volume
Art History
A unit of threedimensional measure of space that comprises a length, a width, and a height.
Chemistry
Calculus
Examples of volume in the following topics:

Lung Volumes and Capacities
 The volume in the lung can be divided into four units: tidal volume, expiratory reserve volume, inspiratory reserve volume, and residual volume.
 It is the sum of the expiratory reserve volume, tidal volume, and inspiratory reserve volume.
 It is, therefore, the sum of the tidal volume and inspiratory reserve volume.
 It is the sum of the residual volume, expiratory reserve volume, tidal volume, and inspiratory reserve volume. .
 Tidal volume is the volume of air inhaled in a single, normal breath.

Volume
 Some common volumes are taken as follows:
 The volume of a sphere: 4/3 times the radius cubed times pi.
 The volume of a solid can be determined by the volume of liquid it displaces when submerged.
 A measuring cup can be used to measure volumes of liquids.
 This cup measures volume in units of cups, fluid ounces and millilitres.

Volumes
 Three dimensional mathematical shapes are also assigned volumes.
 A volume integral is a triple integral of the constant function $1$, which gives the volume of the region $D$.
 Using the triple integral given above, the volume is equal to:
 Triple integral of a constant function $1$ over the shaded region gives the volume.
 Calculate the volume of a shape by using the triple integral of the constant function 1

Charles' and GayLussac's Law: Temperature and Volume
 Charles' Law describes the relationship between the volume and temperature of a gas.
 This law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin); in other words, temperature and volume are directly proportional.
 A car tire filled with air has a volume of 100 L at 10°C.
 If a gas contracts by 1/273 of its volume for each degree of cooling, it should contract to zero volume at a temperature of –273°C; this is the lowest possible temperature in the universe, known as absolute zero.
 The lower a gas' pressure, the greater its volume (Boyle's Law), so at low pressures, the fraction \frac{V}{273} will have a larger value; therefore, the gas must "contract faster" to reach zero volume when its starting volume is larger.

The Effect of the Finite Volume
 Real gases deviate from the ideal gas law due to the finite volume occupied by individual gas particles.
 Ideal gases are assumed to be composed of point masses whose interactions are restricted to perfectly elastic collisions; in other words, a gas particles' volume is considered negligible compared to the container's total volume.
 At high pressures where the volume occupied by gas molecules does not approach zero
 The particles of a real gas do, in fact, occupy a finite, measurable volume.
 At high pressures, the deviation from ideal behavior occurs because the finite volume that the gas molecules occupy is significant compared to the total volume of the container.

Avogadro's Law: Volume and Amount
 Avogadro's Law states that at the same temperature and pressure, equal volumes of different gases contain an equal number of particles.
 V is the volume of the gas, n is the number of moles of the gas, and k is a proportionality constant.
 The barrier moves when the volume of gas expands or contracts.
 What is the relationship between the number of molecules and the volume of a gas?
 (Note: Although the atoms in this model are in a flat plane, volume is calculated using 0.1 nm as the depth of the container.)

Changes in Volume and Pressure
 The effects of changes in volume and pressure on a reversible reaction in chemical equilibrium can be predicted by Le Chatelier's Principle.
 The effects of changes in volume and pressure on chemical equilibrium can be predicted using Le Chatelier's Principle.
 This principle can be applied to changes in temperature, concentration, volume, and pressure.
 One example of the effect of changing volume is shown in .
 As can be seen, a reduction in volume yields an increase in the pressure of the system, because volume and pressure are inversely related.

Shape and Volume
 Form is always considered threedimensional as it exhibits volume—or height, width, and depth.
 Art makes use of both actual and implied volume.
 While threedimensional forms, such as sculpture, have volume inherently, volume can also be simulated, or implied, in a twodimensional work such as a painting.
 Shape, volume, and space—whether actual or implied—are the basis of the perception of reality.
 Define shape and volume and identify ways they are represented in art

Boyle's Law: Volume and Pressure
 Boyle's Law describes the inverse relationship between the pressure and volume of a fixed amount of gas at a constant temperature.
 In this case, the initial pressure is 20 atm (P1), the initial volume is 1 L (V1), and the new volume is 1L + 12 L = 13 L (V2), since the two containers are connected.
 Gases can be compressed into smaller volumes.
 Run the model, then change the volume of the containers and observe the change in pressure.
 What happens to the pressure when the volume changes?

Cylindrical Shells
 Integration, as an accumulative process, can then calculate the integrated volume of a "family" of shells (a shell being the outer edge of a hollow cylinder), giving us the total volume.
 Therefore, the entire integrand, $2\pi x \left  f(x)  g(x) \right  \,dx$, is nothing but the volume of the cylindrical shell.
 By adding the volumes of all these infinitely thin cylinders, we can calculate the volume of the solid formed by the revolution.
 The volume of solid formed by rotating the area between the curves of $f(y)$ and and the lines $y=a$ and $y=b$ about the $x$axis is given by:
 Calculating volume using the shell method.