excluded volume

Examples of excluded volume in the following topics:

• Van der Waals Equation

  • The van der Waals equation modifies the Ideal Gas Law to correct for the excluded volume of gas particles and intermolecular attractions.
  • As the pressure increases, the volume of the container decreases. 
  • The volume occupied by the gas particles is no longer negligible compared to the volume of the container and the volume of the gas particles needs to be taken into account. 
  • where P is the pressure, V is the volume, R is the universal gas constant, and T is the absolute temperature.
  • The b term represents the excluded volume of the gas or the volume occupied by the gas particles.

• The Effect of Intermolecular Forces

  • In the term above, a is a constant specific to each gas and V is the volume. van der Waals also corrected the volume term by subtracting out the excluded volume of the gas.
  • where b is the excluded volume of the gas, R is the universal gas constant, and T is the absolute temperature.

• The Effect of the Finite Volume

  • Real gases deviate from the ideal gas law due to the finite volume occupied by individual gas particles.
  • 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.
  • The van der Waals equation modifies the ideal gas law to correct for this excluded volume, and is written as follows:

• Real Gases

  • (Isotherms refer to the different curves on the graph, which represent a gas' state at different pressure and volume conditions but at constant temperature; "Iso-" means same and "-therm" means temperature—hence isotherm.)
  • For most applications, the ideal gas approximation is reasonably accurate; the ideal gas model tends to fail at lower temperatures and higher pressures, however, when intermolecular forces and the excluded volume of gas particles become significant.
  • Real gases are often modeled by taking into account their molar weight and volume:
  • b is an empirically determined factor that corrects for the excluded volume of gas particles; it is specific for each gas
  • According to the Ideal Gas Equation, PV=nRT, pressure and volume should have an inverse relationship.

• Chronic Obstructive Pulmonary Disease (COPD)

  • No single symptom or sign can adequately confirm or exclude the diagnosis of COPD.
  • The diagnosis of COPD is confirmed by spirometry, a test that measures the forced expiratory volume in one second (FEV1), which is the greatest volume of air that can be breathed out in the first second of a large breath.
  • Spirometry also measures the forced vital capacity (FVC), which is the greatest volume of air that can be breathed out in a whole, large breath.
  • It can be useful to help exclude other lung diseases, such as pneumonia, pulmonary edema or a pneumothorax.
  • A high-resolution computed tomography scan of the chest may show the distribution of emphysema throughout the lungs and can also be useful to exclude other lung diseases.

• Sales Forecast Input

  • includes/excludes amounts capital goods & services, non-capital goods & services, input valued-added tax, with cost of non-capital goods sold
  • Target volume is the unit sales quantity required to meet an earnings goal.
  • Target volume: the volume of sales necessary to generate the profits specified in a company's plans.
  • Target Volume = [Fixed costs + Target Profits] / Contribution per Unit
  • Target Revenue = Target Volume * Selling Price per Unit; or

• Acid-Base Titrations

  • Place the standardized solution into the burette, and indicate its initial volume in a lab notebook.
  • This is the first titration and it is not very precise; it should be excluded from any calculations.
  • (Subtracting the initial volume from the final volume will yield the amount of titrant used to reach the endpoint.)
  • The burette is calibrated to show volume to the nearest 0.001 cm3.
  • Compute the concentration of an unknown acid or base given its volume and the volume and concentration of the standardized titrant.

• Comparison of Enthalpy to Internal Energy

  • A thermodynamic system can be any physical system with a well-defined volume in space.
  • It includes the energy needed to create the system, but excludes the energy needed to displace the system's surrounding or energy displacement due to external forces.
  • For example, if a reaction is held at constant volume, no work is performed and therefore $\Delta U=q$.
  • Therefore, to account for both the possible volume change at constant pressure and the internal energy, enthalpy is used.

• Freshwater Environments

  • The term specifically excludes seawater and brackish water but it does include mineral rich waters such as chalybeate springs.
  • Visualization of the distribution (by volume) of water on Earth.

• 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.