# Volume

Written by Jerry Ratzlaff on . Posted in Thermodynamics

## volume

Volume ( $$V$$ ) is the space occupied by a mass.  Volume is a extensive variable whose values depend on the quantity of substance under study.  It is expressed in terms of length cubed, a quantity of three dimensional space occupied by gas, liquid, or solid.  Volume is a scalar quantity having direction, some of these include area, density, energy, entropy, length, mass, power, pressure, speed, temperature, and work.

### volume formula

$$\large{ V = l w h }$$

$$\large{ V = \frac { m } { \rho } }$$

Where:

$$\large{ V }$$ = volume

$$\large{ h }$$ = height

$$\large{ l }$$ = length

$$\large{ m }$$ = mass

$$\large{ \rho }$$   (Greek symbol rho) = density

$$\large{ w }$$ = width

## Volume Differential

Volume differential ( $$\Delta V$$ ) is the difference between an expanded or reduced volume of a liquid.

### Volume Differential Formula

$$\large{ \Delta V = V_f - V_i }$$

Where:

$$\large{ \Delta V }$$ = volume differential

$$\large{ V_i }$$ = initial volume

$$\large{ V_f }$$ = final volume

## Volumetric Flow Rate

Volumetric flow rate ( $$Q$$ or $$V$$ ) (also called flow rate) is the amount of fluid that flows in a given time past a specific point.

### Volumetric Flow Rate formula

$$\large{ Q = A v }$$

$$\large{ Q = \frac {V} {t} }$$

$$\large{ Q = k i A }$$

Where:

$$\large{ Q }$$ = volumetric flow rate

$$\large{ A }$$ = cross section area

$$\large{ i }$$ = hydraulic gradient

$$\large{ k }$$ = hydraulic conductivity

$$\large{ t }$$ = time

$$\large{ v }$$ = flow velocity

$$\large{ V }$$ = area volume

## Volumetric Thermal Expansion

Volumetric thermal expansion (also known as volume thermal expansion) takes place in gasses and liquids when a change in temperature, volume or type of substance occures.

### Volumetric Thermal Expansion FORMULA

$$\large{ \Delta V = \beta V_o \Delta T }$$

$$\large{ \frac { \Delta V} { V_o } = \beta \Delta T }$$

Where:

$$\large{ \Delta V }$$ = volume differential

$$\large{ \beta }$$   (Greek symbol beta) = volumetric thermal expansion coefficient

$$\large{ \Delta T }$$ = temperature differential

$$\large{ V_o }$$ = origional volume of object

## volumetric Thermal Expansion Coefficient

Volumetric thermal expansion coefficient ( $$\beta$$ ) (also known as coefficient of volumetric thermal expansion) is the ratio of the change in size of a material to its change in temperature.

### Volumetric Thermal Expansion Coefficient FORMULA

$$\large{ \beta = \frac { 1 }{ V } \frac {\Delta A } {\Delta T} }$$

Where:

$$\large{ \beta }$$   (Greek symbol beta) = volumetric thermal expansion coefficient

$$\large{ \Delta A }$$ = area differential

$$\large{ \Delta T }$$ = temperature differential

$$\large{ V }$$ = volume of the object

## Reduced Specific Volume

Reduced specific volume ( $$\upsilon_r$$ ) (pseudo-reduced specific volume) of a fluid is ratio of the specific volume of a substance's critical pressure and temperature.

### Reduced Specific Volume formula

$$\large{ \upsilon_r = \frac {\upsilon p_c}{R^*T_c} }$$

Where:

$$\large{ \upsilon_r }$$    (Greek symbol upsilon) = reduced specific volume

$$\large{ p_c }$$ = critical pressure

$$\large{ R^* }$$ = universal gas constant

$$\large{ T_c }$$ = critical temperature

$$\large{ \upsilon}$$   (Greek symbol upsilon) = specific volume

## Specific Volume

Specific volume ( $$\upsilon$$ ) is the volume in a unit of mass.  Specific volume is a intensive variable whose physical quantity value does not depend on the amount of the substance for which it is measured.  Specific volume is the reciprocal of density, a substance with a higher density will have a lower specific volume.

### Specific Volume formula

$$\large{ \upsilon = \frac{V}{m} }$$

$$\large{ \upsilon = \frac{1}{\rho} }$$

Where:

$$\large{ \upsilon }$$   (Greek symbol upsilon) = specific volume

$$\large{ m }$$ = mass

$$\large{ \rho }$$   (Greek symbol rho) = density

$$\large{ V }$$ = volume

Solve for:

$$\large{ \rho = \frac{1}{\upsilon} }$$

Tags: Equations for Volume