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Specific volume
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In thermodynamics, the specific volume of a substance (symbol: ν, nu) is the quotient of the substance's volume (V) to its mass (m):
It is a mass-specific intrinsic property of the substance. It is the reciprocal of density ρ (rho) and it is also related to the molar volume and molar mass:
The standard unit of specific volume is cubic meters per kilogram (m3/kg), but other units include ft3/lb, ft3/slug, or mL/g.[1]
Specific volume for an ideal gas is related to the molar gas constant (R) and the gas's temperature (T), pressure (P), and molar mass (M) as shown:
Since and
Applications
[edit]Specific volume is commonly applied to:
Imagine a variable-volume, airtight chamber containing a certain number of atoms of oxygen gas. Consider the following four examples:
- If the chamber is made smaller without allowing gas in or out, the density increases and the specific volume decreases.
- If the chamber expands without letting gas in or out, the density decreases and the specific volume increases.
- If the size of the chamber remains constant and new atoms of gas are injected, the density increases and the specific volume decreases.
- If the size of the chamber remains constant and some atoms are removed, the density decreases and the specific volume increases.
Specific volume is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the meter cubed per kilogram (m3/kg or m3·kg−1).
Sometimes specific volume is expressed in terms of the number of cubic centimeters occupied by one gram of a substance. In this case, the unit is the centimeter cubed per gram (cm3/g or cm3·g−1). To convert m3/kg to cm3/g, multiply by 1000; conversely, multiply by 0.001.
Specific volume is inversely proportional to density. If the density of a substance doubles, its specific volume, as expressed in the same base units, is cut in half. If the density drops to 1/10 its former value, the specific volume, as expressed in the same base units, increases by a factor of 10.
The density of gases changes with even slight variations in temperature, while densities of liquid and solids, which are generally thought of as incompressible, will change very little. Specific volume is the inverse of the density of a substance; therefore, careful consideration must be taken account when dealing with situations that involve gases. Small changes in temperature will have a noticeable effect on specific volumes.
The average density of human blood is 1060 kg/m3. The specific volume that correlates to that density is 0.00094 m3/kg. Notice that the average specific volume of blood is almost identical to that of water: 0.00100 m3/kg.[2]
Application examples
[edit]If one sets out to determine the specific volume of an ideal gas, such as super heated steam, using the equation ν = RT/P, where pressure is 2500 lbf/in2, R is 0.596, temperature is 1960 °R. In that case, the specific volume would equal 0.4672 in3/lb. However, if the temperature is changed to 1160 °R, the specific volume of the super heated steam would have changed to 0.2765 in3/lb, which is a 59% overall change.
Knowing the specific volumes of two or more substances allows one to find useful information for certain applications. For a substance X with a specific volume of 0.657 cm3/g and a substance Y with a specific volume 0.374 cm3/g, the density of each substance can be found by taking the inverse of the specific volume; therefore, substance X has a density of 1.522 g/cm3 and substance Y has a density of 2.673 g/cm3. With this information, the specific gravities of each substance relative to one another can be found. The specific gravity of substance X with respect to Y is 0.569, while the specific gravity of Y with respect to X is 1.756. Therefore, substance X will not sink if placed on Y.[3]
Specific volume of solutions
[edit]The specific volume of a non-ideal solution is the sum of the partial specific volumes of the components:
M is the molar mass of the mixture. This can be used instead of volume, as this is intensive property tied to the system.
Table of common specific volumes
[edit]The table below displays densities and specific volumes for various common substances that may be useful. The values were recorded at standard temperature and pressure, which is defined as air at 0 °C (273.15 K, 32 °F) and 1 atm (101.325 kN/m2, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr).[4]
| Substance name | Density | Specific volume[dubious – discuss] |
|---|---|---|
| (kg/m3) | (m3/kg) | |
| Air | 1.225 | 0.816 |
| Ice | 916.7 | 0.00109 |
| Water (liquid) | 1000 | 0.00100 |
| Salt Water | 1030 | 0.00097 |
| Mercury | 13546 | 0.00007 |
| R-22* | 3.66 | 0.273 |
| Ammonia | 0.769 | 1.30 |
| Carbon dioxide | 1.977 | 0.506 |
| Chlorine | 2.994 | 0.334 |
| Hydrogen | 0.0899 | 11.12 |
| Methane | 0.717 | 1.39 |
| Nitrogen | 1.25 | 0.799 |
| Steam* | 0.804 | 1.24 |
* values not taken at standard temperature and pressure
References
[edit]- ^ Moran, Michael (7 December 2010). Fundamentals of Engineering Thermodynamics. Wiley. ISBN 978-0-470-49590-2.
- ^ Silverthorn, Dee (2010). Human Physiology. Pearson. ISBN 978-0-321-55980-7.
- ^ Walker, Jearl (6 April 2007). Fundamentals of Physics. Halliday. ISBN 978-0-470-04472-8.
- ^ "Engineering Tool Box". Retrieved April 14, 2013.
Specific volume
View on Grokipediafrom Grokipedia
Specific volume is a fundamental thermodynamic property defined as the volume occupied by a unit mass of a substance, expressed as , where is the total volume and is the mass, with typical units of cubic meters per kilogram (m³/kg).[1][2]
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 pressure or temperature.[3][1] It is the reciprocal of density (, where is mass per unit volume), providing a measure of how compact or expansive a material is under given conditions.[4][5]
In practical applications, specific volume is essential for analyzing gas behavior via the ideal gas law (, where is pressure, is the specific gas constant, and is temperature), enabling calculations in processes like compression, expansion, and heat transfer in engineering systems.[2] For two-phase mixtures, such as liquid-vapor systems, it is computed as a quality-weighted average: , where is the vapor quality, is the saturated liquid specific volume, and is the saturated vapor specific volume, which is vital for phase change analyses in steam tables and refrigeration cycles.[6][7]
These conversions are based on the relations 1 lb ≈ 0.4536 kg, 1 ft³ ≈ 0.02832 m³, 1 L = 0.001 m³, and 1 g = 0.001 kg.[12]
Specific volume is measured by determining the ratio of volume to mass, with methods varying by phase. For liquids and solids, volumetric displacement techniques are standard, such as using a pycnometer—a flask of known volume filled with the sample and weighed to find mass—or the Archimedes principle for irregular solids by submerging in a fluid to measure displaced volume. For gases, pressure-volume relations are employed, typically by confining the gas in a calibrated container of known volume, measuring the pressure and temperature, and determining mass via weighing or other means, often under controlled conditions to account for compressibility.[8]
[61]
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 density of 2700 kg/m³ at 300 K, yielding a specific volume of about 0.00037 m³/kg.[64] Ice, relevant in cryogenics, shows 0.00109 m³/kg at 273 K with a density of 921 kg/m³, close to liquid water due to similar hydrogen bonding.[64] Dense solids like copper reach 0.00011 m³/kg at 27°C (density 8900 kg/m³), while porous materials such as plywood exhibit higher values around 0.00183 m³/kg (density 545 kg/m³).[64] Temperature-induced expansions can slightly increase these volumes, but compressibility remains negligible for most applications.[64]
Fundamentals
Definition
Specific volume, denoted as , is defined as the ratio of the volume of a substance to its mass , mathematically expressed as .[1] This quantity provides a measure of the space occupied by a unit mass of the material under given conditions.[8] 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.[9] 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.[1][4] 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.[10] 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.[10]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 (kilogram). In engineering contexts, common alternative units include the cubic foot per pound (ft³/lb) in US customary systems and liters per gram (L/g) or cubic centimeters per gram (cm³/g) for smaller-scale measurements.[11] Specific volume is typically denoted by the lowercase letter , representing the volume per unit mass. The molar specific volume, which is the volume per unit amount of substance, is denoted by , where is the total volume and 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 density units. The following table provides key conversion factors to and from the SI unit:| Unit | Abbreviation | Conversion Factor to m³/kg |
|---|---|---|
| Cubic foot per pound | ft³/lb | 1 ft³/lb = 0.06243 m³/kg |
| Liter per gram | L/g | 1 L/g = 1 m³/kg |
| Cubic centimeter per gram | cm³/g | 1 cm³/g = 0.001 m³/kg |
Relations to Other Properties
Relation to Density
Specific volume, denoted as , is defined as the volume per unit mass of a substance, , where is the total volume and is the mass.[13] Density, denoted as , is the mass per unit volume, .[13] Substituting the expression for into the density formula yields the direct mathematical relation , demonstrating that specific volume and density are reciprocals of each other.[8] This inverse relationship arises fundamentally from the definitions, as an increase in volume for a fixed mass decreases density while increasing specific volume.[13] 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 is large (e.g., air at standard conditions has ), corresponding to low density, whereas density highlights compactness, which is more intuitive for dense liquids and solids.[8][14] 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.[8] 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 .[15] This expression links the rate of change of specific volume to the substance's resistance to compression, with the negative sign indicating volume decrease under increasing pressure.[15] As an example, for liquid water at standard temperature and pressure (0°C and 1 atm), the specific volume is approximately , yielding a density of .[16] This calculation illustrates the inverse relation in a common fluid, where small changes in correspond to significant shifts in .[16]Temperature and Pressure Effects
The specific volume of a substance varies with temperature at constant pressure primarily through thermal expansion, quantified by the volumetric thermal expansion coefficient , where is the specific volume and is the temperature.[17] For small temperature changes , this leads to the approximate relation , where is the initial specific volume.[17] This effect arises because increased thermal energy causes particles to vibrate more intensely, increasing intermolecular distances and thus the volume per unit mass.[17] The magnitude of thermal expansion differs markedly across states of matter. Gases exhibit significant expansion with rising temperature at constant pressure, as their low density allows substantial intermolecular separation; for instance, under near-ideal conditions, specific volume is directly proportional to temperature via Charles's law.[18] Liquids show a moderate increase in specific volume, with values typically on the order of to K, reflecting constrained molecular motion compared to gases.[17] Solids, by contrast, display negligible changes, with K or smaller, due to strong interatomic bonds that limit expansion.[17] Pressure influences specific volume at constant temperature through compressibility, defined by the isothermal compressibility , where is pressure.[19] For gases behaving nearly ideally, specific volume decreases inversely with pressure (), as molecules are forced closer together, enabling large volume reductions even at moderate pressures.[20] In liquids, however, low compressibility ( on the order of to Pa) results in minimal specific volume changes, requiring extreme pressures to achieve noticeable compression.[19][21] Solids exhibit even lower compressibility, with volume reductions that are practically insignificant under typical conditions.[19] These dependencies are often visualized in pressure-volume-temperature (PVT) diagrams, where isotherms (constant temperature lines) show specific volume decreasing with pressure, particularly steeply for gases, and isobars (constant pressure lines) illustrate volume increasing with temperature, with the steepest slopes for gases.[22] 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 thermal expansion.[22]Thermodynamic Contexts
Equations of State
Equations of state provide mathematical relations that connect specific volume to other thermodynamic properties such as pressure, temperature, and mass for substances, particularly gases. These equations are essential for predicting the behavior of fluids under varying conditions, enabling calculations in engineering and scientific applications. For ideal gases, the simplest form assumes no intermolecular forces or molecular volume, leading to a direct proportionality between specific volume and temperature at constant pressure. The ideal gas law, derived from the universal gas law , where is pressure, is total volume, is the number of moles, is the universal gas constant, and is temperature, can be expressed in terms of specific volume by substituting (with as mass and as molar mass). This yields , where is the specific gas constant for the substance. This relation holds well for gases at low pressures and high temperatures where deviations from ideality are negligible.[23] Real gases deviate from ideal behavior due to intermolecular attractions and the finite volume of molecules, necessitating corrections to the ideal gas law. The van der Waals equation accounts for these by modifying pressure and volume terms: , where corrects for attractive forces reducing effective pressure, and accounts for the excluded volume per unit mass (with and as mass-specific constants, related to molar constants by , ). This equation better predicts compressibility and phase behavior for gases near condensation. For instance, at high densities, the term becomes significant, reducing the predicted specific volume compared to the ideal case.[24][25] 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: , with mass-specific constants and fitted to experimental data for substances like methane and propane. This form enhances accuracy for non-polar gases at elevated pressures, capturing variations in specific volume more precisely in petroleum and natural gas processes.[26][27][28] For low-density gases, where intermolecular interactions are weak, the virial expansion provides a perturbative approach: , with virial coefficients , , 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 temperature.[26][27][28] In practical thermodynamics, especially for water and steam in power cycles, specific volume is often obtained from tabulated equations of state rather than explicit formulas. Steam tables based on the IAPWS-IF97 formulation provide specific volume as a function of pressure and temperature across liquid, 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.[29][30]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 latent heat. In vaporization, the transition from liquid to vapor phase at constant temperature and pressure involves a significant increase in specific volume due to the expansion of molecules into the gaseous state, requiring substantial latent heat to overcome intermolecular forces. For water at its boiling point of 100°C and standard atmospheric pressure (0.101325 MPa), the specific volume jumps from approximately 0.001044 m³/kg for the saturated liquid to 1.674 m³/kg for the saturated vapor, illustrating the dramatic volume expansion typical of this process. In contrast, fusion—the melting of a solid to a liquid—generally produces a smaller change in specific volume, as the molecular structure shifts from an ordered lattice to a more disordered but still condensed state. For water, this transition exhibits an anomalous behavior where the specific volume decreases slightly upon melting at 0°C, from about 0.001091 m³/kg for ice to 0.001000 m³/kg for liquid water, due to the open hydrogen-bonded structure of ice that occupies more space than the denser liquid phase.[31][32] This density inversion is unique to water and influences phenomena like ice flotation. At the critical point, the distinction between liquid and vapor phases vanishes, and the specific volume becomes continuous without a discontinuous jump, marking the end of the two-phase coexistence region. For water, this occurs at a critical temperature of 373.946 °C (647.096 K) and critical pressure of 22.064 MPa, where the saturated liquid and vapor specific volumes converge to approximately 0.003106 m³/kg (from critical density of 322 kg/m³).[33] The Clapeyron equation quantifies the relationship between the slope of the phase boundary in a pressure-temperature diagram and the changes in specific volume and latent heat during the transition: where is the molar latent heat, is the temperature, and is the change in molar specific volume between phases. This equation, derived from thermodynamic principles of equilibrium, links phase diagram slopes to volumetric expansions and is fundamental for predicting coexistence curves across various transitions.[34]Applications
Engineering Applications
Specific volume is essential in engineering design for thermodynamic processes, enabling precise calculations of work, capacity, and storage requirements in power generation, cooling systems, and material selection. By relating volume per unit mass to pressure and temperature conditions, it facilitates efficient sizing and optimization of components, ensuring safety and performance under operational constraints.[35] In power cycles like the Rankine cycle used in steam power plants, specific volume is integral to work calculations for turbines and pumps, where the shaft work is given by . This integral accounts for the fluid's expansion or compression under varying pressure, with the specific volume derived from steam tables or equations of state at cycle states. For pumps handling incompressible liquids, the work simplifies to , 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 fossil fuel and nuclear plants.[35][36] 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 , where is the compressor displacement rate and is the inlet specific volume, directly affects cooling capacity; lower 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.[37] For piping and storage systems handling pressurized gases, specific volume is used to compute required tank volumes as , with obtained from the ideal gas law or real gas equations at storage pressure and temperature. This ensures sufficient capacity for a desired mass while minimizing material use, as seen in compressed natural gas (CNG) vehicle tanks where high-pressure conditions reduce and thus physical volume needs. Such calculations are vital for safety compliance and cost optimization in chemical processing and energy storage.[38] In material selection for aerospace engineering, 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 thermal insulation in spacecraft and aircraft 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 insulation in cryogenic fuel tanks.[39][40]Fluid Mechanics Applications
In fluid mechanics, specific volume plays a crucial role in analyzing fluid flow, transport phenomena, and hydrodynamic behaviors, particularly where density variations affect momentum and mass conservation. As the reciprocal of density, specific volume directly influences calculations of flow rates and pressure distributions in both incompressible and compressible regimes.[41] The continuity equation, which enforces mass conservation in fluid flows, explicitly incorporates specific volume when expressing mass flow rates. For steady flow through a pipe of cross-sectional area , the mass flow rate is given by , where is the flow velocity; this form highlights how increases in specific volume (due to expansion or heating) inversely affect velocity to maintain constant mass flux.[41][42] Bernoulli's principle, traditionally applied to incompressible flows, requires adaptation for compressible fluids by integrating specific volume as a function of pressure, , to capture density changes along streamlines. In such cases, the energy equation becomes , assuming isentropic conditions, which accounts for work done due to compression or expansion in high-speed flows.[43][44] Cavitation in liquids, a critical concern in pumps and propellers, arises when local pressures drop below the vapor pressure, 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.[45][46] In aerodynamics, variations in specific volume are essential for modeling compressible airflows around aircraft, where Mach numbers exceed 0.3 and density changes impact lift and drag. For instance, as air accelerates over wings, pressure decreases cause specific volume to increase, altering shock wave formation and boundary layer behavior in transonic flight regimes, which informs airfoil design to mitigate compressibility effects.[47][48]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 of the mixture is given by the weighted sum based on mass fractions: where is the mass fraction of component and is the specific volume of the pure component at the same temperature and pressure. This formulation arises from the ideal solution model, which treats the mixture as a linear combination of the pure components' properties.[49] A key assumption in this model is that there is no volume change upon mixing (), meaning the total volume of the solution equals the sum of the volumes of the unmixed components. This condition aligns with Raoult's law, which describes the vapor pressure behavior in ideal solutions and implies negligible intermolecular forces beyond those in the pure states, preserving volume additivity across the composition range.[50] This approach finds practical use in dilute aqueous solutions, where the solute concentration is low enough that solvent-solute interactions mimic ideal behavior, and in gas mixtures at low pressures, where deviations from ideality are minimal. For instance, dry air is often modeled as an ideal mixture of approximately 78% nitrogen and 21% oxygen by volume (closely corresponding to mass fractions due to similar molar masses), yielding a specific volume that is the mass-weighted average of the pure gases' specific volumes at ambient conditions.[50][51]Non-Ideal Solutions
In non-ideal solutions, the specific volume deviates from ideal mixing behavior due to intermolecular interactions that alter the packing efficiency of molecules, leading to either expansion or contraction 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.[52] The excess specific volume, denoted as , is defined as the difference between the actual specific volume of the mixture and the ideal specific volume , where is the mass fraction and is the specific volume of pure component : Positive 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 signifies contraction, resulting from stronger attractive interactions, such as hydrogen bonding in ethanol-water mixtures or dipole interactions in acetone-chloroform systems. For instance, mixing equal volumes of ethanol and water 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-chloroform exhibits negative excess volumes up to -1.0 cm³/mol (≈ -0.011 cm³/g), attributed to complex formation between the carbonyl and hydrogen of chloroform.[53][54][55] Predictive models like COSMO-RS and UNIFAC are employed to estimate specific volumes in non-ideal binary and ternary 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. UNIFAC, 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 process design. These models are particularly valuable for screening solvents in multi-component blends, where direct measurements are impractical.[56][57] Partial specific volumes, , provide insight into the contribution of individual components to the mixture's volume and are defined as the partial derivative of total volume with respect to the mass of component at constant temperature , pressure , and masses of other components : In non-ideal solutions, 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 values (typically 0.7-0.75 cm³/g for proteins) correct for buoyancy and non-ideality, enabling precise characterization of biopolymers in aqueous solutions.[58] Understanding specific volumes in non-ideal solutions is essential in pharmaceuticals for optimizing drug solubility and formulation stability, where excess volume deviations influence the effective concentration and dissolution rates in mixed solvent systems, such as cosolvent mixtures for poorly soluble APIs. In petrochemical blending, these deviations affect storage and transport efficiencies; for example, negative excess volumes in oil stock mixtures lead to shrinkage upon blending, impacting yield calculations and requiring predictive models to minimize economic losses.[59][60]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 where is the specific volume in m³/kg, J/(mol·K) is the universal gas constant, is the temperature in K, is the pressure in Pa, and 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 m³/kg, oxygen (M = 0.032 kg/mol) has m³/kg, and carbon dioxide (M = 0.044 kg/mol) has m³/kg.[61] Specific volume for gases increases proportionally with temperature at constant pressure under the ideal approximation, reflecting thermal expansion. 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 , where temperatures are in K.[61] 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 compressibility factor Z (<1) corrects the ideal law as . For water vapor (steam), the IAPWS-IF97 formulation provides precise tabulations accounting for these effects. At atmospheric pressure and 100°C (saturation conditions), the specific volume of saturated steam is 1.673 m³/kg, slightly less than the ideal value of ≈1.70 m³/kg. At higher pressures, deviations grow; for superheated steam 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 STP for selected common gases and water vapor, derived from measured densities assuming near-ideal behavior:| Gas | Specific Volume (m³/kg) at STP |
|---|---|
| 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 |
| Air | 0.773 |
| Carbon Monoxide (CO) | 0.800 |
| Oxygen (O₂) | 0.700 |
| Argon (Ar) | 0.561 |
| Carbon Dioxide (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, , where is in cubic meters per kilogram (m³/kg) and is in kilograms per cubic meter (kg/m³).[62] Due to their incompressible nature, the specific volumes of liquids and solids remain nearly constant under moderate pressure changes, unlike gases, and are typically on the order of 10^{-3} m³/kg or less, reflecting their compact molecular packing.[63] This property is crucial in engineering for volume calculations in storage, transport, and thermal systems, where small variations often arise from temperature effects rather than pressure.[64] Representative specific volumes for common liquids at standard conditions (near room temperature and atmospheric pressure) are shown in the table below, calculated from established density data. Water, a benchmark liquid, has a specific volume of 0.001 m³/kg at 4°C, corresponding to its maximum density of 1000 kg/m³.[65] Mercury, a dense liquid metal, exhibits a much smaller value of approximately 0.000074 m³/kg at 20°C.[65] Organic liquids like ethanol and olive oil have values around 0.0013 m³/kg and 0.0011 m³/kg, respectively, at 20°C, illustrating moderate variations based on molecular structure.[65]| Liquid | Temperature (°C) | Density (kg/m³) | Specific Volume (m³/kg) |
|---|---|---|---|
| Water | 4 | 1000 | 0.001 |
| Mercury | 20 | 13590 | 0.000074 |
| Ethanol | 20 | 789 | 0.00127 |
| Olive oil | 20 | 911 | 0.00110 |
| Diesel fuel | 15 | 825 (avg.) | 0.00121 |
| Solid | Temperature (K or °C) | Density (kg/m³) | Specific Volume (m³/kg) |
|---|---|---|---|
| Aluminum | 300 K | 2700 | 0.00037 |
| Copper | 27°C | 8900 | 0.00011 |
| Ice | 273 K | 921 | 0.00109 |
| Plywood (Douglas Fir) | Room temp. | 545 | 0.00183 |
| Concrete | Room temp. | 2300 | 0.00043 |