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Chapter 18: Problem 45

Solid water (ice) is slowly warmed from a very low temperature. (a) What minimum external pressure \(p_{1}\) must be applied to the solid if a melting phase transition is to be observed? Describe the sequence of phase transitions that occur if the applied pressure \(p\) is such that \(p

Short Answer

Expert verified
The minimum external pressure \(p_{1}\) for melting phase transition is 1 atm, under which the ice will sublimate. The maximum pressure \(p_{2}\) for boiling transition is 217.7 atm, under which water will be in supercritical fluid state. If the pressure \(p\) is such that \(p_{1}<p<p_{2}\), ice will first melt to water and then to steam before becoming a supercritical fluid.

Step by step solution

01

Analyzing under minimum external pressure \(p_{1}\)

The minimum external pressure that must be applied to solid water for a melting transition to occur is 1 atmosphere (atm). This is because at 1 atm and 0掳C, ice starts to melt and become liquid water.
02

Phase transitions for \(p

When pressure \(p\) is less than minimum pressure \(p_{1}\) for melting (1 atm), then the ice will directly sublimate into water vapor. This is because at pressures below 1 atm, phase transitions go from solid directly to gas (sublimation) without going through the liquid phase.
03

Determine maximum pressure \(p_{2}\)

The phase diagram of water tells us that the pressure at which boiling does not occur is called the critical pressure. For water, this is approximately 217.7 atm. Above this pressure, water is in a supercritical fluid state, where distinction between liquid and gas phases ceases to exist.
04

Phase transitions for \(p_{1}

When the pressure is between \(p_{1}\) (1atm) and \(p_{2}\) (217.7atm), first, ice will melt to water under pressure greater than 1 atm and less than or around 209.9 atm (triple point pressure for water). Then, the water will transition to steam until the critical pressure (217.7 atm) is reached. Beyond the critical pressure, water would be in the supercritical fluid state.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solid Water
Solid water, commonly known as ice, is the solid form of water. Ice is the result of water molecules arranging themselves in a structured lattice formation at lower temperatures.
In this state, the water molecules are held firmly in place by hydrogen bonds, giving ice its solid structure.
At atmospheric pressure of 1 atm, ice remains solid at temperatures below 0掳C.
  • Solid water is less dense than liquid water, which is why ice floats.
  • As ice warms, it begins to weaken its hydrogen bonds.
  • This process leads to phase transitions based on external conditions.
Melting Pressure
Melting pressure refers to the specific external pressure required for ice to transition into its liquid form, water. At standard atmospheric pressure of 1 atm, ice melts at 0掳C.
This is the point where the rigid structure of ice becomes sufficiently flexible to transition into liquid water.
  • Melting occurs when ice absorbs enough energy to break part of its hydrogen bonds.
  • The process requires the least amount of pressure at 1 atm for the melting phase to occur.
In scenarios where the pressure is less than this minimum (i.e., less than 1 atm), ice does not go through a melting phase but rather transitions directly from a solid to a gas鈥攖his phenomenon is known as sublimation.
Sublimation
Sublimation is the direct transition of a substance from its solid phase to its gaseous phase without passing through the liquid phase. This fascinating process occurs under certain conditions of low pressure and temperature.
  • In the case of ice, sublimation can occur at pressures below 1 atm.
  • Instead of melting, ice transitions directly into water vapor.
  • This mechanism allows for the bypassing of the liquid state altogether.
Sublimation is a significant aspect for those studying phase transitions because it showcases how substances can behave differently under varied atmospheric conditions.
Critical Pressure
The critical pressure is the pressure beyond which distinct liquid and gas phases of a substance disappear. For water, this pressure is around 217.7 atm.
  • Above this critical pressure, water cannot boil and remains in a supercritical state.
  • This state blurs the distinction between liquid and gas phases.
  • The critical pressure is crucial for understanding advanced thermodynamics of substances.
When pressure and temperature are above the critical values, water transitions to a supercritical fluid鈥攁 unique phase with properties of both liquid and gas.
Such a state is remarkable for applications involving high-pressure environments.

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Most popular questions from this chapter

\(\mathrm{A}\) welder using a tank of volume \(0.0750 \mathrm{~m}^{3}\) fills it with oxygen (molar mass \(32.0 \mathrm{~g} / \mathrm{mol}\) ) at a gauge pressure of \(3.00 \times 10^{5} \mathrm{~Pa}\) and temperature of \(37.0^{\circ} \mathrm{C}\). The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is \(22.0^{\circ} \mathrm{C},\) the gauge pressure of the oxygen in the tank is \(1.80 \times 10^{5} \mathrm{~Pa}\). Find (a) the initial mass of oxygen and (b) the mass of oxygen that has leaked out.

Consider an ideal gas at \(27^{\circ} \mathrm{C}\) and 1.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. (a) What is the length of an edge of each cube if adjacent cubes touch but do not overlap? (b) How does this distance compare with the diameter of a typical molecule? (c) How does their separation compare with the spacing of atoms in solids, which typically are about \(0.3 \mathrm{nm}\) apart?

An empty cylindrical canister \(1.50 \mathrm{~m}\) long and \(90.0 \mathrm{~cm}\) in diameter is to be filled with pure oxygen at \(22.0^{\circ} \mathrm{C}\) to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.0 atm. The molar mass of oxygen is \(32.0 \mathrm{~g} / \mathrm{mol}\). (a) How many moles of oxygen does this canister hold? (b) For someone lifting this canister, by how many kilograms does this gas increase the mass to be lifted?

Perfectly rigid containers each hold \(n\) moles of ideal gas, one being hydrogen \(\left(\mathrm{H}_{2}\right)\) and the other being neon \((\mathrm{Ne}) .\) If it takes \(300 \mathrm{~J}\) of heat to increase the temperature of the hydrogen by \(2.50^{\circ} \mathrm{C}\), by how many degrees will the same amount of heat raise the temperature of the neon?

A person at rest inhales \(0.50 \mathrm{~L}\) of air with each breath at a pressure of 1.00 atm and a temperature of \(20.0^{\circ} \mathrm{C}\). The inhaled air is \(21.0 \%\) oxygen. (a) How many oxygen molecules does this person inhale with each breath? (b) Suppose this person is now resting at an elevation of \(2000 \mathrm{~m}\) but the temperature is still \(20.0^{\circ} \mathrm{C}\). Assuming that the oxygen percentage and volume per inhalation are the same as stated above, how many oxygen molecules does this person now inhale with each breath? (c) Given that the body still requires the same number of oxygen molecules per second as at sea level to maintain its functions, explain why some people report "shortness of breath" at high elevations.
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