# Abbreviations, Gas Laws

## Pressures

• P b , barometric (ambient) pressure

• P h 2 o , water vapor pressure

## Respiratory Gases

• P a , partial pressure of a gas in alveolar air; for example, P ao 2 , partial pressure of oxygen in the alveolus

• Pa, partial pressure of a gas in arterial blood; for example, Pa o 2 , partial pressure of oxygen in arterial blood

• P v , partial pressure of a gas in mixed venous blood; for example, P vo 2 , partial pressure of oxygen in mixed venous blood

## Volumes

• TV or V t , Tidal volume

• FRC, Functional residual capacity

• RV, Residual volume

• VC, Vital capacity

• FVC, Forced vital capacity

• TLC, Total lung capacity

• V d , Anatomic dead space volume

• V d /V t , Ratio of dead space volume to tidal volume

## Blood Flow

• Q t , cardiac output

## Ventilation

• MV, Minute ventilation

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
O 2 , Oxygen consumption

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
CO 2 , Carbon dioxide consumption

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
a , Alveolar ventilation

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='V˙/Q˙’>V˙/Q˙V˙/Q˙
V ˙ / Q ˙
Ventilation perfusion ratio

## Concentration

• C ao 2 , oxygen content (C) of arterial oxygen

## Fraction (F)

• F ao 2 , fraction of oxygen in alveolar gas

## Hemoglobin

• Hgb, hemoglobin concentration

• HgbO 2 , oxyhemoglobin

• SO 2 , oxygen saturation

## Pressures

• P b , barometric (ambient) pressure

• P h 2 o , water vapor pressure

## Respiratory Gases

• P a , partial pressure of a gas in alveolar air; for example, P ao 2 , partial pressure of oxygen in the alveolus

• Pa, partial pressure of a gas in arterial blood; for example, Pa o 2 , partial pressure of oxygen in arterial blood

• P v , partial pressure of a gas in mixed venous blood; for example, P vo 2 , partial pressure of oxygen in mixed venous blood

## Volumes

• TV or V t , Tidal volume

• FRC, Functional residual capacity

• RV, Residual volume

• VC, Vital capacity

• FVC, Forced vital capacity

• TLC, Total lung capacity

• V d , Anatomic dead space volume

• V d /V t , Ratio of dead space volume to tidal volume

## Blood Flow

• Q t , cardiac output

## Ventilation

• MV, Minute ventilation

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
O 2 , Oxygen consumption

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
CO 2 , Carbon dioxide consumption

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
a , Alveolar ventilation

• <SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='V˙/Q˙’>V˙/Q˙V˙/Q˙
V ˙ / Q ˙
Ventilation perfusion ratio

## Concentration

• C ao 2 , oxygen content (C) of arterial oxygen

## Fraction (F)

• F ao 2 , fraction of oxygen in alveolar gas

## Hemoglobin

• Hgb, hemoglobin concentration

• HgbO 2 , oxyhemoglobin

• SO 2 , oxygen saturation

## The Gas Laws

The behavior of gases is described by the ideal gas equation , which relates volume, pressure, and temperature:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='PV=nRT,’>PV=nRT,PV=nRT,
PV = nRT ,
where P is pressure, V is volume, T is temperature, n is the number of moles of gas molecules, and R is the gas constant, which is fixed at 0.0821.

When nR is constant, the equation can be used to determine changes in pressure, volume, and temperature under different conditions. That is,

<SPAN role=presentation tabIndex=0 id=MathJax-Element-10-Frame class=MathJax style="POSITION: relative" data-mathml='P1×V1T1=P2×V2T2′>P1×V1T1=P2×V2T2P1×V1T1=P2×V2T2
P 1 × V 1 T 1 = P 2 × V 2 T 2

Boyle’s law characterizes the relationship between temperature and volume. That is, if temperature (T 1 and T 2 in the preceding equation) remains constant, pressure will vary inversely to volume:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='P1×V1=P2×V2′>P1×V1=P2×V2P1×V1=P2×V2
P 1 × V 1 = P 2 × V 2

Boyle’s law is used to calculate lung volumes ( Chapter 2 ).

Charles’s law characterizes the relationship between volume and temperature in the presence of a constant pressure. That is, if pressure (P 1 , P 2 ) remains constant, volume and temperature will vary directly:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-12-Frame class=MathJax style="POSITION: relative" data-mathml='P1T1=P2T2′>P1T1=P2T2P1T1=P2T2
P 1 T 1 = P 2 T 2

## Gases

Air is composed of a mixture of gases that exert a pressure. Each individual gas exerts its own pressure, known as its partial pressure . This pressure is generated by the collision of gas molecules along the wall of the container. The partial pressure of the individual gases is the product of the total gas pressure and the proportion of total gas composition made up by the specific gas of interest (see Chapter 5 ). For example, at sea level, the total ambient pressure, also known as the barometric pressure, is 760 mm Hg. (The basic pressure unit in respiratory physiology is millimeters of mercury—mm Hg.) Air is composed of approximately 21% oxygen. Thus, at sea level the partial pressure of oxygen is 0.21 × 760 mm Hg = 160 mm Hg. Small pressure differences are often expressed in cm H 2 O where there is 1.36 cm H 2 O for every 1 mm Hg of pressure.

Dalton’s law states that the total pressure of a gas mixture is equal to the sum of the partial pressure of the gases in a gas mixture. That is, each individual gas in a gas mixture acts independently and exerts its own partial pressure, and the sum of all of the partial pressures is equal to the total pressure. Because the total pressure is fixed, as the pressure exerted by one specific gas increases, the pressure exerted by another must decrease. When water vapor is added or when carbon dioxide is added in the alveolus, the partial pressure of oxygen decreases.

## Vapor Pressure

At the interface of a liquid and an open space, the rate of escape of molecules from the liquid phase equals the rate at which gas molecules return to the liquid phase. The vapor pressure of a gas is defined as the partial pressure exerted by gas molecules when they are in equilibrium between the gas and liquid phase. For the respiratory system, water is the major liquid, and the vapor pressure of water is solely dependent on temperature. Water vapor pressure increases with increasing temperature; at body temperature, this water vapor pressure is 47 mm Hg. The amount of moisture in the air is defined by its relative humidity, which is defined as the ratio of the measured partial presssure of water in the air to the vpaor pressure of water (determined solely on the basis of the temperature of the air). The air that we breathe is usually less than body temperature and rarely fully saturated. Inspired air, however, by the time it reaches the trachea, has been warmed to body temperature and is fully saturated. If the total pressure is 760 mm Hg and water vapor pressure (P h 2 o ) is 47 mm Hg, the remaining 713 mm Hg is equal to the sum of all the remaining gases in the inspired air (Dalton’s law). Thus, in the trachea, the partial pressure of O 2 in the ambient air is now .21 × (760 − 47) = 150 mm Hg, or an approximately 10 mm decrease in the partial pressure of oxygen in the inspired air that enters the nose and mouth.

## Measuring Gas Volumes

Gas volumes can be measured and reported under three conditions. When gas is exhaled into a spirometer or bag, it is reported at ambient temperature and pressure, saturated (ATPS). Gas volumes measured in the lung are reported at body temperature and pressure, saturated (BTPS), while oxygen consumption and carbon dioxide production are reported at standard temperature and pressure, dry (STPD). When reporting gas volumes, it is important to make sure that different volumes have been measured until the same conditions. For example, in going from ATPS to BTPS, there is an increase of volume of approximately 10%.

## Gas Solubility

In the respiratory system, we must also consider the partial pressure of a gas in a liquid phase—namely, the blood. When a liquid is in contact with a gas mixture, the partial pressure of the particular gas in the liquid is the same as its partial pressure in the gas mixture, assuming that full equilibration has occurred. Therefore the partial pressure of the gas acts as the “driving force” for the gas to be carried in the liquid phase.

Henry’s law states that the amount of a gas absorbed by a liquid such as blood, to which it is not chemically combined, is directly proportional to the positive pressure of the gas to which the liquid is exposed and the solubility of the gas in the liquid. For example, if a gas is very soluble in the liquid, more of that particular gas will be carried in a given pressure compared to a less soluble gas. In addition, and most important for the respiratory system, if the liquid is able to bind or carry more of the gas, more of the gas will be transported at a particular partial pressure.

The interaction of hemoglobin in the red blood cells and oxygen allows more oxygen to be transported at any partial pressure and is the major transport system in the body for oxygen (see Chapter 8 ).

The transport and delivery of O 2 from the lungs into the blood and from the blood into the tissue (and vice versa for CO 2 ) are dependent on the gas diffusion laws and is described by Fick’s law (see Fig. 8.2 ).

The diffusion constant for a gas is directly proportional to the solubility of the gas and inversely proportional to the square root of the molecular weight of the gas.

<SPAN role=presentation tabIndex=0 id=MathJax-Element-13-Frame class=MathJax style="POSITION: relative" data-mathml='D=solubilitymolecularweight’>D=solubilitymolecularweightD=solubilitymolecularweight
D = solubility molecular weight