuming 1 mole of water, the volume of the ice would be 20 cm3 (ΔV = 2 cm3).

I don't know how to relate the change in volume to the pressure exerted, though. It's not like I know the geometry of the water and how much area it has to be able to use the equation in 2. Nor do I know how to determine the force exerted by the water as it expands (I know how much mass is being displaced, but don't know how to determine it's acceleration, assuming I need to use Force = Mass x Acceleration).
 
Last edited:
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anisotropic said:
P = force x area

That's wrong.

Not that it changes anything.
 

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