Ch. 18 - Kinetic Theory of Gases

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 18 - Kinetic Theory of Gases

Problem 25b

Chapter 18, Problem 25b

For what range of pressures and temperatures can CO₂ be a liquid? Refer to Fig. 18-6.

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Refer to the phase diagram of CO₂ (Fig. 18.9.6) to identify the regions where CO₂ exists as a liquid. A phase diagram shows the states of matter (solid, liquid, gas) as a function of pressure and temperature.

Locate the triple point on the diagram. The triple point is the specific pressure and temperature where solid, liquid, and gas phases coexist. For CO₂, the triple point occurs at approximately 5.11 atm and 216.6 K.

Identify the critical point on the diagram. The critical point is the highest temperature and pressure at which CO₂ can exist as a liquid. Beyond this point, CO₂ becomes a supercritical fluid. For CO₂, the critical point is approximately 73 atm and 304.2 K.

Determine the range of pressures and temperatures where the liquid phase exists. This is the region between the triple point and the critical point, bounded by the liquid-gas equilibrium curve. The pressure must be greater than 5.11 atm and less than 73 atm, and the temperature must be between 216.6 K and 304.2 K.

Conclude that CO₂ can exist as a liquid only within the specified range of pressures and temperatures. Outside this range, it will either be a solid, gas, or supercritical fluid depending on the conditions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Phase Diagram of CO₂

A phase diagram illustrates the states of a substance (solid, liquid, gas) under varying temperature and pressure conditions. For CO₂, the diagram shows the regions where it exists as a liquid, solid, or gas, and highlights critical points such as the triple point and critical point, which are essential for understanding the conditions under which CO₂ can be a liquid.

Critical Point

The critical point of a substance is the temperature and pressure at which the distinction between liquid and gas phases disappears. For CO₂, this point indicates the maximum temperature and pressure at which it can exist as a liquid. Above this point, CO₂ cannot be liquefied regardless of the pressure applied.

Triple Point

The triple point of a substance is the unique set of conditions at which all three phases (solid, liquid, and gas) coexist in equilibrium. For CO₂, the triple point occurs at a specific temperature and pressure, providing a reference for the conditions under which CO₂ can transition between its phases, including the liquid state.

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