Physics of gases

PHYSICS

Physics of gasesGary Thomas

Stephen Stamatakis

AbstractThis article explores the physical principles of gases that are relevant to

the specialities of anaesthesia and critical care medicine. Points covered

include molecular theory, the gas laws, vaporization, pressure, solubility

and gas flow. Definitions, examples and explanations are given in areas

of particular importance.

Keywords diffusion; gases; gas flow; gas laws; phases; physics;

pressure; solubility; states of matter

There are four fundamental states of matter: gases, liquids, solids and plasmas. The forces of attraction between the atoms and molecules of a compound will determine its state and physico-chemical properties.• Solids have a definite volume and shape. Particles are packed closely together and are incompressible. There is enough thermal energy to produce vibration of particles within the tight lattice.• Liquids have volume but no definite shape. Particles are less tightly packed, and, although there is free movement within the volume, they are incompressible.• Gases have no finite shape or volume. Particles are free to move rapidly in a state of random motion. They are compress-ible and shaped completely by the space in which they are held. Vapours exist as a gas phase in equilibrium with identical liquid or solid matter below its boiling point.• Plasmas are the most prevalent state of matter in the universe, formed by heating atoms to very high temperatures to form ions.

PhasesA phase is a distinct, homogeneous state with no visible bound-ary separating it into parts. Conversion between states is called ‘phase transition’. Phase diagrams or graphs are used to show an equilibrium that exists between thermodynamically distinct physical forms. Water can co-exist as three phases, solid, liquid

Gary Thomas, MB, BCh (Wales), FRCA, is a Consultant Anaesthetist at

Bro Morgannwg NHS Trust, Wales. He graduated from the Welsh

National School of Medicine in 1981, and trained in anaesthesia in

Wales, London (UK) and Melbourne (Australia). His main interests are

anaesthesia for vascular surgery and teaching. He is currently a final

FRCA examiner. Conflicts of interest: none declared.

Stephen Stamatakis, MB, BCh, is a Specialist Trainee 3 in Anaesthesia

currently on the Welsh rotation. He graduated from the University of

Wales College of Medicine, UK. Conflicts of interest: none declared.

ANAESTHESIA AND INTENSIVE CARE MEDICINE 10:1

and gas, at the triple point. The triple point of water is used to define the basic Système International (SI) unit of thermody-namic temperature, Kelvin or K, which is the fraction 1/273.15 K. The symbol T is used to express temperature T0 = 273.15 K, the ice point.

Pressure

Pressure is exerted by a gas as a result of the continual collision of its molecules with the containing wall. It is the force (F) in newtons (N) exerted perpendicularly against an area (m2); thus, 1 N acting over 1 m2 produces a pressure of 1 pascal (Pa)

Pressure = N/m2 = kg/ms2 = Pa

Standard atmospheric pressure (absolute) is measured using a barometer and is defined at sea level and 273 K (0°C). This can be expressed as a number of different units: 1 atmosphere, 760 mm Hg, 101.3 kPa, 1.013 bar or 14.7 lb/in2.

Pressure measured relative to atmospheric is known as gauge pressure. The absolute pressure is the total pressure exerted on a system, which is equal to the gauge.

Standard temperature and pressureStandard temperature and pressure (STP) are the conditions used throughout science to enable comparisons between sets of data. These equate to 1 atmosphere pressure and 0° Celsius (273.15 K).

Partial pressureIn a mixture of ideal gases, each gas exerts a partial pressure. This is the pressure that it would have exerted had it occupied that volume alone. The total pressure of a mixture of gases is equal to the sum of the partial pressures of all of the constituent gases (Dalton’s law). Mathematically, this can be represented as:

PTotal = P1 + P2 + … + Pn

Air contains 78% N2, 20.95% O2, 0.93% argon, 0.038% CO2 and between 1% and 5% water vapour. The partial pressure of oxygen in dry air is 0.209 multiplied by 101.3 kPa, or 21.17 kPa.

Saturated vapour pressure (SVP)This is defined as the pressure exerted by a vapour in equilibrium with liquid of the same substance. A liquid boils at the tempera-ture when its vapour pressure equals atmospheric pressure. The energy required to change a gram of liquid to a gas (phase transi-tion) is called the latent heat of vaporization or enthalpy. This energy breaks down the intermolecular attractive forces.

The pressure gauge reading of a nitrous oxide (N2O) cylinder reflects the SVP at that temperature. The relationship between pressure, volume and the temperature of a gas can be represented and displayed as a series of isotherms (Figure 1).

Critical temperature (Tc )The critical temperature is the temperature at or above which a gas cannot be liquefied, no matter how much pressure is applied. For example, the critical temperature of nitrous oxide (N2O) is 36.5°C, and oxygen (O2) is −118°C.

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PHYSICS

Critical pressure (Pc )This is the pressure required to liquefy a substance at its critical temperature. The critical pressure of N2O is 73 bar.

Pseudocritical temperature (overpressure effect)The pseudocritical temperature is observed with Entonox, a 50:50 mixture of N2O and O2. Oxygen alters the critical temperature of N2O (Poynting effect) to the pseudocritical temperature −6°C. Gas cylinders containing Entonox at a pressure of 137 bar should not be stored below this temperature.

Ideal gasesThe ideal gas is one in which the gas molecules:• are identical• move in a straight line before colliding with each other or the

sides of their container• have collisions that are perfectly elastic with no loss of kinetic

energy• possess negligible volume• move randomly• have no attractive or repulsive forces between them.

The gas laws

These apply to ideal gases within closed systems.

Boyle’s lawBoyle’s law (Figure 2a) states that, for a fixed mass of gas at constant temperature, the pressure (P) and volume

Relationship between pressure and temperature

The relationship between pressure and temperature is shown at three

different temperatures of nitrous oxide (isotherms). Ct represents the critical

temperature isotherm (36.5˚C) and Cp represents the critical pressure at

that temperature. The saturated vapour pressure of nitrous oxide at room

temperature is 55 bar. SVP, saturated vapour pressure

Pressure

Volume

73 bar

Cp

55 bar

SVP

20˚C 40˚C

36.5˚C(Tc)

GasGas

Liquid

Liquid

Vapour

VapourLiquid and

vapour

Figure 1

ANAESTHESIA AND INTENSIVE CARE MEDICINE 10:1 49

(V) are inversely proportional (P ×V = k, where k is a constant).

Pulmonary functional residual capacity (FRC) can be calcu-lated using Boyle’s law and data acquired from a body plethys-mograph using the equation:

P1×V1 = P2×V2

Charles’s lawCharles’s law (Figure 2b) states that the volume occupied by a fixed mass of gas at constant pressure is directly proportional to its absolute temperature (V/T = k).

Third gas lawThis states (Figure 2c) that the pressure of a fixed mass of gas at constant volume is directly proportional to its absolute temperature (P/T = k).

Universal gas equationThe state of a fixed mass of gas is determined by its pressure, volume and temperature according to the universal gas equation (PV = nRT, where n is the amount of substance (mol) and R is the universal gas constant).

Avogadro’s hypothesisThis states that equal volumes of gases at the same temper-ature and pressure contain the same number of molecules (6.023 × 1023, Avogadro’s number). It is the number of mol-ecules of 1 mol of any gas present in a volume of 22.4 litres at STP. For example, 1 mol of O2 (molecular weight 32) at STP contains 6.023 × 1023 molecules, occupies 22.4 litres and weighs 32 g.

Adiabatic processAn adiabatic process is one in which there is no loss or gain of heat. When a compressed gas expands, external work occurs at the expense of internal energy from the gas molecule. The fall in temperature that occurs (Joule–Thompson effect) is the principle behind the working of a cryoprobe. Conversely, compressing a gas increases the pressure and internal energy of a system with heat production and the risk of fires and explosions.

Gas volumesGas volumes obtained in laboratory experiments can be expressed in a number of ways:• ATPS (ambient temperature, pressure and saturated with water vapour)• STPD (standard temperature, pressure and dry)• BTPS (body temperature, pressure and saturated with water vapour).

Diffusion and solubility

Graham’s law describes the relationship between molar mass and rate of diffusion and effusion of a gas:• Diffusion is the rate at which two gases mix.• Effusion is the process of gas molecules escaping through tiny holes in their container.

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PHYSICS

Mathematical relationships of the gas laws

a The mathematical relationship between the volume of a fixed mass of gas and pressure is hyperbolic (Boyle’s law). The gas temperature remains constant.

b The mathematical relationship between the volume of a fixed mass of gas and temperature is linear (Charles’s law). The gas pressure remains constant.

c The mathematical relationship between the pressure of a fixed mass of gas and temperature is linear (Third gas law). The gas volume remains constant.

Pressure

a b c

Pre

ssu

re

Thermodynamic temperature

Thermodynamic temperature

Vo

lum

e

Vo

lum

e

–237°C

0 K

0°C

273 K

100°C

400 K

Figure 2

The rate at which gases diffuse or effuse is inversely propor-tional to the square root of their densities:

Ratediffusion ∝ 1/√density

Fick’s law states that the net diffusion rate across a fluid mem-brane is directly proportional to the partial pressure difference across it and indirectly proportional to the thickness of the membrane.

Henry’s law states that the concentration of a solute gas in a solution at a given temperature is directly proportional to the partial pressure of that gas above the solution.

The Ostwald solubility coefficient is the volume of gas dis-solved in unit volume at ambient temperature and pressure. In anaesthetic practice, these coefficients are quoted in tables, assuming a body temperature of 37°C.

Partition coefficientsPartition coefficients represent the ratio of vapour or gas volume to that in another phase at equilibrium, such as oil–gas, blood–gas


or oil–blood. The oil–gas partition coefficient is relevant to anaesthesia because it measures lipid solubility and therefore the potency, or minimal alveolar concentration (MAC), of an agent. The blood–gas partition determines the solubility of an agent in blood. Anaesthetic agents with a low blood–gas partition coef-ficient are less soluble and high alveolar partial pressures are quickly achieved. The onset and offset of anaesthesia is theoreti-cally more rapid when administering agents with lower blood–gas partition coefficients (Table 1).

Raoult’s law states that, if a solute is added to a liquid, the freezing point and the vapour pressure of the resultant solution is reduced. For example, the addition of salt to water causes the water to freeze below its normal freezing point (0°C) and to boil above its normal boiling point (100°C). These changes are directly proportional to the molality of the solute. They are known as col-ligative properties of solutions and depend upon the number of particles present in a given volume of solvent, not their mass. The measurement of osmolality using an osmometer uses the principle of depression of freezing point by a solute on a solvent.

Physicochemical characteristics of the gases used in anaesthetic practice

Anaesthetic agent Halothane Enflurane Isoflurane Desflurane Sevoflurane Nitrous oxide Xenon

Physicochemical parameter

Oil–gas partition coefficient 220 120 170 18.7 55 3 20

Minimal alveolar

concentration (MAC)

0.76% 1.68% 1.15% 6% 2% 105% 60–70%

Blood–gas partition

coefficient

2.5 1.91 1.4 0.42 0.6 0.47 0.12

Boiling point (°C) 50 56 49 23.5 58.8 −88 −108.1

Saturated vapour

pressure (at 20°C) (kPa)

32.3 23.3 33.2 88.5 23.5 5,500

Table 1


PHYSICS

Gas flow

This is the mass of fluid moving per unit time. The word ‘fluid’ is a very important technical term. It encompasses both gas and liquid. That is, any gas is a fluid and any liquid is a fluid.

Laminar flow is streamlined and ordered, with a parabolic velocity profile. Factors influencing flow (Q) are given by the Hagen–Poiseuille formula:

Q = (ΔP × r4 × π)/(8 × η × L)

where r is radius, l is the length of the tube, ΔP is the pressure difference and η is the viscosity.

Turbulent flow is non-linear and chaotic, with eddying flow profiles. Turbulence is more likely when flow occurs through irregular channels or when bifurcations and bends are encountered.

Q = r2 √ΔP/ρ × L

where ρ is the density.

Reynolds numberReynolds number (RN) is a dimensionless constant influencing the critical velocity of a gas (ν), and therefore the transition from laminar to turbulent flow:

ν = η × RN/ρ x d

where d is the diameter.In the respiratory tract, turbulent flow is more likely in the

nasal passages and trachea, but flow becomes laminar in bron-chioles less than 1 mm in diameter with low gas velocity.

Gas flow through a rotameter may be laminar or turbulent:• At low fresh gas flow rates, the gap between the tube and the bobbin is small and the restriction is approximately tubular; the flow is predominantly laminar and therefore dependent on the vis-cosity of the gas.• At high fresh gas flow rates, the gap between the tube and the bobbin is larger; it has a greater area compared with its length, approximating to flow through an orifice, and is there-fore density dependent. At altitude, the density of a gas is pres-sure dependent, and under hypobaric conditions rotameters will under-read.


ViscosityViscosity (η) of a fluid is a measure of internal resistance to the flow process. The derived SI units of dynamic or absolute viscos-ity are pascal seconds. With an increase in temperature:• gas viscosity increases• liquid viscosity decreases.

The viscosity of a gas is largely independent of pressure.

DensityDensity (ρ) is the mass of 1 mol of gas divided by the volume (22.4 litres) at STP. With an increase in temperature, the density of a gas falls as the molecules become more widely spaced, thus hot air rises.

Bernoulli principleThe Bernoulli principle is observed during flow through a constric-tion. At this point the increased flow, representing kinetic energy, is balanced by a decrease in potential energy manifesting as a fall in pressure. This can be used to entrain air or a nebulizer solution into a fluid stream (Venturi effect). Fixed performance oxygen masks, nebulizers, jet ventilators, Venturi flowmeters, Pitot tubes and gas-scavenging systems utilize these physical principles.

Coanda effectThe Coanda effect describes the tendency of a fluid to adhere to and follow a curved surface during flow. Fluid logic or fluidics is the use of gases to operate the control systems and valves of ventilators. ◆

FURTHER READING

Davey A, Diba A. Ward’s anaesthetic equipment, 5th edn. London:

Elsevier Saunders, 2005.

Davis PD, Kenny G. Basic physics and measurement in anaesthesia,

5th edn. Oxford: Butterworth-Heinemann, 2003.

Magee P, Tooley M. The physics, clinical measurement and equipment

of anaesthetic practice. Oxford: Oxford University Press, 2005.

Muncaster R. A-level physics, 4th edn. Cheltenham: Nelson Thornes,

1993.

Sykes MK, Vickers D, Hull CJ. Principles of measurement and monitoring

in anaesthesia and intensive care, 3rd edn. Oxford: Blackwell

Scientific Publications, 1991.

Tabor D. Gases liquids and solids and other states of matter, 3rd edn.

Cambridge: Cambridge University Press, 1991.


Physics of gases

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