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The physics of ideal gases
hysics of anesthesia; ideal nation, artificial, fhysics of idea; gases: the very The entry point to u~der~~a~d~~g thesis is obstructed by ia can be ~~t~rn~~at~ngand The physics of anest this series of pieces even impenetrable. T is to explore, in a lect e underlying conelate them to the cepts, make them access eration of the devices in front of ader reaction is invited. Questions swers in this informal format would appreciated. References will be limited to key entry points to the literature or classic texts. The purpose is not to review, but to demystify. Although the style wiki be light and personal, the ntent is to maintain a high standard of honesty in t e simplification of come It is hoped that these explanations will ap anesthetists and please even those who are The series begins with the most fundam esia issue, the behavior of gases. *Associate
Professor
of Anaesthesia
Address reprint requests to Dr. Newbower at Department of Anesthesia, Massachusetts General Hospital, Boston, MA 02114. Received for publication May 27, 1988; cepted for publication August 1, 1988. 0 1989 Butterworth
revised
Publishers
J. Chn. Anesth.,
J.989, vol. 1, no. 3
manuscript
w-e are comfortably at vidual collisions transfer stings of rn~rne~t~rn to our skin that we do not perceive because each is so small, and there are so many of them, ap collisionslcm*/second. The life of an individual molecule proceeds on a scale we cannot conceiv ecules every 1C5 cm, whi to 1Ol” collisions/second eaceful life. The meter; co~§e~~e~t~y, s is 1,000 times thei each molecule travels enormous distances between collisions on its scale of distance. gases facts, it is clear th ore like a vacuum t around us are far
ac-
!iard balls, rare
each other
to in-
le E.
A Summary sf the Laws for Ideal Gases1 -
PV = Constant (at constant temperature (T) where P is pressure and V is volume) 2. Cbasles’ law (or Cay Lussac’s law) V = Constant x T (at constant pressure) 3. Avogadro’s hypothesis Equal volumes of all gases at the same temperature and pressure contain the same rmmber of molecules. At standard temperature and pressure the molecules in 1 mole (I gram-molecular volume) of gas occu 22.4 liters. The number of molecules, often called Avogadro’s number, is 6.02 x lo=. 4. Ideal Gas law (following from the above) PV = nRT (where n is the number of moles of gas and R is a specific constant)
of molecules in ea hat (obviously) dou molecules with any ust double the press I force of all those collisions on one unit area of the surface.
The gas giou capture gas (outside. The mass
The average number is the same. T are the same. difference
in these last few paragraphs, just art of the physics of the 17th an Ee I). IJnderstanding the rarefie molecular
nature
of gases we deal with allows us these
~~~ersta~~~~g. You can eed to do nts that verify these physt laws with edical apparatus, the syringe. If you a closed stopcock) a volume of gas in a an mani~ni~te the volume by applying lunger. Note that at the outset, plunger at all, there is pressure r~ I). It pushes the plunger outr does not move, experiencing e inward from the atmosphere.
----FQRCE
re 1. The small arrows symbolize the pressure of surrounding or contained air.
between
of molecul
the inside
the volume change you are If you want to do these experimen must eliminate the friction of
of ideal gases.
ow large the forces produced can become. In ace, such as an air lane fuselage, the individual gas molecule collisions w d up to a prodigious force. A f collisions on the outside of atm.os~beric molecules decreases cause of the rarefied densit altitude. At 35,008 feet th here on the outside is only a x~rn~~e~y4 psi compressure of the air motorized compressors for t assengers. Assume ce between
it Ss
the force
J. Chn. Anesth.,
89
1989, vol. I, no. 3
the forcepushing in would then be 8 psi.That would add up to over 1,000 pounds per square foot, which is the approximate area of one cabin window. It is certainly clear from this calculation why airplane signers need to make the windows small and thic As the plane climbs to altitude, this same logic tells L~Sthat the phenomenal force of 100,000 pound velops on each l@foot square section of cabin pushing outward. Apparently, the repeated stress of rhese forces increasing and relaxing with each takeoff and landing was enough to cause a recent mid-air failure from metal fatigue (perhaps aided by corrosion] in a commercial jetliner in Hawaii. All of these pressures follow from the cumulative effect of individual tiny collisions and reflections of gas molecules with the walls of the chamber containing them. The reader may be interested in calculating the weight of the air in a jetliner cabin.* must be supported at altitude by the t sea level the weight of the contained air is, of course, still there in the cabin, but it is supported by the buoyancy (external upward pressure) the plane experiences from its displacement of the external atmosphere. The buoyancy is less at 35,OO feet because the external atmosphere is less dense. The cost of fuel for carrying the cabin’s heavy air aloft is substantial.
inicaEly in a breathing circuit as the bellows of a mechanical ventilator co volume (Figure 2)? The begins to rise. In resp netted by the patent and leak-tight hose and tracheal tube to the breathing system. Gas flows in a direction, relieving the rise in pressure create bellows when the compression began. At tbe end of inspiration the lungs, chest wall, and diaphragm are stretched by the difference in inside and outside. Therefore, the gas pressure in the breathing circuit is obviously higher, an measured by the airway ing circuit. That gauge is a differential gauge, not an absolute pressure gauge. If you are performing this work by squeezing the bag instead of letting the ventilator power do it, you feel the pressure directly against your fingers. That pressure expands the compliant rubber or plastic tubing as well as increasing the density of the contained gas. *The best of solutions to this probkm, sent to the author, will be considered for publication in a future issue.
A typical anesthesia breathing circuit, rmphasizing the proliferation of compliant tubing associated with the attachment of devices such as humidifiers.
to lost voiume for *he
patient:gas
Which effect is bigger? To must remember that the pressure ii rease measur is the additional pressure over an above the ical atmospheric) absolute pressure at red of expiration). Thus, a clinically large ressure difference of 469 s really just a~ increa
Therefore,
if there
is a total volume
of 5 i in the
chosen tidal. volu
be less as well, and can, however, create
this material
is predictable
from the basic
an exaggerated re resentation of the expansion mpression of the contained iant tubing and the gas as pressure rises from end expiration (A) to end inspi) under positive pressure ventilation.
of
moles
of gas
assumed
that
in all our
expe
an
J. Clin. Anesth.,
?989, vol. I, no. 3
Professor
of Anaesthesia
Address reprint requests to Dr. Newbower at Department of Anesthesia, Massachusetts General Hospital, Boston, MA 02114. Received for publication May 27, 1988; cepted for publication August 1, 1988. 0 1989 Butterworth
revised
Publishers
J. Chn. Anesth.,
J.989, vol. 1, no. 3
manuscript
w-e are comfortably at vidual collisions transfer stings of rn~rne~t~rn to our skin that we do not perceive because each is so small, and there are so many of them, ap collisionslcm*/second. The life of an individual molecule proceeds on a scale we cannot conceiv ecules every 1C5 cm, whi to 1Ol” collisions/second eaceful life. The meter; co~§e~~e~t~y, s is 1,000 times thei each molecule travels enormous distances between collisions on its scale of distance. gases facts, it is clear th ore like a vacuum t around us are far
ac-
!iard balls, rare
each other
to in-
le E.
A Summary sf the Laws for Ideal Gases1 -
PV = Constant (at constant temperature (T) where P is pressure and V is volume) 2. Cbasles’ law (or Cay Lussac’s law) V = Constant x T (at constant pressure) 3. Avogadro’s hypothesis Equal volumes of all gases at the same temperature and pressure contain the same rmmber of molecules. At standard temperature and pressure the molecules in 1 mole (I gram-molecular volume) of gas occu 22.4 liters. The number of molecules, often called Avogadro’s number, is 6.02 x lo=. 4. Ideal Gas law (following from the above) PV = nRT (where n is the number of moles of gas and R is a specific constant)
of molecules in ea hat (obviously) dou molecules with any ust double the press I force of all those collisions on one unit area of the surface.
The gas giou capture gas (outside. The mass
The average number is the same. T are the same. difference
in these last few paragraphs, just art of the physics of the 17th an Ee I). IJnderstanding the rarefie molecular
nature
of gases we deal with allows us these
~~~ersta~~~~g. You can eed to do nts that verify these physt laws with edical apparatus, the syringe. If you a closed stopcock) a volume of gas in a an mani~ni~te the volume by applying lunger. Note that at the outset, plunger at all, there is pressure r~ I). It pushes the plunger outr does not move, experiencing e inward from the atmosphere.
----FQRCE
re 1. The small arrows symbolize the pressure of surrounding or contained air.
between
of molecul
the inside
the volume change you are If you want to do these experimen must eliminate the friction of
of ideal gases.
ow large the forces produced can become. In ace, such as an air lane fuselage, the individual gas molecule collisions w d up to a prodigious force. A f collisions on the outside of atm.os~beric molecules decreases cause of the rarefied densit altitude. At 35,008 feet th here on the outside is only a x~rn~~e~y4 psi compressure of the air motorized compressors for t assengers. Assume ce between
it Ss
the force
J. Chn. Anesth.,
89
1989, vol. I, no. 3
the forcepushing in would then be 8 psi.That would add up to over 1,000 pounds per square foot, which is the approximate area of one cabin window. It is certainly clear from this calculation why airplane signers need to make the windows small and thic As the plane climbs to altitude, this same logic tells L~Sthat the phenomenal force of 100,000 pound velops on each l@foot square section of cabin pushing outward. Apparently, the repeated stress of rhese forces increasing and relaxing with each takeoff and landing was enough to cause a recent mid-air failure from metal fatigue (perhaps aided by corrosion] in a commercial jetliner in Hawaii. All of these pressures follow from the cumulative effect of individual tiny collisions and reflections of gas molecules with the walls of the chamber containing them. The reader may be interested in calculating the weight of the air in a jetliner cabin.* must be supported at altitude by the t sea level the weight of the contained air is, of course, still there in the cabin, but it is supported by the buoyancy (external upward pressure) the plane experiences from its displacement of the external atmosphere. The buoyancy is less at 35,OO feet because the external atmosphere is less dense. The cost of fuel for carrying the cabin’s heavy air aloft is substantial.
inicaEly in a breathing circuit as the bellows of a mechanical ventilator co volume (Figure 2)? The begins to rise. In resp netted by the patent and leak-tight hose and tracheal tube to the breathing system. Gas flows in a direction, relieving the rise in pressure create bellows when the compression began. At tbe end of inspiration the lungs, chest wall, and diaphragm are stretched by the difference in inside and outside. Therefore, the gas pressure in the breathing circuit is obviously higher, an measured by the airway ing circuit. That gauge is a differential gauge, not an absolute pressure gauge. If you are performing this work by squeezing the bag instead of letting the ventilator power do it, you feel the pressure directly against your fingers. That pressure expands the compliant rubber or plastic tubing as well as increasing the density of the contained gas. *The best of solutions to this probkm, sent to the author, will be considered for publication in a future issue.
A typical anesthesia breathing circuit, rmphasizing the proliferation of compliant tubing associated with the attachment of devices such as humidifiers.
to lost voiume for *he
patient:gas
Which effect is bigger? To must remember that the pressure ii rease measur is the additional pressure over an above the ical atmospheric) absolute pressure at red of expiration). Thus, a clinically large ressure difference of 469 s really just a~ increa
Therefore,
if there
is a total volume
of 5 i in the
chosen tidal. volu
be less as well, and can, however, create
this material
is predictable
from the basic
an exaggerated re resentation of the expansion mpression of the contained iant tubing and the gas as pressure rises from end expiration (A) to end inspi) under positive pressure ventilation.
of
moles
of gas
assumed
that
in all our
expe
an
J. Clin. Anesth.,
?989, vol. I, no. 3