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The Gas Laws-a tutorial

Created: 10/6/2005


There is no getting away from physics, both in the real world and in the exam. People tend to leave the Physics portion of their revision quite late and some of the concepts may take a little more work to understand that the pure memorisation of the other clinical sciences. The important concept to remember for Physics is, if there is a definition start with it, if it can be classified; classify, and if you can think of examples, give them!


This is an overview of the gas laws. I will deal with origins, definitions, constants and Anaesthetic relevance, and use a bicycle pump like never before.

The origins of the Gas laws came out of experimental work conducted during the seventeenth and eighteenth centuries by several people who we will meet later

These experiments ultimately gave us the three gas laws, and the theoretical construct that arises from the gas laws is the concept of an ideal gas. This is a gas that does obey the laws completely under all circumstances. As the laws break down at the extremes of temperature and pressures, there is no gas that obeys all the laws perfectly. In our practical day-to-day use at room temperature they can be assumed to do so. This simplifies our consideration of them.


What is a gas?

A gas is a substance that is in its gaseous phase, but is above its critical temperature.

Critical temperature is the temperature above which a gas cannot be liquefied no matter how high the pressure.

A vapour in contrast is a substance in the gaseous phase but is below its critical temperature.

What is pressure?

Pressure is defined as "the force per unit area acting at right angles to the surface under consideration”

Pressure = Force/Area

The unit of pressure is the Pascal. Pressure is the consequence of molecular bombardment of the surface by the gas. Kinetic energy is transferred to the surface and a force is produced that creates the pressure. If the volume falls, the pressure goes up because the area for collisions fall and so more kinetic energy transfer per unit area, and so an increase in pressure.

What is temperature?

“This is a measure of the average kinetic energy in a system and translates to the degree of hotness or coldness of that system”

Temperature is measured in our clinical practice in the Celsius or Fahrenheit scales. In Physics it is the Kelvin. The divisions of the Kelvin and Celsius scale are the same but the start points differ. 0oC is 273K, so body temperature is 310K on this scale.

Now let’s consider the gas laws, each deal with one of three variables: Pressure, Volume and Temperature. Each law holds one constant and observes the variation in the other two. Remember the constant for each law and the rest should be easy! Since we are in the world of Physics, temperature is measured in Kelvin, pressure is in Pascals and volume is in Litres.

Boyle’s law

Robert Boyle made the discovery that the volume of a gas decreased as the pressure was raised. To think of it another way, if you put your thumb over the end of a bicycle pump and push the plunger down, it gets harder to hold your thumb on. In other words the pressure goes up as the volume goes down.

“For a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume”

P is proportional to 1 / V or PV = K (a constant)

Charles’ Law

This law was discovered by Jacques Charles in 1787, but refined by Joseph Louis Gay-Lussac in 1808.

Charles found that for a fixed mass of gas under constant pressure the temperature of the gas varied directly with the volume.

“For a fixed mass of gas at a constant pressure, the volume is directly proportional to the temperature”

V is proportional to T or V / T = K

The Pressure Law

The final variable to keep constant is volume.

“For a fixed mass of gas at a constant volume, the pressure is directly proportional to the temperature”

P is proporional to T or P / T = K

The Universal Gas Law

Combining all the gas laws together yields and important equation: the universal or ideal gas law.

PV = nRT


n = the number of moles of the gas

R = the universal gas constant ( 8.31 J K-1)

Remember only an ideal gas obeys this and previous laws exactly and, you guessed it, such a gas doesn’t exist! Real gases however, follow the law in our practice as they are at low pressures, and well above their liquefaction temperatures.

As an example consider a medical oxygen cylinder. Its physical volume is about 5 litres. What volume of oxygen is available to us?

Using the Universal gas law, applying it for standard pressure 1.01 X105 Pa and at room temperature 298K. The pressure of this cylinder is 137 X105 Pa.


P1V1 =nRT1 Where P1, V1 and T1 are the variables before expansion.


P2V2 =nRT2 Where P2, V2 and T2 are the variables after expansion.

Since we are assuming that the gas is allowed to expand slowly T1 = T2, and the number of moles of the gas, n, is the same at the beginning and the end.

So P1V1 = P2V2

Therefore V2 = P1V1 /P2 = 137 x105 x 5/1.01 x105

So V2 is 652 litres.

Which at basal oxygen flows of 0.25 l/min is enough for 43 hours. At 2 litres per minute flow this gives us 5 hours. So the Universal gas law allows us to calculate approximately how much oxygen we have for those ambulance transfers before we run out. The down side is that ventilators consume further gas so the actual time available is even less!

Dalton’s Law of partial pressure

John Dalton observed that the total pressure of a gas mixture was the sum of the pressures of each of the gases if they were to exist on their own.

Therefore P mixture = P1+P2+P3 + …

This means that to calculate the total pressure in a cylinder for a mixture of gases just add up all the partial pressures.

So if a cylinder of gas mixture at 400 kPa contains 21% oxygen and 79% helium, then if the oxygen existed on its own it would exert a partial pressure of

21% of 400 kPa = 88 kPa

The helium therefore exerts a partial pressure of 400 – 88 = 312 kPa

Henry’s Law

Henry’s law states that for a gas-liquid interface the amount of the gas that dissolves in the liquid is proportional to its partial pressure. So Henry’s law helps to predict how much gas will be dissolved in the liquid. The actual amount also depends on the solubility of the gas as well as its partial pressure.

Graham’s Law of Effusion

Thomas Graham found that the rate of diffusion was inversely proportional to the square root of the molecular mass of the gas. So the larger the molecule the slower it diffuses. Effusion relates to the both the direction and the rate of change of diffusion. In our consideration this could be from alveolus to the plasma.

So Rate of effusion is proportional to 1/Molecular mass

This explains the second gas effect when using nitrous and a volatile in Oxygen

Rate of effusion of A/Rate of effusion of B = Square root of molecular mass of B/Square root of molecular mass of A

So if B is more massive than A, A will effuse out of the alveolus quicker than B, leaving behind more of B and so raising its concentration. Since, for example, halothane is more massive than nitrous oxide, Graham’s law will indicate that the nitrous will diffuse quicker and so raise the concentration of the halothane in the alveolus.


AnaesthesiaUK would like to thank Dr Lliam Edger for writing this article.

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