Gay Lussacs Law Application Essays

Boyle's Law

As volume increases, the pressure of the gas decreases in proportion:
P1V1 = P2V2

Boyle's 1660 publication, "New Experiments Physico-Mechanicall, Touching the Spring of the Air, and its Effects" has been covered brilliantly by JB West (yes, John B. West, of West's Physiology).

In brief summary, the law states that at any given temperature, the product of pressure and volume is constant. Conversely, as you change one, the other will change predictably.

Boyle's apparatus

Boyle wrote an extensive essay (in the form of a letter to his nephew) detailing his experiment- to be precise, his 43 experiments - on the behaviour of vacuum and rarified gas. Of the engravings he commissioned for this publication, some are selected for display above - not for the purposes of education, but to recall a time when experimental apparatus was lovingly rendered by artists, rather than by software.

Boyle's experiment is discussed in great detail in the course of West's article. In short, Boyle evacuated a huge glass bulb using a ratcheted piston, and then observed what happens to the stuff he put in there. The bulb was huge - around 28 litres - and he was apparenty able to reduce it to a pressure of 22.8mmHg, according to the recently developed Toricellian mercury barometer. Among the objects which enjoyed a brief exposure to such a vacuum were lamb's bladders, burning candles, coals, loaded pistols, insects, as well as several unlucky birds and mice, who "droop and appear sick, and very soon after [were] taken with as violent and irregular Convulsions as are wont to be observ’d in Poultry, when their heads are wrung off" as air was removed from the chamber. Unfortunately, there being no Priestley for another hundred years or so, Boyle was unaware of oxygen, and piles of dead animals were generated in the course of his experiments. The exception to the rule were house snails: apparently, they were entirely unaffected by the extremes of pressure, and continued to function normally in the near-vacuum. This was no accident - a little digging has revealed that in fact molluscs are the kings of anoxia, and many bivalves live their lives at about 1.0ppm of pO2 (0.00072 mmHg), so at around 5mmHg the snails were probably quite comfortable.

Anyway, the key issue is that for any given constant temperature the pressure of any gas can be predicted from its mass and the volume of the chamber it occupies. West finishes his assessment of Boyle's works by saying that "modern students who are interested in high-altitude physiology should be aware of this classic book".

Charles's Law

The volume of a gas is directly proportional to its absolute temperature.

 

The law was published by Joseph Louis Gay-Lussac who credited Jaques Charles with its discovery. Apparently, the unpublished material from which this law was derived dates to 1787. A certain team of chemistry teachers has an excellent entry regarding these two chemists, complete with snide remarks regarding Charles' appearance (looks drunk, they say).

Charles's contribution to gas laws derives much of its success from his excited attempts to replicate Joseph and Etienne Montgolfier's hot air balloon experiences. The first hydrogen balloon, of Charles' design, was a rubberised silk bag filled with the hydrogen which was produced when vast quantities of sulfuric acid were poured over approximately 1000kg of iron filings. The resulting gas was hot - so hot, in fact, that it had to be cooled by passing though lead pipes. Observers then remarked that as the gas cooled, so the balloon deflated. The experiment came to a splendid conclusion after the hydrogen balloon came to rest some ten miles away near the village of Gonesse, whose villagers apparently tore it to shreds with a variety of improvised weapons.

Enraged villagers destroying Charle's hydrogen balloon. Apparently it made weird noises and had a foul odour. (c 1783)

Fortunately, this early balloon was too small to carry Charles himself. Though he himself did not publish anything of scientific merit, J.L.Gay-Lussac published on his behalf. A specific experiment was the inspiration for what we now (mostly) call Charles's Law. Five balloons of similar volumes were filled with different gases, and then heated to about 80C°. The resulting expansion was measured, and was noted to be the same irrsepective of the gas involved.

Gay-Lussac's law

The pressure of a gas is directly proportional to its temperature.

 

This was the direct extension of Charles's law. It is variably credited to Gay-Lussac and Guillaume Amontons, both of whom had arrived at certain conclusions regarding the behaviour of gases of fixed mass and fixed volume. A translation of Gay-Lussac's original publication can be found online.

Avogadro's law

The volume occupied by an ideal gas is proportional to the number of moles of gas.

Specifically, the molar volume of an ideal gas ( the space occupied by 1 mole of the "ideal" gas, or any gas for that matter ) is 22.4 litres at standard temperature and pressure.

 

In other words, for any gas, at any temperature and pressure, there will be the same amount of molecules present in the specified volume.

Avogadro's law is of particular interest because it uncovers a fundamental constant value, which is encountered everywhere: the Universal Gas Constant, R. This constant is also a feature of Boyle's and Charles's laws, the equations of which can be rearranged to demonstrate it. R is the constant of proportionality which relates the energy scale to the temperature scale; it is expressed as work (joules) per degree per mole. Its approximate value is 8.314.

The Ideal Gas Law

This is the mutant offspring of Boyle's, Charles's, Gay-Lussac's and Avogadro's principles.

PV = nRT

Where

  • P is the pressure of the gas
  • V is the volume of the gas
  • n is the number of moles of the gas
  • R is the Universal Gas Constant (8.314)
  • T is the absolute tempterature of the gas in Kelvin.
 

Alright. So one of the gas laws you'll see in class is going to be Gay Lussac's law. And Gay Lussac actually explained the relationship between pressure and temperature when the volume remains constant. Let's actually look at this ourselves.

So we have a container here and it's a five litre container of and has, inside has gas particles. Okay it's at room temperature and the gas particles are heating in some sort of pressure, that's fine. Let's say we heat it up. So we're increasing the, increasing the temperature and the kinetic energy of the particles within the, within the five litre container, it's increasing as well. And they're heating the gas at the sides of the container at high speeds. And so what's going to happen, as long as the temperature, sorry. As long as the volume remains constant which it is, the pressure inside the container is going to increase dramatically depending on how much the temperature is increasing. So let's talk about this relationship. We know it's a direct relationship. As temperature increases, so does pressure. And conversely, as temperature decreases, so does pressure. So temperature and pressure have a good relationship as long as the volume remains constant.

Okay. So let's put this in mathematical formula. Pressure one over temperature one equals to pressure two over temperature two. Because this is direct relationship, they are divided by each other. The temperature we're going to make sure it's in kelvin and the reason we make sure it's in kelvin is because we want to make sure that there's no negative numbers on the denominator and kelvin's the only temperature scale that actually only has positive numbers. So we're going to make sure this is in kelvin and this is our, this is Gay Lussac's law mathematically.

Graphically we can put the temperature on the x axis and pressure on the y axis. We know that as we increase temperature, we also increase pressure creating a positive slope.

Okay. Let's actually look at this in demonstration. So what I have right here, I'm going to put my goggles on. Make sure we're safe. Safety comes first. We have what I'm having on this hot plate is a coke can as you can see. And I'm heating it up. Let's say the gas particles inside the container are heating up also and they're heating the pressure of the soda can at high speed. But it actually it's open so it has a place to escape so the pressure inside the container is equal to the pressure outside here and so everything is all good. What I'm going to do is I'm going to flipping the can over into this ice water bath sealing the container. And what's that, what's going to happen is the temperature is going to drop and the pressure inside the container is also going to drop. And but the pressure outside is going to remain the same. so what is going to happen? Let's see.

So, as you can see it actually didn't take much at all. What happened was the pressure outside was so much greater than the pressure inside because we had dropped the temperature so dramatically that it actually pushed on the can and crashed it as you can see. Completely crashed it.

Okay. Don't try that home. Alright. Let's turn this off and let's go solve a problem together. Okay. So the pressure in a car tyre is 1.88 atmospheres. That's our first pressure at 25 degrees celsius, there's our first temperature. What will be the pressure if the temperature warms up to 37 degrees celsius? Okay. So first I want to make sure these temperatures are in kelvin not in celsius. I'm going to change them. 25 degrees celsius plus 273 is equal to 298 kelvin. 37 degrees celsius, it should be degrees celsius plus 273 is equal to 310 kelvin. Okay, so my first pressure when I woke up, I put the tyre pressure at 1.88 atmospheres. And the temperature outside was 298 kelvin. We don't know pressure at the end of the day when it's 37 degrees celsius. We don't know it. So we're going to say x over 310 kelvin. We cross multiply 1.88 times 310 divided by 298 and it's going to give me 1.96 atmospheres.

The pressure inside the tyre is actually going to increase as expected because temperature also increased. So this is an example of Gay Lussac's law in an everyday application.

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