Other gas laws - Boyle's Law and Charles' Law This page takes a simple look at Boyle's Law and Charles' Law, and is suitable for 16 - 18 year old chemistry students doing a course the equivalent of UK A level. The aim is simply to show how these laws relate to Kinetic Theory (in a non-mathematical way), and to the ideal gas equation. Before you waste time on this, be sure that you actually need to know about it. Certainly in the UK exam system, it is pretty rare for chemistry students to be expected to know either of these laws these days. They have been almost completely replaced by the ideal gas equation. Statement For a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure. That means that, for example, if you double the pressure, you will halve the volume. If you increase the pressure 10 times, the volume will decrease 10 times.You can express this mathematically as pV = constant Is this consistent with pV = nRT ?
That means that everything on the right-hand side of pV = nRT is constant, and so pV is constant - which is what we have just said is a result of Boyle's Law. Simple Kinetic Theory explanation I'm not going to try to prove the relationship between pressure and volume mathematically - I'm just showing that it is reasonable. This is easiest to see if you think about the effect of decreasing the volume of a fixed mass of gas at constant temperature. Pressure is caused by gas molecules hitting the walls of the container. With a smaller volume, the gas molecules will hit the walls more frequently, and so the pressure increases. You might argue that this isn't actually what Boyle's Law says - it wants you to increase the pressure first and see what effect that has on the volume. But, in fact, it amounts to the same thing. If you want to increase the pressure of a fixed mass of gas without changing the temperature, the only way you can do it is to squeeze it into a smaller volume. That causes the molecules to hit the walls more often, and so the pressure increases. Statement For a fixed mass of gas at constant pressure, the volume is directly proportional to the kelvin temperature. That means, for example, that if you double the kelvin temperature from, say to 300 K to 600 K, at constant pressure, the volume of a fixed mass of the gas will double as well. You can express this mathematically as V = constant x T Is this consistent with pV = nRT ?
If you rearrange the pV = nRT equation by dividing both sides by p, you will get V = nR/p x T But everything in the nR/p part of this is constant. That means that V = constant x T, which is Charles' Law. Simple Kinetic Theory explanation Again, I'm not trying to prove the relationship between pressure and volume mathematically - just that it is reasonable. Suppose you have a fixed mass of gas in a container with a moveable barrier - something like a gas syringe, for example. The barrier can move without any sort of resistance.  The barrier will settle so that the pressure inside and outside is identical. Now suppose you heat the gas, but not the air outside. The gas molecules will now be moving faster, and so will hit the barrier more frequently, and harder. Meanwhile, the air molecules on the outside are hitting it exactly as before. Obviously, the barrier will be forced to the right, and the volume of the gas will increase. That will go on until the pressure inside and outside is the same. In other words, the pressure of the gas will be back to the same as the air again. So we have fulfilled what Charles' Law says. We have a fixed mass of gas (nothing has been added, and nothing has escaped). The pressure is the same before and after (in each case, the same as the external air pressure). And the volume increases when you increase the temperature of the gas. What we haven't shown, of course, is that there is a "directly proportional" relationship. It can be done, but it needs some maths. © Jim Clark 2010 (modified October 2013)
Boyle's law, also referred to as the Boyle–Mariotte law, or Mariotte's law (especially in France), is an experimental gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated as:
Mathematically, Boyle's law can be stated as:
or
where P is the pressure of the gas, V is the volume of the gas, and k is a constant. Boyle's Law states that when the temperature of a given mass of confined gas is constant, the product of its pressure and volume is also constant. When comparing the same substance under two different sets of conditions, the law can be expressed as: P 1 V 1 = P 2 V 2 . {\displaystyle P_{1}V_{1}=P_{2}V_{2}.}showing that as volume increases, the pressure of a gas decreases proportionally, and vice versa. Boyle's Law is named after Robert Boyle, who published the original law in 1662.[3] HistoryThe relationship between pressure and volume was first noted by Richard Towneley and Henry Power in the 17th century.[4][5] Robert Boyle confirmed their discovery through experiments and published the results.[6] According to Robert Gunther and other authorities, it was Boyle's assistant, Robert Hooke, who built the experimental apparatus. Boyle's law is based on experiments with air, which he considered to be a fluid of particles at rest in between small invisible springs. Boyle may have begun experimenting with gases due to an interest in air as an essential element of life;[7] for example, he published works on the growth of plants without air.[8] Boyle used a closed J-shaped tube and after pouring mercury from one side he forced the air on the other side to contract under the pressure of mercury. After repeating the experiment several times and using different amounts of mercury he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume occupied by it.[9] The French physicist Edme Mariotte (1620–1684) discovered the same law independently of Boyle in 1679,[10] after Boyle had published it in.[9] Mariotte did, however, discover that air volume changes with temperature.[11] Thus this law is sometimes referred to as Mariotte's law or the Boyle–Mariotte law. Later, in 1687 in the Philosophiæ Naturalis Principia Mathematica, Newton showed mathematically that in an elastic fluid consisting of particles at rest, between which are repulsive forces inversely proportional to their distance, the density would be directly proportional to the pressure,[12] but this mathematical treatise is not the physical explanation for the observed relationship. Instead of a static theory, a kinetic theory is needed, which was provided two centuries later by Maxwell and Boltzmann. This law was the first physical law to be expressed in the form of an equation describing the dependence of two variable quantities.[9] DefinitionBoyle's law demonstrations The law itself can be stated as follows:
Or Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant. Therefore, when the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved. Relation with kinetic theory and ideal gasesBoyle's law states that at constant temperature the volume of a given mass of a dry gas is inversely proportional to its pressure. Most gases behave like ideal gases at moderate pressures and temperatures. The technology of the 17th century could not produce very high pressures or very low temperatures. Hence, the law was not likely to have deviations at the time of publication. As improvements in technology permitted higher pressures and lower temperatures, deviations from the ideal gas behavior became noticeable, and the relationship between pressure and volume can only be accurately described employing real gas theory.[13] The deviation is expressed as the compressibility factor. Boyle (and Mariotte) derived the law solely by experiment. The law can also be derived theoretically based on the presumed existence of atoms and molecules and assumptions about motion and perfectly elastic collisions (see kinetic theory of gases). These assumptions were met with enormous resistance in the positivist scientific community at the time, however, as they were seen as purely theoretical constructs for which there was not the slightest observational evidence. Daniel Bernoulli (in 1737–1738) derived Boyle's law by applying Newton's laws of motion at the molecular level. It remained ignored until around 1845, when John Waterston published a paper building the main precepts of kinetic theory; this was rejected by the Royal Society of England. Later works of James Prescott Joule, Rudolf Clausius and in particular Ludwig Boltzmann firmly established the kinetic theory of gases and brought attention to both the theories of Bernoulli and Waterston.[14] The debate between proponents of energetics and atomism led Boltzmann to write a book in 1898, which endured criticism until his suicide in 1906.[14] Albert Einstein in 1905 showed how kinetic theory applies to the Brownian motion of a fluid-suspended particle, which was confirmed in 1908 by Jean Perrin.[14] EquationThe mathematical equation for Boyle's law is: P V = k {\displaystyle PV=k}where P denotes the pressure of the system, V denotes the volume of the gas, k is a constant value representative of the temperature and volume of the system. So long as temperature remains constant the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will remain constant. However, due to the derivation of pressure as perpendicular applied force and the probabilistic likelihood of collisions with other particles through collision theory, the application of force to a surface may not be infinitely constant for such values of V, but will have a limit when differentiating such values over a given time. Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure P must decrease proportionally. Conversely, reducing the volume of the gas increases the pressure. Boyle's law is used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. The initial and final volumes and pressures of the fixed amount of gas, where the initial and final temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation: P 1 V 1 = P 2 V 2 . {\displaystyle P_{1}V_{1}=P_{2}V_{2}.}Here P1 and V1 represent the original pressure and volume, respectively, and P2 and V2 represent the second pressure and volume. Boyle's law, Charles's law, and Gay-Lussac's law form the combined gas law. The three gas laws in combination with Avogadro's law can be generalized by the ideal gas law. Human breathing systemBoyle's law is often used as part of an explanation on how the breathing system works in the human body. This commonly involves explaining how the lung volume may be increased or decreased and thereby cause a relatively lower or higher air pressure within them (in keeping with Boyle's law). This forms a pressure difference between the air inside the lungs and the environmental air pressure, which in turn precipitates either inhalation or exhalation as air moves from high to low pressure.[15] See alsoRelated phenomena:
Other gas laws:
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With the temperature remaining constant when the volume of gas is double the pressure will be
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