Monday, January 22, 2018

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Fluid Mechanics - Gas Laws

The Ideal Gas Law relates pressure, volume, molecular quantity, and temperature of an ideal gas together in one neat mathematical expression:
 

Where,

  P = Absolute pressure (atmospheres)

  V = Volume (liters)

  n = Gas quantity (moles)

  R = Universal gas constant (0.0821 L atm / mol K)

  T = Absolute temperature (K)

 

An alternative form of the Ideal Gas Law uses the number of actual gas molecules (N) instead of the number of moles of molecules (n):

 

Where,

  P = Absolute pressure (atmospheres)

  V = Volume (liters)

  N = Gas quantity (molecules)

  k = Boltzmann’s constant (1.38 × 10-23 J / K)

  T = Absolute temperature (K)


Although no gas in real life is ideal, the Ideal Gas Law is a close approximation for conditions of modest gas density, and no phase changes (gas turning into liquid or visa-versa). 

Since the molecular quantity of an enclosed gas is constant, and the universal gas constant must be constant, the Ideal Gas Law may be written as a proportionality instead of an equation:


 

Several “gas laws” are derived from this Ideal Gas Law. They are as follows:

 

 

You will see these laws referenced in explanations where the specified quantity is constant (or very nearly constant).

For non-ideal conditions, the “Real” Gas Law formula incorporates a corrected term for the compressibility of the gas:

Where,

  P = Absolute pressure (atmospheres)

  V = Volume (liters)

  Z = Gas compressibility factor (unitless)

  n = Gas quantity (moles)

  R = Universal gas constant (0.0821 L atm / mol K)

  T = Absolute temperature (K)

 

The compressibility factor for an ideal gas is unity (Z = 1), making the Ideal Gas Law a limiting case of the Real Gas Law. Real gases have compressibility factors less than unity (< 1). What this means is real gases tend to compress more than the Ideal Gas Law would predict (i.e. occupies less volume for a given amount of pressure than predicted, and/or exerts less pressure for a given volume than predicted).

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