surface-to-volume ratio

(noun)

the amount of surface area per unit volume of an object or collection of objects; decreases as volume increases

Examples of surface-to-volume ratio in the following topics:

  • Limiting Effects of Diffusion on Size and Development

    • An important concept in understanding the efficiency of diffusion as a transportation mechanism is the surface-to-volume ratio.
    • Recall that any three-dimensional object has a surface area and volume; the ratio of these two quantities is the surface-to-volume ratio.
    • The surface-to-volume ratio of a sphere is 3/r; as the cell gets bigger, its surface-to-volume ratio decreases, making diffusion less efficient .
    • The surface-to-volume ratio of a sphere decreases as the sphere gets bigger.
    • The surface area of a sphere is 4πr2 and it has a volume of (4/3)πr3 which makes the surface-to-volume ratio 3/r.

  • Cell Size

    • Cell size is limited in accordance with the ratio of cell surface area to volume.
    • Therefore, as a cell increases in size, its surface area-to-volume ratio decreases.
    • The higher the surface area to volume ratio they have, the more effective this process can be.
    • Notice that as a cell increases in size, its surface area-to-volume ratio decreases.
    • The cell on the left has a volume of 1 mm3 and a surface area of 6 mm2, with a surface area-to-volume ratio of 6 to 1, whereas the cell on the right has a volume of 8 mm3 and a surface area of 24 mm2, with a surface area-to-volume ratio of 3 to 1.

  • Characteristics of Prokaryotic Cells

    • The capsule enables the cell to attach to surfaces in its environment.
    • You may remember from your high school geometry course that the formula for the surface area of a sphere is 4πr2, while the formula for its volume is 4/3πr3.
    • Therefore, as a cell increases in size, its surface area-to-volume ratio decreases.
    • If the cell grows too large, the plasma membrane will not have sufficient surface area to support the rate of diffusion required for the increased volume.
    • Notice that as a cell increases in size, its surface area-to-volume ratio decreases.When there is insufficient surface area to support a cell's increasing volume, a cell will either divide or die.The cell on the left has a volume of 1 mm3 and a surface area of 6 mm2, with a surface area-to-volume ratio of 6 to 1, whereas the cell on the right has a volume of 8 mm3 and a surface area of 24 mm2, with a surface area-to-volume ratio of 3 to 1.

  • Lung Volumes and Capacities

    • The energy necessary to re-inflate the lung could be too great to overcome.
    • The residual volume is the only lung volume that cannot be measured directly because it is impossible to completely empty the lung of air.
    • The ratio of these values (FEV1/FVC ratio) is used to diagnose lung diseases including asthma, emphysema, and fibrosis.
    • If the FEV1/FVC ratio is high, the lungs are not compliant (meaning they are stiff and unable to bend properly); the patient probably has lung fibrosis.
    • It takes a long time to reach the maximal exhalation volume.

  • The Work of Breathing

    • There are two ways to keep the alveolar ventilation constant: increase the respiratory rate while decreasing the tidal volume of air per breath (shallow breathing), or decrease the respiratory rate while increasing the tidal volume per breath.
    • By lowering the surface tension of the alveolar fluid, it reduces the tendency of alveoli to collapse.
    • Surfactant works like a detergent to reduce the surface tension, allowing for easier inflation of the airways.
    • They breathe at a very high lung volume to compensate for the lack of airway recruitment.
    • The ratio of FEV1 (the amount of air that can be forcibly exhaled in one second after taking a deep breath) to FVC (the total amount of air that can be forcibly exhaled) can be used to diagnose whether a person has restrictive or obstructive lung disease.

  • 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 $D$.
    • That is to say:
    • 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.

  • Lung Capacity and Volume

    • Lung volumes and capacities refer to phases of the respiratory cycle; lung volumes are directly measured while capacities are inferred.
    • An FEV1/FVC ratio of >80% indicates a restrictive lung disease like pulmonary fibrosis or infant respiratory distress syndrome.
    • To make sure that the inhaled air gets to the lungs, we need to breathe slowly and deeply.
    • Lung volumes and lung capacities refer to the volume of air associated with different phases of the respiratory cycle.
    • Determination of the residual volume is more difficult as it is impossible to "completely" breathe out.

  • Surface Tension

    • Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force.
    • Whereas the volume of a gas depends entirely on the pressure, the volume of a liquid is largely independent of the atmospheric pressure.
    • If no force acts normal (perpendicular) to a tensioned surface, the surface must remain flat.
    • In order for the surface tension forces to cancel out this force due to pressure, the surface must be curved.
    • That is to say, there is an energy difference between the interior and the surface: to move a molecule from the interior to the surface requires energy.

  • Shape and Volume

    • Shape refers to an area in two-dimensional space that is defined by edges; volume is three-dimensional, exhibiting height, width, and depth.
    • A "plane" refers to any surface area within space.
    • In two-dimensional art, the "picture plane" is the flat surface that the image is created upon, such as paper, canvas or wood.
    • Three-dimensional figures may be depicted on the flat picture plane through the use of the artistic elements to imply depth and volume, as seen in the painting "Flowers in a Jug" by Hans Memling .
    • Three-dimensional figures may be depicted on the flat picture plane through the use of the artistic elements to imply depth and volume.

  • Charles' and Gay-Lussac's Law: Temperature and Volume

    • What will the expanded volume of the tire be after driving the car has raised the temperature of the tire to 40°C?
    • The plots show that the ratio $\frac{V}{T}$ (and thus $\frac{\Delta V}{\Delta T}$) is a constant at any given pressure.
    • 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.
    • Discusses the relationship between volume and temperature of a gas, and explains how to solve problems using Charles' Law.