Fact-checked by Grok 2 weeks ago

Specific volume

Specific volume is a fundamental thermodynamic property defined as the volume occupied by a unit mass of a substance, expressed as v = \frac{V}{m}, where V is the total volume and m is the mass, with typical units of cubic meters per kilogram (m³/kg). As an intensive property, specific volume remains independent of the system's size and is crucial for determining the thermodynamic state of a substance, often alongside or . It is the reciprocal of (v = \frac{1}{\rho}, where \rho is mass per unit volume), providing a measure of how compact or expansive a is under given conditions. In practical applications, specific volume is essential for analyzing gas behavior via the (Pv = RT, where P is , R is the specific , and T is ), enabling calculations in processes like , , and in systems. For two-phase mixtures, such as liquid-vapor systems, it is computed as a quality-weighted : v = (1 - x) v_f + x v_g, where x is the , v_f is the saturated liquid specific volume, and v_g is the saturated vapor specific volume, which is vital for phase change analyses in steam tables and cycles.

Fundamentals

Definition

Specific volume, denoted as v, is defined as the ratio of the volume V of a substance to its mass m, mathematically expressed as v = \frac{V}{m}. This quantity provides a measure of the space occupied by a unit mass of the material under given conditions. Physically, specific volume represents the volumetric extent per unit mass, which is essential for analyzing how substances expand or contract in response to changes in their state, such as during heating or compression. Unlike extensive properties like total volume, which scale with the size of the system, specific volume is an intensive property, remaining constant regardless of the amount of substance considered. The concept of specific volume emerged in the 19th century within the developing field of thermodynamics, where it helped standardize measurements of volume in engineering analyses, particularly for heat engines and gas behavior. Early uses appear in works like Clapeyron's 1834 diagrams for thermodynamic cycles and later in van der Waals' 1873 equation for real gases, reflecting its role in precise property characterization.

Units and Notation

The SI unit for specific volume is the cubic meter per kilogram (m³/kg), derived from the base units of volume (cubic meter) and mass (). In engineering contexts, common alternative units include the cubic foot per (ft³/lb) in customary systems and liters per gram (L/g) or cubic centimeters per gram (cm³/g) for smaller-scale measurements. Specific volume is typically denoted by the lowercase letter v, representing the volume per unit mass. The molar specific volume, which is the volume per unit amount of substance, is denoted by \bar{v} = V/n, where V is the total volume and n is the number of moles./03%3A_Conservation_of_Mass/3.06%3A_Density_Specific_Volume_Specific_Weight_and_Specific_Gravity) Conversion between units is straightforward using standard factors, as specific volume scales inversely with units. The following table provides key conversion factors to and from the unit:
UnitAbbreviationConversion Factor to m³/kg
per ft³/lb1 ft³/lb = 0.06243 m³/kg
Liter per gramL/g1 L/g = 1 m³/kg
Cubic centimeter per gramcm³/g1 cm³/g = 0.001 m³/kg
These conversions are based on the relations 1 ≈ 0.4536 , 1 ft³ ≈ 0.02832 m³, 1 L = 0.001 m³, and 1 g = 0.001 . Specific volume is measured by determining the ratio of to , with methods varying by . For liquids and , volumetric displacement techniques are standard, such as using a pycnometer—a flask of known filled with the sample and weighed to find —or the for irregular by submerging in a to measure displaced . For gases, pressure- relations are employed, typically by confining the gas in a calibrated container of known , measuring the and , and determining via weighing or other means, often under controlled conditions to account for .

Relations to Other Properties

Relation to Density

Specific volume, denoted as v, is defined as the volume per unit mass of a substance, v = V / m, where V is the total and m is the . , denoted as \rho, is the mass per unit , \rho = m / V. Substituting the expression for v into the density formula yields the direct mathematical \rho = 1 / v, demonstrating that specific volume and are reciprocals of each other. This inverse relationship arises fundamentally from the definitions, as an increase in for a fixed decreases while increasing specific volume. The reciprocal nature has practical implications in characterizing material states: specific volume emphasizes the "sparsity" or openness of a substance's structure, particularly useful for gases where v is large (e.g., air at standard conditions has v \approx 0.8 \, \mathrm{m}^3/\mathrm{kg}), corresponding to low , whereas density highlights compactness, which is more intuitive for dense liquids and solids. For instance, this distinction aids in comparing phases, as gases exhibit high specific volumes and low densities due to greater intermolecular spacing, while liquids show the opposite. Specific volume also connects to compressibility through its partial derivative with respect to pressure. The isothermal compressibility , which quantifies volume change under constant temperature, is defined as \kappa_T = -\frac{1}{v} \left( \frac{\partial v}{\partial P} \right)_T. This expression links the rate of change of specific volume to the substance's resistance to , with the negative sign indicating volume decrease under increasing . As an example, for liquid at (0°C and 1 atm), the specific volume is approximately v \approx 0.001 \, \mathrm{m}^3/\mathrm{kg}, yielding a of \rho = 1 / v \approx 1000 \, \mathrm{kg}/\mathrm{m}^3. This calculation illustrates the inverse relation in a common fluid, where small changes in v correspond to significant shifts in \rho.

Temperature and Pressure Effects

The specific volume of a substance varies with at constant primarily through , quantified by the volumetric thermal expansion coefficient \alpha = \frac{1}{v} \left( \frac{\partial v}{\partial T} \right)_P, where v is the specific volume and T is the . For small temperature changes \Delta T, this leads to the approximate relation v(T) \approx v_0 (1 + \alpha \Delta T), where v_0 is the initial specific volume. This effect arises because increased causes particles to vibrate more intensely, increasing intermolecular distances and thus the volume per unit mass. The magnitude of thermal expansion differs markedly across states of matter. Gases exhibit significant expansion with rising at constant pressure, as their low allows substantial intermolecular separation; for instance, under near-ideal conditions, specific volume is directly proportional to via . Liquids show a moderate increase in specific volume, with \alpha values typically on the order of $10^{-3} to $10^{-4} K^{-1}, reflecting constrained molecular motion compared to gases. Solids, by contrast, display negligible changes, with \alpha \approx 3 \times 10^{-5} K^{-1} or smaller, due to strong interatomic bonds that limit expansion. Pressure influences specific volume at constant temperature through compressibility, defined by the isothermal compressibility \kappa_T = -\frac{1}{v} \left( \frac{\partial v}{\partial P} \right)_T, where P is pressure. For gases behaving nearly ideally, specific volume decreases inversely with pressure (v \propto 1/P), as molecules are forced closer together, enabling large volume reductions even at moderate pressures. In liquids, however, low compressibility (\kappa_T on the order of $10^{-9} to $10^{-10} Pa^{-1}) results in minimal specific volume changes, requiring extreme pressures to achieve noticeable compression. Solids exhibit even lower compressibility, with volume reductions that are practically insignificant under typical conditions. These dependencies are often visualized in diagrams, where isotherms (constant lines) show specific volume decreasing with , particularly steeply for gases, and isobars (constant lines) illustrate volume increasing with , with the steepest slopes for gases. Such representations highlight the contrasting behaviors: gases occupy a broad region with hyperbolic isotherms and linear isobars, while liquids and solids cluster near constant volume, underscoring their relative incompressibility and limited .

Thermodynamic Contexts

Equations of State

Equations of state provide mathematical relations that connect specific volume to other thermodynamic properties such as , , and mass for substances, particularly gases. These equations are essential for predicting the behavior of fluids under varying conditions, enabling calculations in and scientific applications. For gases, the simplest form assumes no intermolecular forces or molecular volume, leading to a direct between specific volume and at constant . The , derived from the universal gas law PV = n R_u T, where P is , V is total volume, n is the number of moles, R_u is the universal , and T is , can be expressed in terms of specific volume v = V/m by substituting n = m/M (with m as mass and M as ). This yields P v = R T, where R = R_u / M is the specific for the substance. This relation holds well for gases at low pressures and high temperatures where deviations from ideality are negligible. Real gases deviate from ideal behavior due to intermolecular attractions and the finite volume of molecules, necessitating corrections to the . The accounts for these by modifying and volume terms: \left( P + \frac{a}{v^2} \right) (v - b) = R T, where a corrects for attractive forces reducing effective , and b accounts for the per unit (with a and b as mass-specific constants, related to molar constants by a = a_u / M^2, b = b_u / M). This equation better predicts and phase behavior for gases near . For instance, at high densities, the a/v^2 term becomes significant, reducing the predicted specific volume compared to the ideal case. Other equations of state extend these corrections for specific applications. The Redlich-Kwong equation, developed for hydrocarbons, improves upon van der Waals by introducing temperature dependence in the attraction term: P = \frac{R T}{v - b} - \frac{a}{\sqrt{T} v (v + b)}, with mass-specific constants a and b fitted to experimental data for substances like and . This form enhances accuracy for non-polar gases at elevated pressures, capturing variations in specific volume more precisely in and processes. For low-density gases, where intermolecular interactions are weak, the provides a perturbative approach: \frac{P v}{R T} = 1 + \frac{B(T)}{v} + \frac{C(T)}{v^2} + \cdots, with virial coefficients B(T), C(T), etc., representing pairwise, three-body, and higher-order interactions on a mass-specific basis. This series converges well at low densities, allowing specific volume to be solved iteratively from pressure and . In practical , especially for and in cycles, specific volume is often obtained from tabulated equations of state rather than explicit formulas. tables based on the IAPWS-IF97 formulation provide specific volume as a function of and across , vapor, and supercritical regions, derived from fundamental thermodynamic relations and experimental data. These tables, standardized by organizations like ASME, facilitate efficient lookups for specific volumes in saturated and superheated states, essential for cycle efficiency calculations without solving complex equations.

Phase Changes

During phase transitions, the specific volume of a substance undergoes characteristic changes that reflect the underlying molecular rearrangements, often accompanied by the absorption or release of . In , the transition from to vapor at constant and involves a significant increase in specific volume due to the of molecules into the gaseous state, requiring substantial to overcome intermolecular forces. For at its of 100°C and standard (0.101325 MPa), the specific volume jumps from approximately 0.001044 m³/kg for the saturated to 1.674 m³/kg for the saturated vapor, illustrating the dramatic volume typical of this process. In contrast, fusion—the of a solid to a —generally produces a smaller change in specific volume, as the molecular shifts from an ordered to a more disordered but still condensed state. For , this transition exhibits an anomalous behavior where the specific volume decreases slightly upon at 0°C, from about 0.001091 m³/kg for to 0.001000 m³/kg for , due to the open hydrogen-bonded of that occupies more space than the denser . This density inversion is unique to and influences phenomena like ice flotation. At the critical point, the distinction between and vapor phases vanishes, and the specific volume becomes continuous without a discontinuous jump, marking the end of the two-phase coexistence region. For , this occurs at a critical of 373.946 °C (647.096 K) and critical of 22.064 , where the saturated and vapor specific volumes converge to approximately 0.003106 m³/ (from critical density of 322 /m³). The Clapeyron equation quantifies the relationship between the slope of the phase boundary in a - and the changes in specific volume and during the transition: \frac{dp}{dT} = \frac{L}{T \Delta v}, where L is the , T is the , and \Delta v is the change in specific volume between phases. This equation, derived from thermodynamic principles of , links phase slopes to volumetric expansions and is fundamental for predicting coexistence curves across various transitions.

Applications

Engineering Applications

Specific volume is essential in engineering design for thermodynamic processes, enabling precise calculations of work, , and storage requirements in power generation, cooling systems, and . By relating volume per unit to and conditions, it facilitates efficient sizing and optimization of components, ensuring safety and performance under operational constraints. In power cycles like the used in steam power plants, specific volume is integral to work calculations for turbines and pumps, where the shaft work is given by W = \int v \, dP. This integral accounts for the fluid's expansion or compression under varying pressure, with the specific volume v derived from steam tables or equations of state at cycle states. For pumps handling incompressible liquids, the work simplifies to W_p = v (P_2 - P_1), highlighting the minimal contribution due to low liquid specific volumes compared to vapors in turbines. These calculations are critical for determining cycle efficiency and component sizing in and nuclear plants. In refrigeration engineering, specific volume governs compressor sizing within vapor-compression cycles by influencing the mass flow rate for a fixed volumetric displacement volume. The mass flow rate \dot{m} = \dot{V} / v, where \dot{V} is the compressor displacement rate and v is the inlet specific volume, directly affects cooling capacity; lower v at the evaporator outlet allows higher mass flow and thus greater refrigeration effect for the same compressor size. This principle guides refrigerant selection and system design to balance efficiency and compactness in applications like air conditioning and industrial chillers. For and systems handling pressurized gases, specific volume is used to compute required volumes as V = m \cdot v, with v obtained from the or real gas equations at storage pressure and temperature. This ensures sufficient capacity for a desired m while minimizing use, as seen in (CNG) vehicle where high-pressure conditions reduce v and thus physical volume needs. Such calculations are vital for safety compliance and cost optimization in chemical processing and . In material selection for , low-density syntactic foams (with densities around 0.03–0.15 g/cm³ or 30–150 kg/m³, corresponding to specific volumes of approximately 0.007–0.033 m³/kg) are chosen for in and structures. These foams provide lightweight barriers against extreme temperatures during launch and re-entry, reducing overall vehicle mass while maintaining structural integrity. For instance, polymethacrylimide foams such as ROHACELL® exhibit low thermal conductivity, enabling effective in cryogenic fuel tanks.

Fluid Mechanics Applications

In , specific volume plays a crucial role in analyzing , , and hydrodynamic behaviors, particularly where density variations affect and mass conservation. As the reciprocal of , specific volume v = 1/\rho directly influences calculations of and pressure distributions in both incompressible and compressible regimes. The , which enforces mass conservation in fluid flows, explicitly incorporates specific volume when expressing s. For steady flow through a of cross-sectional area A, the \dot{m} is given by \dot{m} = \rho A u = A u / v, where u is the ; this form highlights how increases in specific volume (due to or heating) inversely affect to maintain constant . Bernoulli's principle, traditionally applied to incompressible flows, requires adaptation for compressible fluids by integrating specific volume as a function of , v(P), to capture density changes along streamlines. In such cases, the energy equation becomes \int_{P_1}^{P_2} v \, dP + \frac{u_2^2}{2} + gz_2 = \frac{u_1^2}{2} + gz_1, assuming isentropic conditions, which accounts for work done due to or in high-speed flows. Cavitation in liquids, a critical concern in pumps and propellers, arises when local pressures drop below the , causing the specific volume to increase dramatically as liquid vaporizes into bubbles with much higher specific volume (typically 1000 times that of the liquid). This phase change leads to bubble formation and subsequent collapse, generating shock waves that erode surfaces and reduce efficiency in centrifugal pumps operating under vacuum-like conditions at inlets. In , variations in specific volume are essential for modeling compressible airflows around aircraft, where numbers exceed 0.3 and changes impact and . For instance, as air accelerates over wings, decreases cause specific volume to increase, altering formation and behavior in flight regimes, which informs design to mitigate effects.

Specific Volume in Solutions

Ideal Solutions

In ideal solutions, the specific volume of the mixture is determined by the principle of volume additivity, assuming no interactions between components that would alter the total volume. The specific volume v of the is given by the weighted based on mass fractions: v = \sum y_i v_i where y_i is the mass fraction of component i and v_i is the specific volume of the pure component i at the same and . This formulation arises from the model, which treats the as a of the pure components' properties. A key assumption in this model is that there is no volume change upon mixing (\Delta v_{\text{mix}} = 0), meaning the total of the solution equals the sum of the volumes of the unmixed components. This condition aligns with , which describes the behavior in solutions and implies negligible intermolecular forces beyond those in the pure states, preserving volume additivity across the composition range. This approach finds practical use in dilute aqueous solutions, where the solute concentration is low enough that solvent-solute interactions mimic behavior, and in gas mixtures at low pressures, where deviations from ideality are minimal. For instance, dry air is often modeled as an mixture of approximately 78% and 21% oxygen by volume (closely corresponding to mass fractions due to similar masses), yielding a specific volume that is the mass-weighted average of the pure gases' specific volumes at ambient conditions.

Non-Ideal Solutions

In non-ideal solutions, the specific volume deviates from ideal mixing behavior due to intermolecular interactions that alter the packing of molecules, leading to either or upon mixing. Unlike ideal solutions where the total volume is the sum of partial volumes weighted by mass fractions, real mixtures exhibit an excess specific volume that quantifies these deviations. This excess arises from factors such as hydrogen bonding, dipole-dipole attractions, or steric hindrance, which disrupt the additive nature of volumes in pure components. The excess specific volume, denoted as \Delta v^E, is defined as the difference between the actual specific volume v of the mixture and the ideal specific volume \sum y_i v_i, where y_i is the mass fraction and v_i is the specific volume of pure component i: \Delta v^E = v - \sum y_i v_i Positive \Delta v^E indicates volume expansion, often due to weaker interactions between unlike molecules compared to like molecules, as seen in binary mixtures like methanol-benzene, where repulsive forces lead to looser packing. Conversely, negative \Delta v^E signifies contraction, resulting from stronger attractive interactions, such as bonding in - mixtures or dipole interactions in acetone- systems. For instance, mixing equal volumes of and yields a total volume less than 100 mL, corresponding to a negative excess molar volume of about -1.3 cm³/mol (or ≈ -0.041 cm³/g on a mass basis) at equimolar composition at 298 K. Similarly, acetone- exhibits negative excess volumes up to -1.0 cm³/mol (≈ -0.011 cm³/g), attributed to complex formation between the carbonyl and hydrogen of . Predictive models like COSMO-RS and are employed to estimate specific volumes in non-ideal and systems without extensive experimental data. COSMO-RS, a quantum chemistry-based approach, computes surface charge densities (sigma-profiles) to derive activity coefficients and excess properties, including excess molar volumes, enabling accurate predictions for complex mixtures; for example, it reproduces experimental excess volumes for acetonitrile-water azeotropes within 5% error. , a group-contribution method, parameterizes interactions between functional groups to model excess Gibbs energy, from which excess volumes can be derived via thermodynamic relations, proving useful for multicomponent systems in . These models are particularly valuable for screening solvents in multi-component blends, where direct measurements are impractical. Partial specific volumes, \bar{v}_i, provide insight into the contribution of individual components to the mixture's volume and are defined as the partial derivative of total volume V with respect to the mass m_i of component i at constant temperature T, pressure P, and masses of other components m_j: \bar{v}_i = \left( \frac{\partial V}{\partial m_i} \right)_{T,P,m_j} In non-ideal solutions, \bar{v}_i varies with composition due to non-additive effects and is crucial in osmometry for determining molecular weights of solutes, especially macromolecules, by relating osmotic pressure to concentration while accounting for volume changes. For instance, in membrane osmometry, accurate \bar{v}_i values (typically 0.7-0.75 cm³/g for proteins) correct for buoyancy and non-ideality, enabling precise characterization of biopolymers in aqueous solutions. Understanding specific volumes in non-ideal solutions is essential in pharmaceuticals for optimizing solubility and , where excess volume deviations influence the effective concentration and rates in mixed systems, such as mixtures for poorly soluble . In petrochemical blending, these deviations affect storage and transport efficiencies; for example, negative excess volumes in stock mixtures lead to shrinkage upon blending, impacting yield calculations and requiring predictive models to minimize economic losses.

Common Values

Gases and Vapors

For gases and vapors, the specific volume is typically large due to the low density of these phases, making them highly compressible compared to condensed matter. The ideal gas approximation provides a foundational estimate, given by the relation v = \frac{R T}{P M} where v is the specific volume in m³/kg, R = 8.314 J/(mol·K) is the universal gas constant, T is the temperature in K, P is the pressure in Pa, and M is the molar mass in kg/mol. This equation assumes negligible intermolecular forces and molecular volume, valid at low pressures (near 1 atm) and moderate temperatures. For instance, at standard temperature and pressure (STP: 273.15 K, 101.325 kPa), nitrogen (M = 0.028 kg/mol) has v \approx 0.800 m³/kg, oxygen (M = 0.032 kg/mol) has v \approx 0.700 m³/kg, and carbon dioxide (M = 0.044 kg/mol) has v \approx 0.506 m³/kg. Specific volume for gases increases proportionally with temperature at constant under the approximation, reflecting . For dry air (effective M ≈ 0.029 kg/mol) at 101.325 kPa, values are approximately 0.773 m³/kg at 0°C, 0.844 m³/kg at 25°C, and 1.056 m³/kg at 100°C. These can be computed as v(T) = v_{\text{STP}} \times (T / 273.15), where temperatures are in . Real gases and vapors deviate from ideality at high pressures, where repulsive forces dominate and reduce the effective volume available to molecules, leading to lower specific volumes than predicted. The Z (<1) corrects the ideal law as Pv = ZRT/M. For (), the IAPWS-IF97 formulation provides precise tabulations accounting for these effects. At and 100°C ( conditions), the specific volume of saturated is 1.673 m³/kg, slightly less than the ideal value of ≈1.70 m³/kg. At higher pressures, deviations grow; for at 10 MPa and 320°C, IAPWS-IF97 gives v = 0.0268 m³/kg, compared to an ideal estimate of ≈0.0274 m³/kg. The following table lists specific volumes at for selected common gases and , derived from measured densities assuming near-ideal behavior:
GasSpecific Volume (m³/kg) at
Hydrogen (H₂)11.12
Helium (He)5.60
Neon (Ne)1.111
Methane (CH₄)1.394
Ammonia (NH₃)1.300
Water Vapor (H₂O)1.244
Nitrogen (N₂)0.800
Air0.773
Carbon Monoxide (CO)0.800
Oxygen (O₂)0.700
(Ar)0.561
(CO₂)0.506

Liquids and Solids

For liquids and solids, specific volume is defined as the volume occupied per unit mass and is the reciprocal of density, v = 1 / \rho, where v is in cubic meters per (m³/) and \rho is in per cubic meter (/m³). Due to their incompressible nature, the specific volumes of liquids and solids remain nearly constant under moderate changes, unlike gases, and are typically on the order of 10^{-3} m³/ or less, reflecting their compact molecular packing. This property is crucial in for calculations in , , and thermal systems, where small variations often arise from effects rather than . Representative specific volumes for common liquids at standard conditions (near and ) are shown in the table below, calculated from established data. , a liquid, has a specific volume of 0.001 m³/kg at 4°C, corresponding to its maximum of 1000 kg/m³. Mercury, a dense metal, exhibits a much smaller value of approximately 0.000074 m³/kg at 20°C. Organic liquids like and have values around 0.0013 m³/kg and 0.0011 m³/kg, respectively, at 20°C, illustrating moderate variations based on molecular structure.
LiquidTemperature (°C)Density (kg/m³)Specific Volume (m³/kg)
Water410000.001
Mercury20135900.000074
207890.00127
209110.00110
15825 (avg.)0.00121
For solids, specific volume similarly derives from density and spans a wide range depending on material type, from low-density organics to high-density metals. Aluminum, a common structural metal, has a of 2700 kg/m³ at 300 K, yielding a specific volume of about 0.00037 m³/kg. , relevant in , shows 0.00109 m³/kg at 273 K with a of 921 kg/m³, close to liquid water due to similar hydrogen bonding. Dense solids like reach 0.00011 m³/kg at 27°C ( 8900 kg/m³), while porous materials such as exhibit higher values around 0.00183 m³/kg ( 545 kg/m³). Temperature-induced expansions can slightly increase these volumes, but remains negligible for most applications.
SolidTemperature (K or °C)Density (kg/m³)Specific Volume (m³/kg)
Aluminum300 K27000.00037
Copper27°C89000.00011
273 K9210.00109
Plywood (Douglas Fir)Room temp.5450.00183
Room temp.23000.00043

References

  1. [1]
    1.2 Definitions and Fundamental Ideas of Thermodynamics - MIT
    Specific properties are extensive properties per unit mass and are denoted by lower case letters. For example: $\displaystyle \textrm{specific volume} = V/m = v ...
  2. [2]
    [PDF] Ideal Gas Law With Specific Volume
    In other words, specific volume. (usually denoted as \(v\)) is the volume occupied by a unit mass of gas and is expressed in cubic meters per kilogram (m³/kg).
  3. [3]
    [PDF] Pressure, temperature, specific volume.pdf
    • One of two independent intensive properties which determines the. state of a system.
  4. [4]
    types of properties
    For instance, specific volume is simply the reciprocal of density. There is an important relationship between specific properties and extensive properties.
  5. [5]
    [PDF] LECTURE NOTES ON THERMODYNAMICS
    May 17, 2025 · ... Specific Volume: the volume per unit mass, known as v = V/m. – m3 kg , and. – ft3 lbm . • Density: the mass per unit volume, the inverse of ...
  6. [6]
    [PDF] Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics
    Hence, the specific volume of the liquid-vapor mixture is the specific volume of the liquid (vl) plus the mass fraction that has turned to vapor multiplied by ...
  7. [7]
    [PDF] THERMODYNAMICS I: PHASES - UAH
    Specific volume of a two-phase mixture is dependent on the quality. The higher the quality at a given temperature or pressure, the higher the specific volume:.Missing: definition | Show results with:definition
  8. [8]
    Specific Volume
    The specific volume of the original tank is the same as the specific volume in each half. The "specific" of specific volume simply means "divided by mass".
  9. [9]
    mechanics -
    The specific volume is the reciprocal of the density of the material, which is the mass per unit volume: r = (1/v) = (m/V). The "Specific Gravity" of a ...
  10. [10]
    None
    Below is a merged response summarizing the information from all provided segments on "Specific Volume and Volume per Mass in 19th Century Thermodynamics." To retain all details in a dense and organized manner, I will use a combination of narrative text and a table in CSV format for key data points. The narrative provides an overview and context, while the table captures specific mentions, standardization details, historical developments, and useful URLs from each segment.
  11. [11]
  12. [12]
    Specific Volume Converter
    Free online specific volume converter - converts between 8 units of specific volume, including cubic meter/kilogram, cubic centimeter/gram, liter/kilogram ...
  13. [13]
    3.6: Density, Specific Volume, Specific Weight, and Specific Gravity
    Aug 5, 2022 · A molar specific volume is also defined similarly as the volume per unit mole and is given the symbol v ¯ . What would be the units for ...
  14. [14]
    [PDF] 1 Phase Transitions
    The fact that the critical isotherm is horizontal in the p−v diagram means that the isothermal compressibility κT = −(1/v)(∂v/∂p) is infinite. Now we ...
  15. [15]
    Water - Specific Volume vs. Temperature - The Engineering ToolBox
    Online calculator, figures and tables showing Specific Volume of water at temperatures ranging from 0-370 °C and 32 - 700 °F - Imperial and IS Units.
  16. [16]
    1.3 Thermal Expansion – University Physics Volume 2
    Use the equation for linear thermal expansion Δ L = α L Δ T to calculate the change in length, Δ L . Use the coefficient of linear expansion α for steel from ...
  17. [17]
    4.3: Compressibility and Expansivity
    ### Summary of Isothermal Compressibility
  18. [18]
    Pressure-Volume-Temperature Diagram
    Explore the thermodynamic space PVT of an ideal gas and see relationships between isochors, isobars, and isotherms and their partial derivatives.
  19. [19]
    Equation Of State (Ideal Gas) | Glenn Research Center - NASA
    Jul 7, 2025 · If we divide both sides of the general equation by the mass of the gas, the volume becomes the specific volume, which is the inverse of the gas ...
  20. [20]
    [PDF] Ideal-Gas / Van der Waals Equation of State
    Ideal-Gas / Van der Waals Equation of State. Van der Waals equation: RT bv v a. P. =−. +. ) )( (. 2 where v (= 1/ ) is the specific volume. If a and b are both ...
  21. [21]
    2.12: Van der Waals' Equation - Chemistry LibreTexts
    Jul 7, 2024 · Van der Waals' equation says that the volume of a real gas is the volume that would be occupied by non-interacting point masses, V i ⁢ d ⁢ e ⁢ a ...
  22. [22]
    [PDF] Overview of Equations of State (EOS) - ASGMT
    The Soave-Redlich-Kwong (SRK) EOS (Soave, 1972) is a cubic EOS, similar to the Peng-Robison EOS. The main difference between the SRK and the Peng-Robison EOS is ...
  23. [23]
    [PDF] Equation of state for hydrocarbons and water - Webthesis
    In Redlich and Kwong (RK, 1949) equation they included the temperature of the system to the van der Waals attraction term to consider its effects on the ...
  24. [24]
    [PDF] Gases and the Virial Expansion
    Feb 7, 2013 · The Virial Expansion. • For systems of very low density, the ideal gas equation of state is approximately correct. – On average, particles ...
  25. [25]
    Document Download: R7-97(2012): Revised Release on IAPWS IF97
    May 29, 2018 · This formulation is recommended for industrial use (primarily the steam power industry) for the calculation of thermodynamic properties of ordinary water.
  26. [26]
    [PDF] Standardized STEAM Property Tables - ASME
    This page shows the properties specific volume, enthalpy, and entropy of H2O at three different pressures. The values above the horizontal lines in the chart ...
  27. [27]
    [PDF] Density of Water (g/cm3) at Temperatures from 0°C (liquid state) to ...
    Density of Water (g/cm3) at Temperatures from 0°C (liquid state) to 30.9°C by 0.1°C increments.<|separator|>
  28. [28]
    [PDF] David C. Ailion Physics 3760 Date: 11/05/14 Thermodynamics ...
    Nov 14, 2014 · If the change in specific volume on melting is –9.05 x 10-5 m3/kg, then calculate the change of melting temperature due to change of pressure.<|separator|>
  29. [29]
    [PDF] Lecture 9: Phase Transitions - Matthew D. Schwartz
    The specific volume changes smoothly from liquid to gas if we pass through the critical point, so the phase transition at this point is second order. At ...
  30. [30]
    8.4 The Clausius-Clapeyron Equation - MIT
    The fact that all known substances in the two-phase region fulfill the Clausius-Clapeyron equation provides the general validity of the 1st and 2nd laws of ...Missing: source | Show results with:source
  31. [31]
    Theory of Rankine Cycle - Equations and Calculation - Nuclear Power
    dH = dQ + Vdp. In this equation, the term Vdp is a flow process work. This work, Vdp, is used for open flow systems like a turbine or a pump in which there ...Missing: ∫ | Show results with:∫
  32. [32]
    [PDF] ME 24-221 THERMODYNAMICS I Solutions to extra problems in ...
    Nov 29, 2000 · C.V. Pump Rev adiabatic. -wP = h2 - h1 ; s2 = s1 since incompressible it is easier to find work as. -wp = ∫ v dP = v1 (P2 - P1) = 0.00101 ...
  33. [33]
    Compressor Capacity - an overview | ScienceDirect Topics
    It is easy to see that B is less than A, however the mass flow rate is higher with B because of the lower specific volume of the vapour at the compressor inlet.
  34. [34]
    Compressed Air - Storage Volume - The Engineering ToolBox
    The storage volume for a compressed gas can be calculated by using Boyle's Law. pa Va = pc Vc. = constant (1). where. pa = atmospheric pressure (14.7 psia, ...
  35. [35]
    Aerospace and Aviation | Space - Evonik Industries
    ROHACELL® foams offer extremely low thermal conductivity to insulate first stage cryogenics and isotropic behavior that can withstand high lateral forces.Missing: volume | Show results with:volume
  36. [36]
    Continuity Equation - Fluid Flow - Engineering Library
    The continuity equation expresses the relationship between mass flow rates at different points in a fluid system under steady-state flow conditions.Missing: critical | Show results with:critical
  37. [37]
    5.2 Mass and energy conservation equations in a control volume
    v : specific volume of the working fluid, in m3/kg. The conservation of mass, also called the continuity equation, states that mass cannot be created or ...Missing: mechanics | Show results with:mechanics
  38. [38]
    [PDF] Compressible Flow
    (where v = specific volume = 1/ρ). ∴ ρ = p c. Hence z dp ρ ... (16.7) is the Bernoulli's equation for compressible flow undergoing adiabatic process.
  39. [39]
    [PDF] Introduction to Compressible Flow
    • Equation of State – Ideal Gas Law. RT p ρ. = Temperature is absolute and the specific volume is. (volume per unit mass): ρ. 1. = v. K). J/(kg. 287 .97kg/kmol.
  40. [40]
    [PDF] Method for prediction of pump cavitation performance for various ...
    A method for predicting the cavitation performance of pumps with various liquids, liquid temperatures, and rotative speeds is presented. tal studies used in ...
  41. [41]
    Chapter 1 - Cavitation and Bubble Dynamics - Christopher E. Brennen
    Dec 1, 2000 · Figure 1.1 shows typical graphs of pressure, p, temperature, T, and specific volume, V, in which the state of the substance is indicated.
  42. [42]
    [PDF] Equations, Tables and Charts for Compressible Flow
    specific volume, normal force. I ∞ So velocity components parallel and perpendicular respectively, to free-stream flow direction velocity components normal ...
  43. [43]
    A-3: Basics of Aerodynamics - Eagle Pubs
    This is called specific volume of an element of air. For a low-speed flow field (Mach number < 0.3), the compressibility effects can be negligible (small and ...
  44. [44]
    Mixtures of Ideal Gas - an overview | ScienceDirect Topics
    where wi is the mass fraction of ideal gas i in the mixture and vi is the specific volume of that gas determined at the pressure and temperature of the mixture ...
  45. [45]
    Ideal Solution - an overview | ScienceDirect Topics
    ... mixing of an ideal solution. Hence, the entropy of mixing is equal to S ... The specific volume vk does not depend on the concentration in an ideal system.
  46. [46]
    Air - Composition and Molecular Weight - The Engineering ToolBox
    Air is a mixture of several gases, where the two most dominant components in dry air are 21 vol% oxygen and 78 vol% nitrogen . Oxygen has a molar mass of 15. ...
  47. [47]
    Excess molar volumes and deviation in viscosities of binary liquid ...
    Dec 6, 2011 · Positive values of excess molar volumes show that volume expansion is taking place causing rupture of H-bonds in self associated alcohols. The ...
  48. [48]
    Excess volumes and excess heat capacities of water + ethanol at ...
    The excess volumes are all negative with the minimum being around x1 = 0.62. The excess heat capacities are positive with a highly asymmetric dependence on ...
  49. [49]
    Excess volumes of mixing - ScienceDirect.com
    Excess volumes of chloroform + acetone, + ether, and + dioxan; of acetone + benzene, + carbon tetrachloride, and + carbon disulphide; and of benzene + n-hexane ...
  50. [50]
    COSMO-RS theory - SCM
    In this equation qi is the surface area of the molecular volume of compound i, xi is the molar fraction of compound i in the solution, and λ is a COSMO-RS ...
  51. [51]
    Analysis of the UNIFAC-Type Group-Contribution Models at the ...
    The Modified UNIFAC model for predicting activity coeffs. presented in this work is based on the well-known UNIFAC model. Two changes are introduced in Modified ...<|separator|>
  52. [52]
    The Partial Specific Volumes, in Aqueous Solution, of Three Proteins
    Determination of hydration and partial specific volume ... Examination of the dissociation of multichain proteins in guanidine hydrochloride by membrane osmometry.
  53. [53]
    Drug Solubility: Importance and Enhancement Techniques - PMC
    Various techniques are used for the enhancement of the solubility of poorly soluble drugs which include physical and chemical modifications of drug and other ...Missing: petrochemicals | Show results with:petrochemicals
  54. [54]
    Effect of the Chemical Composition on Excess Volume of Mixtures ...
    Blending of oil stocks with hydrocarbons form non-ideal mixtures, for which excess volumes can be positive or negative depending to the nature of species.Missing: petrochemical | Show results with:petrochemical
  55. [55]
    Density of Gases - The Engineering ToolBox
    Densities and molecular weights of common gases like acetylene, air, methane, nitrogen, oxygen and others ... 1 kg/m3 = 0.0624 lbm/ft3. Note that even if pounds ...
  56. [56]
    NIST Guide to the SI, Chapter 8
    Jan 28, 2016 · 8.6.9 Specific volume​​ SI unit: cubic meter per kilogram (m3/kg). Definition: volume of a substance divided by its mass: ν = V / m. Note: ...
  57. [57]
  58. [58]
    Thermodynamic Properties Common Liquids , Solids, and Foods
    Thermodynamic Properties Common Liquids , Solids, and Foods ; Steel, mild. 7,830. 0.500. Woods, soft (fir, pine, etc.) 513 ; Tungsten. 19,400. 0.130 ...
  59. [59]
    Liquid Densities - The Engineering ToolBox
    Densities of common liquids like acetone, beer, oil, water and more. ; Acetonitrile, 20, 783 ; Acrolein, 20, 840 ; Acrolonitrile, 25, 801 ; Alcohol, ethyl (ethanol) ...