What is "specific volume"

Volume \Vol"ume\, n. [F., from L. volumen a roll of writing, a book, volume, from volvere, volutum, to roll. See Voluble.]

1. A roll; a scroll; a written document rolled up for keeping or for use, after the manner of the ancients. [Obs.]

   The papyrus, and afterward the parchment, was joined together [by the ancients] to form one sheet, and then rolled upon a staff into a volume (volumen).
   --Encyc. Brit.

2. Hence, a collection of printed sheets bound together, whether containing a single work, or a part of a work, or more than one work; a book; a tome; especially, that part of an extended work which is bound up together in one cover; as, a work in four volumes.

   An odd volume of a set of books bears not the value of its proportion to the set.
   --Franklin.

   4. Anything of a rounded or swelling form resembling a roll; a turn; a convolution; a coil.

   So glides some trodden serpent on the grass, And long behind wounded volume trails.
   --Dryden.

   Undulating billows rolling their silver volumes.
   --W. Irving.

   4. Dimensions; compass; space occupied, as measured by cubic units, that is, cubic inches, feet, yards, etc.; mass; bulk; as, the volume of an elephant's body; a volume of gas.

   5. (Mus.) Amount, fullness, quantity, or caliber of voice or tone.

   Atomic volume, Molecular volume (Chem.), the ratio of the atomic and molecular weights divided respectively by the specific gravity of the substance in question.

   Specific volume (Physics & Chem.), the quotient obtained by dividing unity by the specific gravity; the reciprocal of the specific gravity. It is equal (when the specific gravity is referred to water at 4[deg] C. as a standard) to the number of cubic centimeters occupied by one gram of the substance.

n. (context physics English) The volume of unit mass of a substance; the reciprocal of its density

In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density and an intrinsic property of matter as well. Specific volume is defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the cubic meter per kilogram (m^3/kg).

$\ v = \frac{V}{m}\ = {\rho}^{-1}$

Specific volume for an ideal gas is also equal to the gas constant (R) multiplied by the temperature and then divided by the pressure multiplied by molar mass of that ideal gas .

Since $\ PV = {nRT} \ (n = \frac{m}{M })$ $\ v = \frac{V}{m}$ , $\ v = \frac{R T}{PM }$

Typically, the specific volume of a substance is expressed in terms such as $\frac{\mathrm{m^3}}{\mathrm{kg}}$, $\frac{\mathrm{ft^3}}{\mathrm{lbm}}$, $\frac{\mathrm{ft^3}}{\mathrm{slug}}$, or $\frac{\mathrm{mL}}{\mathrm{g}}$ .