Chapter 3 - Evaluating Properties
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Questions and Answers

What is the change in internal energy for 1 kg of air moving from state 1 to state 2?

  • 214.07 kJ
  • 991.34 kJ (correct)
  • 1500 kJ
  • 1205.41 kJ

    • In a closed system where no work is done, what does the energy balance equation simplify to?

  • DKE + DPE + DU = 0
  • Q = m(u2 – u1) (correct)
  • Q + W = DKE + DPE + DU
  • Q = W

    • What is a characteristic of a pure substance?

  • Its properties vary significantly with changes in temperature.
  • It can exist in multiple phases with different compositions.
  • It consists of heterogeneous materials.
  • Its chemical composition is uniform and invariable. (correct)

    • What does the exponent 'n' represent in the equation pV^n = constant for a polytropic process?

    <p>The type of process occurring (D)</p> Signup and view all the answers

    Which properties are considered intensive properties for a simple compressible system?

    <p>Density and specific enthalpy (B), Pressure and specific volume (D)</p> Signup and view all the answers

    What defines a phase in thermodynamics?

    <p>A quantity of matter that is homogeneous in composition and structure. (C)</p> Signup and view all the answers

    Which of the following describes a process when n equals 0?

    <p>Constant-pressure process (D)</p> Signup and view all the answers

    For an ideal gas, what type of process occurs when n equals 1?

    <p>Isothermal process (D)</p> Signup and view all the answers

    Which scenario would be classified as a two-phase liquid-vapor mixture?

    <p>Water in a glass with ice cubes. (B)</p> Signup and view all the answers

    Why are velocity and elevation excluded from intensive properties in simple compressible systems?

    <p>Their values are arbitrary and depend on datum choices. (D)</p> Signup and view all the answers

    What does the state principle indicate for a simple compressible system?

    <p>It describes intensive properties that determine system equilibrium. (C)</p> Signup and view all the answers

    What does quality refer to in a two-phase liquid-vapor mixture?

    <p>The extent of vapor present in the mixture. (B)</p> Signup and view all the answers

    When is the ideal gas model generally applicable?

    <p>At high temperatures and low pressures. (D)</p> Signup and view all the answers

    What state is referred to when the temperature is lower than the saturation temperature at a given pressure?

    <p>Compressed liquid state (C)</p> Signup and view all the answers

    What happens to the specific volume when a two-phase liquid-vapor mixture is heated at constant pressure?

    <p>It increases considerably. (B)</p> Signup and view all the answers

    What is the quality, x, of a saturated liquid state?

    <p>0 (D)</p> Signup and view all the answers

    At which state is the entire liquid converted into vapor?

    <p>Saturated vapor state (C)</p> Signup and view all the answers

    What type of diagram is created by projecting the p-v-T surface onto the pressure-specific volume plane?

    <p>p-v diagram (D)</p> Signup and view all the answers

    In a two-phase liquid-vapor mixture, what does the ratio of the mass of vapor to the total mass represent?

    <p>Quality of the mixture (B)</p> Signup and view all the answers

    Which state corresponds to the maximum specific volume within a two-phase mixture during heating?

    <p>Saturated vapor state (A)</p> Signup and view all the answers

    What is a characteristic of the saturated liquid state in terms of temperature and pressure?

    <p>Temperature is equal to the saturation temperature at that pressure. (C)</p> Signup and view all the answers

    What is the formula for specific enthalpy (h) in terms of internal energy (u) and pressure-volume work (pv)?

    <p>h = u + pv (D)</p> Signup and view all the answers

    Which property is developed as an intensive property in Chapter 6?

    <p>Specific entropy (s) (B)</p> Signup and view all the answers

    What is the specific volume (v) of superheated water vapor at 10 MPa and 400°C?

    <p>0.02641 m3/kg (D)</p> Signup and view all the answers

    How is specific volume determined for a state that does not exactly match property table values?

    <p>Using linear interpolation between adjacent entries (B)</p> Signup and view all the answers

    At 8°C, how is the specific volume of saturated liquid calculated from the property table?

    <p>Divide vf × 10^3 by 1000 (D)</p> Signup and view all the answers

    What does the quality, x, represent in a two-phase liquid-vapor mixture?

    <p>The ratio of vapor mass to total mass (C)</p> Signup and view all the answers

    At states where the pressure is small relative to the critical pressure, what value can the compressibility factor Z be approximated to?

    <p>1 (A)</p> Signup and view all the answers

    Which of the following properties is not included in the tabulated properties of Tables A-4 and A-5?

    <p>Specific heat capacity (c) (A)</p> Signup and view all the answers

    What does the equation $pV = mRT$ (Eq. 3.33) represent in the context of the ideal gas model?

    <p>Pressure-volume relationship based on mass (D)</p> Signup and view all the answers

    In the context of thermodynamics, what is the significance of specific enthalpy (h)?

    <p>It includes contributions from pressure-volume work (pv). (D)</p> Signup and view all the answers

    Which equation indicates that the specific internal energy for a gas modeled as an ideal gas depends primarily on temperature?

    <p>u = u(T) (D)</p> Signup and view all the answers

    Which of the following equations correctly relates specific enthalpy, internal energy, and the ideal gas equation?

    <p>h = u + pv (B)</p> Signup and view all the answers

    What is the main criterion for using the ideal gas model effectively in engineering thermodynamics?

    <p>The states must be located on the generalized compressibility chart (B)</p> Signup and view all the answers

    What does the universal gas constant R equal when expressed in kJ/kmol∙K?

    <p>8.314 (D)</p> Signup and view all the answers

    In an ideal gas, how does the specific heat $c_v$ vary?

    <p>It is a function of temperature alone (C)</p> Signup and view all the answers

    Under what conditions is the ideal gas model justified for use?

    <p>In limiting cases where pressure is low compared to critical pressure (B)</p> Signup and view all the answers

    What is the relationship between specific enthalpy and temperature for an ideal gas?

    <p>Specific enthalpy depends only on temperature. (A)</p> Signup and view all the answers

    Which equation represents the change in specific internal energy for an ideal gas under constant specific heat?

    <p>u(T2) - u(T1) = cv[T2 - T1] (D)</p> Signup and view all the answers

    What is the suggested method for evaluating changes in specific internal energy and enthalpy for ideal gases?

    <p>Utilizing ideal gas tables. (D)</p> Signup and view all the answers

    When is it inappropriate to use the equation h2 - h1 = cp[T2 - T1]?

    <p>When calculating for large temperature intervals. (A)</p> Signup and view all the answers

    In a rigid tank with air heated from 300 K to 1500 K, what should be neglected to determine the heat transfer?

    <p>Both kinetic and potential energy changes. (B)</p> Signup and view all the answers

    Which parameters are necessary to determine the change in specific enthalpy using Table A-22?

    <p>Initial and final temperatures. (B)</p> Signup and view all the answers

    What does the specific heat capacity cp for an ideal gas depend on?

    <p>Temperature alone. (D)</p> Signup and view all the answers

    What is the value of h2 - h1 if h1 = 300.19 kJ/kg and h2 = 1635.97 kJ/kg?

    <p>1335.78 kJ/kg (A)</p> Signup and view all the answers

    Flashcards

    Phase

    A region with uniform composition and physical structure. It can be solid, liquid, or gas.

    Pure Substance

    A substance with constant chemical composition, even when in different phases.

    Simple Compressible System

    A system where pressure, temperature, and specific volume are the primary determinants of its state.

    Intensive Properties

    The values of pressure, temperature, specific volume, and other properties that determine a system's state.

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    p-v-T Surface

    A graph showing the relationship between pressure, volume, and temperature for a substance.

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    Saturation Temperature

    The temperature at which a substance starts changing from liquid to gas.

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    Saturation Pressure

    The pressure at which a substance starts changing from liquid to gas.

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    Two-Phase Liquid-Vapor Mixture

    A mixture of liquid and gas phases of the same substance.

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    What is a p-v diagram?

    A p-v diagram is created by projecting the p-v-T surface onto the pressure-specific volume plane.

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    What is a T-v diagram?

    A T-v diagram is created by projecting the p-v-T surface onto the temperature-specific volume plane.

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    What is a compressed liquid state?

    A compressed liquid state is a liquid state where the temperature is lower than the saturation temperature corresponding to the pressure at the state.

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    What is a saturated liquid state?

    A saturated liquid state is a state where the liquid is about to vaporize, with any additional heat transfer resulting in vapor formation.

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    What is a two-phase liquid-vapor mixture?

    A two-phase liquid-vapor mixture is a state where both liquid and vapor phases coexist in equilibrium. The ratio of vapor mass to total mass is called quality, x.

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    What is a saturated vapor state?

    A saturated vapor state is a state where the last bit of liquid has vaporized, and any additional heat transfer results in an increase in temperature.

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    What is quality, x?

    Quality, x, is the ratio of the mass of vapor present to the total mass of the mixture in a two-phase liquid-vapor mixture. It ranges from 0 for saturated liquid to 1 for saturated vapor.

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    What is saturation temperature, Tsat?

    The saturation temperature, Tsat, is the temperature at which a substance changes phase from liquid to vapor at a given pressure. It's the temperature where the liquid and vapor phases exist in equilibrium.

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    Enthalpy (h)

    The sum of internal energy and the product of pressure and specific volume.

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    Entropy (s)

    A property that measures the degree of randomness or disorder within a substance.

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    Linear Interpolation

    A process where the values of specific properties of a substance are calculated between known values based on a straight line assumption.

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    Saturation Data

    Data that represents the state of a substance at its boiling point, where both liquid and vapor phases coexist.

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    Quality (x)

    The ratio of the mass of vapor to the total mass of the liquid-vapor mixture in a two-phase system.

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    Specific Volume of Saturated Liquid (vf)

    The specific volume of a substance in its liquid phase at saturation conditions.

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    Specific Volume of Saturated Vapor (vg)

    The specific volume of a substance in its vapor phase at saturation conditions.

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    Specific Volume of a Two-Phase Mixture

    The process of determining the specific volume of a two-phase mixture using quality and saturation data.

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    Ideal Gas

    A gas that follows the ideal gas law, where the compressibility factor Z is approximately 1, and the specific internal energy depends only on temperature.

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    Ideal Gas Law

    The equation pv = RT, where p is pressure, v is specific volume, R is the specific gas constant, and T is temperature. It holds true for gases behaving ideally.

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    Internal Energy of Ideal Gas

    The internal energy of an ideal gas depends only on temperature. This means that the specific internal energy can be expressed as u = u(T).

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    Enthalpy of Ideal Gas

    The enthalpy of an ideal gas depends only on temperature, and can be expressed as h = u(T) + RT, where u(T) is the internal energy and RT is the product of the gas constant and temperature.

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    Specific Heat at Constant Volume (cv) of Ideal Gas

    The specific heat at constant volume (cv) of an ideal gas is also a function of temperature alone, as the internal energy is only dependent on temperature.

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    Ideal gas internal energy

    The specific internal energy of an ideal gas depends only on its temperature.

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    Internal Energy Change for Ideal Gas

    For an ideal gas, the change in specific internal energy is calculated as cv(T2-T1), where cv is the specific heat at constant volume and T1 and T2 are the initial and final temperatures respectively.

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    Ideal gas enthalpy

    The specific enthalpy of an ideal gas depends only on its temperature.

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    Enthalpy Change for Ideal Gas

    For an ideal gas, the change in specific enthalpy is calculated as cp(T2-T1), where cp is the specific heat at constant pressure and T1 and T2 are the initial and final temperatures respectively.

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    Ideal gas tables

    Tables A-22 and A-23 provide specific internal energy and enthalpy values for various gases at different temperatures, simplifying calculations.

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    Closed System Energy Balance

    The closed system energy balance is used to analyze energy transfer processes in a system with fixed boundaries, neglecting kinetic and potential energy changes.

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    Closed System Energy Balance for Ideal Gas

    The closed system energy balance equation for an ideal gas accounts for heat transfer and internal energy changes.

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    Specific Enthalpy Change using Tables

    Using the ideal gas tables, we can determine the change in specific enthalpy for a process of air at different temperatures, even when there's a significant temperature difference.

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    Polytropic Process

    A thermodynamic process where the product of pressure (p) and volume (V) raised to the power 'n' remains constant. The exponent 'n' can vary depending on the process, influencing the relationship between pressure and volume.

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    Quasiequilibrium Process

    A process that occurs so slowly that the system remains in equilibrium at all times. It is an idealized process used for analyzing real-world systems.

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    Isobaric Process

    A process where the pressure of the system remains constant while other properties like volume and temperature change.

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    Specific Internal Energy (u)

    The specific internal energy (u) represents the internal energy per unit mass. It is a crucial property for analyzing energy changes within a system.

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    Closed System

    A system where no mass enters or leaves, but energy can be exchanged with the surroundings.

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    Study Notes

    Chapter 3: Evaluating Properties

    • This chapter covers evaluating properties within a thermodynamic context.
    • Learning outcomes include explaining phases, pure substances, and the state principle for simple compressible systems.
    • Knowledge of p-v-T surfaces, saturation temperature, pressure, two-phase liquid-vapor mixtures, quality, enthalpy, and specific heats is essential.
    • Analyzing closed systems, including applying energy balances with property data, is another key element.
    • Students should be able to sketch and interpret T-v, p-v, and phase diagrams and retrieve data from Tables A-1 through A-23.
    • Applying the ideal gas model is pertinent, including when using it is warranted.

    Phase

    • A phase is a quantity of matter that is homogeneous throughout in chemical composition and physical structure.
    • A homogeneous phase is either all solid, all liquid, or all vapor (gas).
    • Examples include:
      • Air is a gas phase.
      • Water with ice is liquid and solid water.
      • Salad dressings are different liquid phases.

    Pure Substance

    • A pure substance displays a uniform and invariable chemical composition across all its phases.
    • A pure substance can have multiple phases but must maintain the same chemical composition within each phase.
    • Examples include:
      • Drinking water (with ice cubes) is a pure substance because each phase (ice and liquid) has the same composition.
      • A fuel/air mixture in an engine can be considered a pure substance pre-ignition.

    State Principle for Simple Compressible Systems

    • Simple compressible systems comprise commonly encountered pure substances listed in Tables A-2 through A-18, A-22, and A-23.
    • At equilibrium, a simple compressible system's intensive state is defined by its intensive properties, including temperature, pressure, specific volume, density, specific internal energy, and specific enthalpy.
    • Properties like velocity and elevation are not relevant to the state principle as they are based on arbitrary datums.
    • Not all intensive properties are independent. Some are related by definition (e.g., density = 1/v). Others are defined through experimental data.
    • For a simple compressible system, values of any two independent intensive properties define all other intensive properties (state principle/state postulate).
      • Commonly used alternative sets include (T, v) and (p, v). (p, T) is not always an independent set.

    p-v-T Surface

    • The p-v-T surface shows how pressure varies with temperature and specific volume for pure substances.
    • Single-phase regions inside the surface include solid, liquid, and vapor states.
    • Two-phase regions are between the single-phase regions, where two phases (e.g., liquid-vapor) coexist in equilibrium.
    • The dome-shaped region formed by the two-phase liquid-vapor states is known as the vapor dome.
    • Lines bordering the vapor dome are the saturated liquid and saturated vapor lines.
    • The critical point is where the saturated liquid and vapor lines meet.
    • Critical temperature (Tc) is the highest temperature at which liquid and vapor can coexist.
    • Critical pressure (Pc) is the pressure at the critical point.

    Projections of the p-v-T Surface

    • Projections provide graphical representations of thermodynamic properties.
    • A phase diagram (projection onto the pressure-temperature plane) is a graphical tool.
    • Saturation temperature is the temperature at which a phase change occurs at a given pressure.
    • Saturation pressure is the pressure at which a phase change occurs at a given temperature.
    • Pressure and temperature are not independent within two-phase regions.

    Phase Change

    • A closed system containing liquid water at a given temperature and pressure may undergo a phase change with increasing temperature and/or pressure.
    • Compressed liquid states have temperatures below the saturation temperature of the liquid, for given pressure.
    • Saturated liquid states represent the start of phase changes, where temperature and pressure are now fixed.
    • Saturated vapor states represent a temperature at which the last of the liquid is vaporized under given pressure.
    • Superheated vapor states represent temperatures above the saturation temperature under given pressure.

    Property Approximations for Liquids/Compressed Liquid Approximation

    • Approximate values for v, u, and h in the compressed liquid region can be obtained using saturated liquid data.
    • The values of v and u vary little with pressure at a fixed temperature in compressed liquids, so approximations (Eqs. 3.11 and 3.12) can be used
    • An approximate value of h can also be found (Eqs. 3.11, 3.12 and 3.13)
    • When the term (p − psat(T)) is small, h(T,p) is approximately equal to h(T)

    Steam Tables

    • Steam tables present the properties of water in a specific format.
    • Table A-4 encompasses superheated vapor.
    • Table A-5 is related to compressed liquid water.
    • Tables A-2 and A-3 describe two-phase liquid-vapor mixtures.

    Single-Phase Regions

    • Independent temperature and pressure typically define single phases.
    • Tables A-4 and A-5 contain properties for superheated water vapor and compressed liquid water, expressed as functions of pressure and temperature.
    • Properties such as temperature (T), pressure (P), specific volume (v), specific internal energy (u), and specific enthalpy (h) are tabulated.
    • Enthalpy is defined as u + pv and specific entropy, s, is an intensive property described in Chapter 6.

    Two-Phase Liquid-Vapor Region

    • Pressure and temperature are dependent within a two-phase region; the quality or x is needed to fix the state.
    • Specific volume, internal energy (u), and enthalpy (h) can be calculated with the quality parameter in this region
      • V = Vf + x(Vg − Vf)
      • u = uf + x(ug − uf)
      • h = hf + x(hg − hf)

    Ideal Gas Model

    • The ideal gas model is applicable when pressure is lower than critical pressure.
    • The behavior of ideal gases at different states can be studied under a generalized compressibility chart.   - In the ideal gas model, the relationship between PV and T is mathematically derived via R. 
    • Internal energy and enthalpy are only dependent on temperature in an ideal gas.
    • Ideal gas properties like enthalpy (h) and internal energy (u) can be found using tables A-21, A-22, & A-23  

    Specific Heats

    • Specific heats (cp and cv) are closely related to internal energy (u) and enthalpy (h), offering valuable insights into thermodynamic behavior.
    • The specific heats can vary based on the substance and conditions.
    • For an incompressible substance, cp=cv = c.
    • In the ideal gas model, specific heats are also temperature-dependent.

    Polytropic Process

    • A polytropic process describes a quasiequilibrium process obeying pvn = constant, where the exponent n changes per condition.
    • Constant-pressure, constant-volume, and constant-temperature processes are subsets of the polytropic process based on various values of n.

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    Description

    Test your knowledge on key concepts in thermodynamics, including internal energy changes, properties of pure substances, and phase characteristics. This quiz covers various processes and fundamental principles relevant to simple compressible systems and ideal gases.

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