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The partial specific volume v i ¯ , {\displaystyle {\bar {v_{i}}},} express the variation of the extensive volume of a mixture in respect to composition
Partial_specific_volume
Volume occupied per unit mass
{V}{m}}={\frac {RT}{PM}}} Specific volume is commonly applied to: Molar volume Volume (thermodynamics) Partial molar volume Imagine a variable-volume, airtight chamber
Specific_volume
Change in a property of a mixture component with respect to amount
partial molar property. The partial molar volume is broadly understood as the contribution that a component of a mixture makes to the overall volume of
Partial_molar_property
Heat required to raise the temperature of a given unit of mass of a substance
constant volume, respectively. The specific heat capacity of a material on a per-mass basis is c = ∂ C ∂ m , {\displaystyle c={\frac {\partial C}{\partial m}}
Specific_heat_capacity
Mass per unit volume
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ρ (the
Density
Topics referred to by the same term
PSV may refer to: Papa Stour Airstrip (IATA code PSV) Partial specific volume Peak systolic velocity Petit Saint Vincent, an island south of St. Vincent
PSV
Thermodynamic quantity
ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV).
Heat_capacity_ratio
Physical property of matter
dQ=\left({\frac {\partial U}{\partial T}}\right)_{V}dT+\left({\frac {\partial U}{\partial V}}\right)_{T}dV+pdV} For a constant volume ( d V = 0 {\displaystyle
Heat_capacity
Extensive parameter used to describe a thermodynamic system's state
thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property
Volume_(thermodynamics)
Serum albumin protein derived from cows
(monomer), 6.7 (dimer) Diffusion constant, D20,W × 10−7 cm2/s: 5.9 Partial specific volume, V20: 0.733 Intrinsic viscosity, η: 0.0413 Frictional ratio, f/f0:
Bovine_serum_albumin
Derivative of a function with multiple variables
{\partial ^{2}f}{\partial y\,\partial x}}={\frac {\partial }{\partial y}}\left({\frac {\partial f}{\partial x}}\right)=(f'_{x})'_{y}=f''_{xy}=\partial _{yx}f=\partial
Partial_derivative
Properties independent of system size, and proportional to system size
refractive index specific heat capacity, cp specific internal energy, u specific rotation, [α] specific volume, v standard reduction potential, E° surface
Intensive and extensive properties
Intensive_and_extensive_properties
Parameter used to calculate the volume change of a fluid or solid in response to pressure
V ∂ p {\displaystyle \beta =-{\frac {1}{V}}{\frac {\partial V}{\partial p}}} , where V is volume and p is pressure. The choice to define compressibility
Compressibility
Equation of the state of a hypothetical ideal gas
written in terms of the specific volume v, the reciprocal of density, as p v = R specific T . {\displaystyle pv=R_{\text{specific}}T.} It is common, especially
Ideal_gas_law
Measure of energy in a thermodynamic system
(mass per unit volume), h is the specific enthalpy (enthalpy per unit mass), ρh represents the enthalpy density (enthalpy per unit volume), dV denotes an
Enthalpy
Type of thermodynamic potential
{\displaystyle \left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Q_{\mathrm {ele} },p}=-\left({\frac {\partial S}{\partial Q_{\mathrm {ele} }}}\right)_{T
Gibbs_free_energy
Number and arrangement of multiple folded protein subunits in a multi-subunit complex
mass can be inferred from its volume using the partial specific volume of 0.73 ml/g. However, volume measurements are less certain than mass measurements
Protein_quaternary_structure
Tendency of matter to change volume in response to a change in temperature
{\frac {1}{V}}\left({\frac {\partial V}{\partial T}}\right)_{p}={\frac {1}{V_{m}}}\left({\frac {\partial V_{m}}{\partial T}}\right)_{p}={\frac {1}{V_{m}}}\left({\frac
Thermal_expansion
Energy contained within a system
T\left({\frac {\partial S}{\partial T}}\right)_{V}} is the heat capacity at constant volume C V . {\displaystyle C_{V}.} The partial derivative of S {\displaystyle
Internal_energy
Protein without a fixed 3D structure
also be a sign of disorder. Folded proteins have a high density (partial specific volume of 0.72-0.74 mL/g) and commensurately small radius of gyration
Intrinsically disordered proteins
Intrinsically_disordered_proteins
Thermodynamic cycle for spark ignition piston engines
giving the terms units of joules/kg (specific energy), meters3/kg (specific volume), or joules/(kelvin·kg) (specific entropy, heat capacity) etc. and would
Otto_cycle
T}}\right)_{P}\quad =-{\frac {T}{N}}\,{\frac {\partial ^{2}G}{\partial T^{2}}}} Specific heat at constant volume c V = T N ( ∂ S ∂ T ) V = − T N ∂ 2 A ∂ T
Material properties (thermodynamics)
Material_properties_(thermodynamics)
Equations in thermodynamics
\over V}\left({\partial V \over \partial p}\right)_{T,N{\text{ or }}S,N}} Specific heat (per-particle) at constant pressure or constant volume c p or V =
Thermodynamic_equations
Equation describing a state of matter under a given set of conditions
between volume and temperature: V 1 T 1 = V 2 T 2 . {\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}.} Dalton's law (1801) of partial pressure
Equation_of_state
State variables for near-critical fluids
the Peng–Robinson equation of state. The reduced specific volume (or "pseudo-reduced specific volume") of a fluid is computed from the ideal gas law at
Reduced_properties
Type of differential equation
mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The
Partial_differential_equation
Partial differential relations in thermodynamics
{\frac {\partial }{\partial x_{j}}}\left({\frac {\partial \Phi }{\partial x_{i}}}\right)={\frac {\partial }{\partial x_{i}}}\left({\frac {\partial \Phi }{\partial
Maxwell_relations
Thermodynamic process in which no mass or heat is exchanged with surroundings
expressed as E = γP, where γ is the ratio of specific heats at constant pressure and at constant volume ( γ = Cp/Cv) and P is the pressure of the gas
Adiabatic_process
Thermodynamic process with no change in enthalpy
H; or specific enthalpy, h. If a steady-state, steady-flow process is analysed using a control volume, everything outside the control volume is considered
Isenthalpic_process
Refrigerator that uses a heat source
a low partial pressure environment, thus extracting heat from its surroundings (e.g. the refrigerator's compartment). Because of the low partial pressure
Absorption_refrigerator
{\displaystyle \pi _{T}} . It is defined as a partial derivative of internal energy with respect to volume at constant temperature: π T = ( ∂ U ∂ V ) T
Internal_pressure
Mathematical model which approximates the behavior of real gases
where U is the internal energy ĉV is the dimensionless specific heat capacity at constant volume, approximately 3/2 for a monatomic gas, 5/2 for diatomic
Ideal_gas
Phenomenon of non-ideal fluids changing temperature
gas. Combined with the specific heat capacity at constant pressure c P = ( ∂ h / ∂ T ) P {\displaystyle c_{P}=(\partial h/\partial T)_{P}} it allows the
Joule–Thomson_effect
Absorption refrigerator invented in 1930
databases Specific heat capacity c = {\displaystyle c=} T {\displaystyle T} ∂ S {\displaystyle \partial S} N {\displaystyle N} ∂ T {\displaystyle \partial T}
Einstein_refrigerator
Observational basis of thermodynamics
Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations
Laws_of_thermodynamics
Thermodynamic cycle
gas turbine featuring intermittent combustion (Holzwarth 150 kW, constant volume combustion) 1923 First exhaust-gas turbocharger to increase the power of
Brayton_cycle
Physical law for entropy and heat
function of its entropy S, volume V, and mol number N, i.e. U = U (S, V, N), then the temperature is equal to the partial derivative of the internal energy
Second_law_of_thermodynamics
Idealized thermodynamic cycle
in the same ratio as QH/TH. When a Carnot cycle is plotted on a pressure–volume diagram (Figure 1), the isothermal stages follow the isotherm lines for
Carnot_cycle
Force distributed over an area
conjugate to volume. It is defined as a derivative of the internal energy of a system: p = − ( ∂ U ∂ V ) S , N , {\displaystyle p=-\left({\frac {\partial U}{\partial
Pressure
Thermodynamic process in which pressure remains constant
the molar specific heat capacity at constant pressure (cp) is 7/2R or 29.1006 J mol−1 deg−1. The molar heat capacity at constant volume (cv) is 5/2R
Isobaric_process
Body of matter in a state of internal equilibrium
conceptual basis of thermodynamics requires some type of wall: a small volume element of a continuous medium subject to a thermodynamic change will exchange
Thermodynamic_system
Thermodynamic cycle
issued 1886-02-16 Clerk, Dugald (1913). The gas, petrol, and oil engine, Volume 2. J. Wiley. p. 210. Heywood, John B. Internal Combustion Engine Fundamentals
Atkinson_cycle
Thermodynamic process of a closed system in which volume remains constant
U = d Q {\displaystyle dU=dQ} Using the definition of specific heat capacity at constant volume, cv = (dQ/dT)/m, where m is the mass of the gas, we get
Isochoric_process
Solvent property in polymer science
osmotic pressure ( Π {\displaystyle \Pi } ) and the solvent's partial specific volume ( v s {\displaystyle v_{s}} ): Δ μ 1 = − v s Π {\displaystyle \Delta
Theta_solvent
Property of a thermodynamic system
, N ⇒ ⋯ ⇒ d S = d Q T {\displaystyle T:={\left({\frac {\partial U}{\partial S}}\right)}_{V,N}\ \Rightarrow \ \cdots \ \Rightarrow \ \mathrm {d}
Entropy
Method of separating particles in a mixture
pellets.[citation needed] Sedimentation depends on mass, shape, and partial specific volume of a macromolecule, as well as solvent density, rotor size and
Differential_centrifugation
State of thermodynamic systems where no net flow of matter or energy occurs
states that gases dissolve in direct proportion to their partial pressures. By influencing the partial pressure on the top of a closed system, this would help
Thermodynamic_equilibrium
Law of physics
assumption.[citation needed] On the other hand, the molar specific heat at constant volume of a monatomic classical ideal gas, such as helium at room
Third_law_of_thermodynamics
Physical law for definition of temperature
P1V1/N1 = P2V2/N2 where Pi is the pressure in the ith system, Vi is the volume, and Ni is the amount (in moles, or simply the number of atoms) of gas.
Zeroth_law_of_thermodynamics
Volume of fluid which passes per unit time
dynamics, the volumetric flow rate (also known as volume flow rate, or volume velocity) is the volume of fluid which passes per unit time; usually it is
Volumetric_flow_rate
Thermodynamic process
exactly define intensive quantities (such as pressure, temperature, specific volume, specific entropy) of the system at any instant during the whole process;
Quasistatic_process
Law of thermodynamics establishing the conservation of energy
variables S, entropy, and V, volume: U = U (S, V). In these terms, T, the system's temperature, and P, its pressure, are partial derivatives of U with respect
First_law_of_thermodynamics
Theorem in calculus
represents a volume in three-dimensional space) which is compact and has a piecewise smooth boundary S (also indicated with ∂ V = S {\displaystyle \partial V=S}
Divergence_theorem
Function describing equilibrium states of a system
Entropy (S) Pressure (P) Temperature (T) Volume (V) Chemical composition Pressure altitude Specific volume (v) or its reciprocal density (ρ) Particle
State_function
Thermodynamic cycle
databases Specific heat capacity c = {\displaystyle c=} T {\displaystyle T} ∂ S {\displaystyle \partial S} N {\displaystyle N} ∂ T {\displaystyle \partial T}
Miller_cycle
Engine combustion process
{\displaystyle p} is pressure and V the volume or v {\displaystyle v} the specific volume if the process is placed on a unit mass basis. The idealized Diesel
Diesel_cycle
Thermodynamic process that is reversible and adiabatic
{\displaystyle C_{p}} = molar specific heat at constant pressure, C v {\displaystyle C_{v}} = molar specific heat at constant volume. Gas laws Adiabatic process
Isentropic_process
Scalar physical quantities representing system states
temperature and convex function of volume. ( ∂ 2 H ∂ P 2 ) S , N ≤ 0 {\displaystyle {\biggl (}{\frac {\partial ^{2}H}{\partial P^{2}}}{\biggr )}_{S,N}\leq 0}
Thermodynamic_potential
Type of energy transfer
_{S_{1}}^{S_{2}}\left({\frac {\partial H}{\partial S}}\right)_{P}\mathrm {d} S+\int _{P_{1}}^{P_{2}}\left({\frac {\partial H}{\partial P}}\right)_{S}\mathrm {d}
Heat
English physical chemist
Davies, David Gwynne; Bury, Charles R. (1930). "CCLXXXIX.—The partial specific volume of potassium n-octoate in aqueous solution". J. Chem. Soc.: 2263–2267
Charles_Rugeley_Bury
Equations on thermodynamic quantities
the volume of the system constant, the change of entropy satisfies d S = ( ∂ S ∂ T ) V d T {\displaystyle dS=\left({\frac {\partial S}{\partial T}}\right)_{V}dT}
Fundamental thermodynamic relation
Fundamental_thermodynamic_relation
Imaginary volume through which a substance's flow is modeled and analyzed
dp={\frac {\partial p}{\partial t}}dt+{\frac {\partial p}{\partial x}}dx+{\frac {\partial p}{\partial y}}dy+{\frac {\partial p}{\partial z}}dz} (the total
Control_volume
Thermodynamic phase transition energy
used the term in the context of calorimetry where a heat transfer caused a volume change in a body while its temperature was constant. In contrast to latent
Latent_heat
Diagram showing the relationship between pressure and volume in a system
[citation needed] Note that in some cases specific volume will be plotted on the x-axis instead of volume, in which case the area under the curve represents
Pressure–volume_diagram
Thermodynamic process
relation: p V n = C {\displaystyle pV^{n}=C} where p is the pressure, V is volume, n is the polytropic index, and C is a constant. The polytropic process
Polytropic_process
Thermodynamic potential
{-{\frac {\partial }{\partial \beta }}e^{-\beta E_{r}}}{Z}}={\frac {-{\frac {\partial }{\partial \beta }}\sum _{r}e^{-\beta E_{r}}}{Z}}=-{\frac {\partial \log
Helmholtz_free_energy
Assembly of heat engines that work in tandem from the same source of heat
electrical load, because duct burners can have very good efficiency with partial loads. It can enable higher steam production to compensate for the failure
Combined-cycle_power_plant
Version of the second law of thermodynamics
databases Specific heat capacity c = {\displaystyle c=} T {\displaystyle T} ∂ S {\displaystyle \partial S} N {\displaystyle N} ∂ T {\displaystyle \partial T}
Clausius_theorem
Thermodynamic cycle that includes the basic Stirling engine
isentropic processes featured in the Carnot cycle are replaced by two constant-volume regeneration processes. The cycle is reversible, meaning that if supplied
Stirling_cycle
Process whose direction can be reversed
reversibility, since expansion work, which can be visualized on a pressure–volume diagram as the area beneath the equilibrium curve, is different for different
Reversible process (thermodynamics)
Reversible_process_(thermodynamics)
Model that is used to predict the performance of steam turbine systems
equations[1] is derived from the energy and mass balance for a control volume. Q ˙ in m ˙ = h 3 − h 2 , {\displaystyle {\frac {{\dot {Q}}_{\text{in}}}{\dot
Rankine_cycle
Equations definiting head capacities in thermodynamics
_{S}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial P}}\right)_{S}\,} A corresponding expression for the difference in specific heat capacities (intensive
Relations between heat capacities
Relations_between_heat_capacities
Initial step in the phase transition or molecular self-assembly of a substance
before a new phase or self-organised structure appears. For example, if a volume of water is cooled (at atmospheric pressure) significantly below 0 °C, it
Nucleation
Mathematical sequence satisfying a specific pattern
elements of the arithmetic and the geometric sequence, respectively. This partial sum has the closed-form expression S n = a b − ( a + n d ) b r n 1 − r
Arithmetico-geometric sequence
Arithmetico-geometric_sequence
German physicist and physiologist (1821–1894)
seem linear, a fact that is used in current electronic devices to control volume. Helmholtz paved the way in experimental studies on the relationship between
Hermann_von_Helmholtz
Type of energy transfer
system, which always occur in conjugate pairs, for example pressure and volume or magnetic flux density and magnetization. In the International System
Work_(thermodynamics)
Pair of values which express a thermodynamic system's internal energy
pairs of conjugate variables such as temperature and entropy, pressure and volume, or chemical potential and particle number. In fact, all thermodynamic potentials
Conjugate variables (thermodynamics)
Conjugate_variables_(thermodynamics)
isentrope drawn on the specific volume versus pressure plane. Specifically, the Landau derivative is a second derivative of specific volume with respect to pressure
Landau_derivative
Opposition that a system presents to an acoustic pressure
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic
Acoustic_impedance
System that converts heat or thermal energy to mechanical work
sink) isobaric (at constant pressure) isometric/isochoric (at constant volume), also referred to as iso-volumetric adiabatic (no heat is added or removed
Heat_engine
Measure of how much alcohol is in a liquid
causes a decrease in volume. The phenomenon of volume changes due to mixing dissimilar solutions is called "partial molar volume". Water and ethanol are
Alcohol_by_volume
Set of quasilinear hyperbolic equations governing adiabatic and inviscid flow
thermodynamics is the opposite of the partial derivative of the specific internal energy with respect to the specific volume: p ( v , s ) = − ∂ e ( v , s ) ∂
Euler equations (fluid dynamics)
Euler_equations_(fluid_dynamics)
Quantifiable conditions of a thermodynamic system at a specific time
thermodynamics, a thermodynamic state of a system is its condition at a specific time; that is, fully identified by values of a suitable set of parameters
Thermodynamic_state
Relations between flows and forces, or gradients, in thermodynamic systems
{\partial s}{\partial t}}+\nabla \cdot \mathbf {J} _{s}={\frac {\partial s_{c}}{\partial t}}} where ∂ s c / ∂ t {\textstyle {\partial s_{c}}/{\partial t}}
Onsager_reciprocal_relations
Concentration of water vapour in the air
widely employed: absolute, relative, and specific. Absolute humidity is the mass of water vapor per volume of air (in grams per cubic meter). Relative
Humidity
Concept in general relativity and quantum field theory
surrounding any volume in spacetime limits the information content of the volume. Thus the number of degrees of freedom in any volume is bounded and not
Black_hole_thermodynamics
Process that cannot be undone or reversed
would be irreversible because you couldn't add or remove heat or change the volume to return the system to its initial state. Thus, if the system is always
Irreversible_process
Heat exchanged by a body or thermodynamic system
unchanged certain other macroscopic variables of the body or system, such as volume or pressure. Sensible heat is in contrast to latent heat, which is the amount
Sensible_heat
Thermodynamic process in which temperature remains constant
gas volume. For an isothermal (constant temperature T), reversible process, this integral equals the area under the relevant PV (pressure-volume) isotherm
Isothermal_process
Physical quantity of hot and cold
function of the volume and entropy of a homogeneous system in thermodynamic equilibrium, thermodynamic absolute temperature appears as the partial derivative
Temperature
Linked cyclic series of thermodynamic processes
Decrease in pressure (P), Increase in volume (v), Decrease in temperature (T) 2→3: Isochoric cooling: Constant volume(v), Decrease in pressure (P), Decrease
Thermodynamic_cycle
Mathematical models of heat pumps and refrigeration
absorption cycle is similar to the compression cycle, but depends on the partial pressure of the refrigerant vapor. In the absorption system, the compressor
Heat pump and refrigeration cycle
Heat_pump_and_refrigeration_cycle
Variation on the Rankine thermodynamic cycle
electricity on small to medium size scaled power plants. The problem of high specific investment costs for machinery, such as steam boilers, are overcome due
Organic_Rankine_cycle
Branch of thermodynamics
{\displaystyle \sigma =\sum _{i,j}L_{ij}{\frac {\partial F_{i}}{\partial x_{i}}}{\frac {\partial F_{j}}{\partial x_{j}}}} The second law of thermodynamics requires
Non-equilibrium thermodynamics
Non-equilibrium_thermodynamics
Passage of a system from an initial to a final state of thermodynamic equilibrium
shown. Each process has a well-defined start and end point in the pressure-volume state space. In this particular example, processes 1 and 3 are isothermal
Thermodynamic_process
forces are balanced. Since V equals the particle mass m times its partial specific volume ν ¯ {\displaystyle {\bar {\nu }}} , the equilibrium condition may
Mason–Weaver_equation
Correction factor which describes the deviation of a real gas from ideal gas behavior
reduced specific volume must be found. Unlike the reduced pressure and temperature, the reduced specific volume is not found by using the critical volume. The
Compressibility_factor
Performance measure of a device that uses thermal energy
heat engine due to temperature, called the Carnot efficiency. Second, specific types of engines have lower limits on the ideal efficiency of the engine
Thermal_efficiency
Integral of drug concentration in blood plasma over time
elimination. The amount eliminated by the body (mass) = clearance (volume/time) * AUC (mass*time/volume).[citation needed] In pharmacokinetics, bioavailability generally
Area under the curve (pharmacokinetics)
Area_under_the_curve_(pharmacokinetics)
Z ∂ T ) V {\displaystyle U=Nk_{\text{B}}T^{2}\left({\frac {\partial \ln Z}{\partial T}}\right)_{V}} S = U T + N k B ln Z − N k ln N + N k {\displaystyle
Table of thermodynamic equations
Table_of_thermodynamic_equations
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