volume

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 Gay-Lussac'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 three-dimensional as it exhibits volume—or height, width, and depth.
  • Art makes use of both actual and implied volume.
  • While three-dimensional forms, such as sculpture, have volume inherently, volume can also be simulated, or implied, in a two-dimensional 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.