Volume (thermodynamics)

The volume of a thermodynamic system typically refers to the volume of the working fluid, such as, for example, the fluid within a piston. Changes to this volume may be made through an application of work, or may be used to produce work. An isochoric process however operates at a constant-volume, thus no work can be produced. Many other thermodynamic processes will result in a change in volume. A polytropic process, in particular, causes changes to the system so that the quantity ${\displaystyle pV^{n}}$ is constant (where ${\displaystyle p}$ is pressure, ${\displaystyle V}$ is volume, and ${\displaystyle n}$ is the polytropic index, a constant). Note that for specific polytropic indexes a polytropic process will be equivalent to a constant-property process. For instance, for very large values of ${\displaystyle n}$ approaching infinity, the process becomes constant-volume.

Gases are compressible, thus their volumes (and specific volumes) may be subject to change during thermodynamic processes. Liquids, however, are nearly incompressible, thus their volumes can be often taken as constant. In general, compressibility is defined as the relative volume change of a fluid or solid as a response to a pressure, and may be determined for substances in any phase. Similarly, thermal expansion is the tendency of matter to change in volume in response to a change in temperature.

Many thermodynamic cycles are made up of varying processes, some which maintain a constant volume and some which do not. A vapor-compression refrigeration cycle, for example, follows a sequence where the refrigerant fluid transitions between the liquid and vapor states of matter.

Typical units for volume are ${\displaystyle \mathrm {m^{3}} }$ (cubic meters), ${\displaystyle \mathrm {l} }$ (liters), and ${\displaystyle \mathrm {ft} ^{3}}$ (cubic feet).

Mechanical work performed on a working fluid causes a change in the mechanical constraints of the system; in other words, for work to occur, the volume must be altered. Hence volume is an important parameter in characterizing many thermodynamic processes where an exchange of energy in the form of work is involved.

Volume is one of a pair of conjugate variables, the other being pressure. As with all conjugate pairs, the product is a form of energy. The product ${\displaystyle pV}$ is the energy lost to a system due to mechanical work. This product is one term which makes up enthalpy ${\displaystyle H}$:

${\displaystyle H=U+pV,\,}$

where ${\displaystyle U}$ is the internal energy of the system.

The second law of thermodynamics describes constraints on the amount of useful work which can be extracted from a thermodynamic system. In thermodynamic systems where the temperature and volume are held constant, the measure of "useful" work attainable is the Helmholtz free energy; and in systems where the volume is not held constant, the measure of useful work attainable is the Gibbs free energy.

Similarly, the appropriate value of heat capacity to use in a given process depends on whether the process produces a change in volume. The heat capacity is a function of the amount of heat added to a system. In the case of a constant-volume process, all the heat affects the internal energy of the system (i.e., there is no pV-work, and all the heat affects the temperature). However, in a process without a constant volume, the heat addition affects both the internal energy and the work (i.e., the enthalpy); thus the temperature changes by a different amount than in the constant-volume case and a different heat capacity value is required.

Specific volume (${\displaystyle \nu }$) is the volume occupied by a unit of mass of a material.[1] In many cases the specific volume is a useful quantity to determine because, as an intensive property, it can be used to determine the complete state of a system in conjunction with another independent intensive variable. The specific volume also allows systems to be studied without reference to an exact operating volume, which may not be known (nor significant) at some stages of analysis.

The specific volume of a substance is equal to the reciprocal of its mass density. Specific volume may be expressed in ${\displaystyle {\frac {\mathrm {m^{3}} }{\mathrm {kg} }}}$, ${\displaystyle {\frac {\mathrm {ft^{3}} }{\mathrm {lb} }}}$, ${\displaystyle {\frac {\mathrm {ft^{3}} }{\mathrm {slug} }}}$, or ${\displaystyle {\frac {\mathrm {mL} }{\mathrm {g} }}}$ .

${\displaystyle \nu ={\frac {V}{m}}={\frac {1}{\rho }}}$

where, ${\displaystyle V}$ is the volume, ${\displaystyle m}$ is the mass and ${\displaystyle \rho }$ is the density of the material.

For an ideal gas,

${\displaystyle \nu ={\frac {{\bar {R}}T}{P}}}$

where, ${\displaystyle {\bar {R}}}$ is the specific gas constant, ${\displaystyle T}$ is the temperature and ${\displaystyle P}$ is the pressure of the gas.

Specific volume may also refer to molar volume.

• Volumetric flow rate