Book cover for Thermodynamics: An Engineering Approach

Thermodynamics: An Engineering Approach

Yunus A. Cengel, Michael A. Boles

ISBN #9781259822674

9th Edition

2,694 Questions

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59,300 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter covers the fundamental thermodynamic properties of pure substances, emphasizing the various phases observed—compressed liquids, saturated mixtures, and superheated vapors. By exploring key concepts such as quality, critical and triple points, and interpreting property diagrams (T–v, P–v, P–T), students learn to analyze phase-change processes. The chapter also bridges ideal and real gas behavior through the ideal-gas law and advanced equations of state, which are essential for performing accurate energy balance calculations and tackling design challenges in various industrial applications.

Learning Objectives

1

Describe the phase behavior of pure substances including compressed liquids, saturated mixtures, and superheated vapors.

2

Explain the significance of key concepts such as quality (x), critical and triple points, and the use of property diagrams (T–v, P–v, P–T).

3

Apply the ideal-gas law and various real?gas equations of state (e.g., van der Waals, Beattie-Bridgeman, Benedict-Webb-Rubin, Virial) to analyze deviations in real gases.

4

Interpret phase equilibrium data and perform energy balance calculations relevant to industrial applications such as power generation and refrigeration.

Key Concepts

CONCEPT

DEFINITION

Pure Substance

A material with a constant chemical composition and consistent properties throughout, regardless of phase.

Phase Behavior

The study of changes between different states of matter (e.g., liquid, vapor, solid) under varying conditions of temperature and pressure.

Compressed Liquid

A liquid that is at a pressure higher than its saturation pressure at a given temperature, with properties similar to a subcooled liquid.

Saturated Liquid/Vapor

States where the substance is at the phase change boundary; saturated liquid is about to vaporize, while saturated vapor is about to condense.

Superheated Vapor

A vapor that is at a temperature higher than its saturation temperature at a given pressure.

Quality (x)

The mass fraction of vapor in a saturated liquid–vapor mixture, often expressed as a percentage.

Critical Point

The end point of the phase equilibrium curve, beyond which liquid and vapor phases become indistinguishable.

Triple Point

The unique condition at which all three phases (solid, liquid, and vapor) coexist in equilibrium.

Property Diagrams (T–v, P–v, P–T)

Graphical representations used to depict the relationships between temperature, pressure, and specific volume in phase-change processes.

Ideal-Gas Equation

A simplified equation of state (PV = nRT) applied to gases under certain conditions, useful for calculating various thermodynamic properties.

Real-Gas Equations of State

Equations (such as van der Waals, Beattie-Bridgeman, Benedict-Webb-Rubin, and Virial) that account for interactions between molecules and the finite size of molecules to predict real gas behavior.

Compressibility Factor (Z)

A factor used to measure deviations of a real gas from ideal-gas behavior, typically expressed as Z = PV/(nRT).

Reference State and Reference Values

Baseline conditions defined for substances that are used to determine relative thermodynamic properties.

Vapor Pressure and Phase Equilibrium

The pressure exerted by a vapor in equilibrium with its liquid or solid form at a given temperature, critical for understanding phase transitions.

Enthalpy—A Combination Property

A thermodynamic quantity representing the total heat content of a system, used in energy balance calculations.

Example Problems

Example 1

A propane tank is filled with a mixture of liquid and vapor propane. Can the contents of this tank be considered a pure substance? Explain.

Example 2

Is iced water a pure substance? Why?

Example 3

What is the difference between saturated vapor and superheated vapor?

Example 4

What is the difference between saturated liquid and compressed liquid?

Example 5

If the pressure of a substance is increased during a boiling process, will the temperature also increase or will it remain constant? Why?
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Step-by-Step Explanations

QUESTION

Given a saturated liquid–vapor mixture with a known specific volume, how do you determine the quality of the mixture?

STEP-BY-STEP ANSWER:

Step 1: Identify the specific volumes of the saturated liquid (v_f) and saturated vapor (v_g) from property tables.
Step 2: Use the overall specific volume (v) of the mixture and set up the relation: v = (1-x)*v_f + x*v_g.
Step 3: Rearrange the equation to solve for quality x: x = (v - v_f) / (v_g - v_f).
Step 4: Substitute known numerical values and compute x.
Final Answer: x, expressed as a fraction or percentage, represents the mass fraction of vapor in the mixture.

Quality (x) Calculation

QUESTION

How do you apply the ideal-gas equation to estimate the properties of a superheated vapor?

STEP-BY-STEP ANSWER:

Step 1: Write down the ideal-gas equation: PV = nRT.
Step 2: Convert the mass of the vapor to moles using its molar mass.
Step 3: Rearrange the equation to solve for the desired property (e.g., specific volume V/n or pressure P) using known variables.
Step 4: Compare the computed value with experimental data to assess the deviation, which may be corrected using a compressibility factor (Z).
Final Answer: The calculated property using the ideal-gas law provides an approximation, which is refined by accounting for real-gas behavior.

Using the Ideal-Gas Equation

QUESTION

How do you use a T–v diagram to determine the state of a pure substance?

STEP-BY-STEP ANSWER:

Step 1: Locate the given temperature on the T–v diagram.
Step 2: Identify the range of specific volumes corresponding to the saturated liquid and saturated vapor lines.
Step 3: Compare the system’s specific volume to the diagram: if it lies below the saturated liquid line, it's a compressed liquid; if between the lines, it’s a mixture; if above the saturated vapor line, it’s a superheated vapor.
Step 4: Use the diagram to determine additional properties such as pressure that correspond with the phase.
Final Answer: The T–v diagram aids in identifying whether the substance exists as a liquid, vapor, or a mixture based on its temperature and specific volume.

Phase Diagram Interpretation

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Common Mistakes

  • Assuming that all gases behave ideally without accounting for deviations expressed by the compressibility factor.
  • Confusing the saturated liquid state with a compressed liquid state due to similar property values.
  • Misinterpreting property diagrams by not correctly identifying the boundaries of phase-change regions.
  • Failing to correctly convert measurement units when applying the ideal-gas equation or other equations of state.
  • Overlooking the significance of the critical and triple points in phase equilibrium analysis.