Volume

Written by Jerry Ratzlaff on . Posted in Thermodynamics

volume 10Volume, abbreviated as 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 formulas

\(\large{  V = l \; w \; h  }\)   
\(\large{  V = \frac{ m  }{ \rho  }   }\)  (density) (mass)
\(\large{ V =   a^3 }\) (cube)
\(\large{ V= \frac{1}{2} \; \pi \; a^2 \;h   }\) (elliptic paraboloid)
\(\large{ V = \frac {n \; R \; T}{p} }\) (ideal gas law
\(\large{ V = \frac{l\;b\;h}{2} }\) (isosceles triangle wedge)
\(\large{ V = \pi\; r^2\;h }\) (oblique cylinder)
\(\large{ V = \frac {1}{3}\; \pi\; r^2 }\) (right cone)
\(\large{ V = \pi\; r^2\;h }\) (right cylinder)
\(\large{ V = \pi\; a_a \;b_a\; h }\) (right elliptic cylinder)
\(\large{ V = \frac {3\; \sqrt {3} }     { 2 }  \; a^2\;h     }\) (right hexagon prism)
\(\large{ V = \pi\; r_i^2\;h }\) (right hollow cylinder (inside) )
\(\large{ V = \pi\; h \left(R_o^2 - r_i^2  \right) }\) (right hollow cylinder (object) )
\(\large{ V= \frac {1}{4} \;  \sqrt { 5\; \left ( 5+2\; \sqrt {5} \right) } \;a^2\;h }\) (right pentagonal prism)
\(\large{ V= \frac{5}{6}\; r\;a\;h }\)  (right pentagonal pyramid)
\(\large{ V= a\;b\;h }\) (right rectangular prism)
\(\large{ V=a^2\;h }\) (right square prism)
\(\large{ V=  a^2\;  \frac{h}{3} }\) (right square pyramid)
\(\large{ V=\frac{1}{6}\; h_b\;a\;h }\) (right triangular prism)
\(\large{ V = \frac{l\;a\;b}{2} }\) (right triangle wedge)
\(\large{ V =  \frac{4}{3} \; \pi \;r^3  }\) (sphere)
\(\large{ V = 2 \; \pi^2 \; R_s\; r_s^2  }\) (torus)

Where:

\(\large{ V }\) = volume

\(\large{ A_b }\) = base area

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

\(\large{ a, b, c }\) = edge

\(\large{ h }\) = height

\(\large{ h_b }\) = height base

\(\large{ l } \) = length

\(\large{ a_a }\) = length semi-major axis

\(\large{ b_a }\) = length semi-minor axis

\(\large{ n }\) = number of moles of gas

\(\large{ m }\) = mass

\(\large{ n }\) = mole

\(\large{ \pi }\) = Pi

\(\large{ p }\) = pressure

\(\large{ r }\) = radius

\(\large{ r_s }\) = radius of sphere

\(\large{ R_s }\) = radius of center of sphere

\(\large{ r_i }\) = inside radius

\(\large{ R_o }\) = outside radius

\(\large{ p_s }\) = shape parameter

\(\large{ R }\) = specific gas constant (gas constant)

\(\large{ tan }\) = tangent

\(\large{ T }\) = temperature

\(\large{ w }\) = width

 

Tags: Equations for Volume