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Chapter 3: Problem 3

A system consists of liquid water in equilibrium with a gaseous mixture of air and water vapor. How many phases are present? Does the system consist of a pure substance? Explain. Repeat for a system consisting of ice and liquid water in equilibrium with a gaseous mixture of air and water vapor.

Short Answer

Expert verified
The first system has 2 phases and is not a pure substance. The second system has 3 phases and is also not a pure substance.

Step by step solution

01

Identify Phases in Liquid Water and Air System

In the system consisting of liquid water in equilibrium with a gaseous mixture of air and water vapor, identify the distinct physical states present. Liquid water constitutes one phase, while the gaseous mixture (containing both air and water vapor) constitutes a second phase.
02

Determine Pure Substance in Liquid Water and Air System

Determine whether the system is a pure substance. Since it consists of both liquid water and a gaseous mixture of air and water vapor, which are chemically different, it is not a pure substance.
03

Identify Phases in Ice, Liquid Water, and Air System

In the system consisting of ice, liquid water, and a gaseous mixture of air and water vapor, identify the distinct physical states present. Ice is one phase, liquid water is a second phase, and the gaseous mixture (containing both air and water vapor) constitutes a third phase.
04

Determine Pure Substance in Ice, Liquid Water, and Air System

Determine whether the system is a pure substance. Since it consists of ice, liquid water, and a gaseous mixture of air and water vapor, which are chemically different, it is not a pure substance.

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Key Concepts

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

phase equilibrium
Phase equilibrium refers to a state where different phases of a substance exist together without changing over time. For example, in the exercise, liquid water and water vapor are in equilibrium because they exist together consistently in the same environment. Phase equilibrium is key for determining how phases coexist. When you have liquid water and a gaseous mixture of air and water vapor, these components interact without transitioning to another phase, indicating that equilibrium is achieved.
pure substance
A pure substance consists of a single type of matter. It has consistent chemical properties and composition throughout. In the exercise, the system with liquid water and water vapor with air doesn鈥檛 qualify as a pure substance because it contains different chemical components鈥攊t has air mixed in. Similarly, a system with ice, liquid water, and water vapor is not a pure substance, given the presence of chemically different air and water phases. A true pure substance would be just ice, just water, or just water vapor alone.
thermodynamic analysis
Thermodynamic analysis involves studying energy interactions and phase behaviors within a system. By identifying the phases, like liquid water and gaseous mixtures in the exercise, you can predict the system's behavior under varying conditions. The goal is to understand how different variables鈥攕uch as temperature and pressure鈥攚ill affect phases of a substance. This analysis is crucial in industrial and scientific applications, such as the design of thermal systems and predicting the efficiency of energy-transfer processes.
water-vapor systems
Water-vapor systems demonstrate how water coexists in liquid and gas forms. In the exercise, liquid water and water vapor coexist, reflecting natural phase interactions. Additionally, ice, liquid water, and water vapor in the second part of the exercise show how these phases can be present together under specific conditions. Understanding these systems helps in predicting weather patterns, designing HVAC systems, and optimizing industrial processes where phase transitions play a crucial role.

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Most popular questions from this chapter

Water contained in a piston-cylinder assembly, initially at \(300^{\circ} \mathrm{F}\), a quality of \(90 \%\), and a volume of \(6 \mathrm{ft}^{3}\), is heated at constant temperature to saturated vapor. If the rate of heat transfer is \(0.3 \mathrm{Btu} / \mathrm{s}\), determine the time, in min, for this process of the water to occur. Kinetic and potential energy effects are negligible.

A well-insulated, rigid tank contains \(1.5 \mathrm{~kg}\) of Refrigerant \(134 \mathrm{~A}\), initially a two-phase liquid-vapor mixture with a quality of \(60 \%\) and a temperature of \(0^{\circ} \mathrm{C}\). An electrical resistor transfers energy to the contents of the tank at a rate of \(2 \mathrm{~kW}\) until the tank contains only saturated vapor. For the refrigerant, locate the initial and final states on a \(T-v\) diagram and determine the time it takes, in \(s\), for the process.

Air undergoes a polytropic process in a piston-cylinder assembly from \(p_{1}=1\) bar, \(T_{1}=295 \mathrm{~K}\) to \(p_{2}=7\) bar. The air is modeled as an ideal gas and kinetic and potential energy effects are negligible. For a polytropic exponent of \(1.6\), determine the work and heat transfer, each in \(\mathrm{kJ}\) per \(\mathrm{kg}\) of air, (a) assuming constant \(c_{v}\) evaluated at \(300 \mathrm{~K}\). (b) assuming variable specific heats. Using \(I T\), plot the work and heat transfer per unit mass of air for polytropic exponents ranging from \(1.0\) to \(1.6 .\) Investigate the error in the heat transfer introduced by assuming constant \(c_{v}\).

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) contained in a piston-cylinder arrangement, initially at 6 bar and \(400 \mathrm{~K}\), undergoes an expansion to a final temperature of \(298 \mathrm{~K}\), during which the pressure-volume relationship is \(p V^{1.2}=\) constant. Assuming the ideal gas model for the \(\mathrm{CO}_{2}\), determine the final pressure, in bar, and the work and heat transfer, each in \(\mathrm{kJ} / \mathrm{kg}\).

A piston-cylinder assembly contains propane, initially at \(27^{\circ} \mathrm{C}, 1\) bar, and a volume of \(0.2 \mathrm{~m}^{3}\). The propane undergoes a process to a final pressure of 4 bar, during which the pressure- volume relationship is \(p V^{\mathrm{L} .1}=\) constant. For the propane, evaluate the work and heat transfer, each in kJ. Kinetic and potential energy effects can be ignored.
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