GAS LAW'S
DISCUSSION
introduction
The gas laws are a set of intuitively obvious statements to most everyone in the Western world today. It's hard to believe that there was ever a time when they weren't understood. And yet someone had to notice these relationships and write them down. For this reason, many students are taught the three most important gas laws by the names of their discoverers. However, since the laws are known by different names in different countries and (more importantly) since I can never remember who gets credit for which law without referring to notes, I will not follow this convention.
pressure-volume (constant temperature)
What happens to the volume of a gas as the pressure on it changes. Let's try the following experiment using equipment that might be found in your kitchen Marshmallows are a mixture of sugar, air, and gelatin. Sugar makes them sweet, air makes them fluffy, and gelatin makes them elastic. Marshmallows are a frozen foam and are mostly air by volume. When placed in a vacuum pump, they expand as the pressure decreases. Break the seal on their container and they shrink during the return to normal atmospheric pressure. Since the vacuum pump pulls on the marshmallows hard enough to burst some of the air bubbles, they are actually a bit smaller and more shriveled at the end of this experiment. This illustrates a fundamental, yet important, property of gases. The pressure of a gas is inversely proportional to its volume when temperature is constant. Symbolically…
This correlation was discovered independently by Robert Boyle (1627–1691) of Ireland in 1662 andEdme Mariotte (1620–1684) of France in 1676. In Great Britain, America, Australia, the West Indies and other remnants of the British Empire it is called Boyle's law, while in Continental Europe and other places it is called Mariotte's law. Mariotte added the important provision that temperature remain constant. Boyle neglected to mention it, but the data he used to derive his law were most likely collected during a period in which the temperature did not experience any significant change. Since the gas needs to be in thermal equilibrium with its environment (or some other heat reservoir) to maintain an even temperature, the pressure-volume relationship normally applies only to "slow" processes. The marshmallow-vacuum experiment shown above is an example of a "slow" process. The pressure is reduced at a rate slow enough that heat from the environment is able to keep the jar and its contents at nearly room temperature. Such a transformation that takes place without a change in temperature is said to be isothermal.
What happens to the volume of a gas as the pressure on it changes. Let's try the following experiment using equipment that might be found in your kitchen Marshmallows are a mixture of sugar, air, and gelatin. Sugar makes them sweet, air makes them fluffy, and gelatin makes them elastic. Marshmallows are a frozen foam and are mostly air by volume. When placed in a vacuum pump, they expand as the pressure decreases. Break the seal on their container and they shrink during the return to normal atmospheric pressure. Since the vacuum pump pulls on the marshmallows hard enough to burst some of the air bubbles, they are actually a bit smaller and more shriveled at the end of this experiment. This illustrates a fundamental, yet important, property of gases. The pressure of a gas is inversely proportional to its volume when temperature is constant. Symbolically…
This correlation was discovered independently by Robert Boyle (1627–1691) of Ireland in 1662 andEdme Mariotte (1620–1684) of France in 1676. In Great Britain, America, Australia, the West Indies and other remnants of the British Empire it is called Boyle's law, while in Continental Europe and other places it is called Mariotte's law. Mariotte added the important provision that temperature remain constant. Boyle neglected to mention it, but the data he used to derive his law were most likely collected during a period in which the temperature did not experience any significant change. Since the gas needs to be in thermal equilibrium with its environment (or some other heat reservoir) to maintain an even temperature, the pressure-volume relationship normally applies only to "slow" processes. The marshmallow-vacuum experiment shown above is an example of a "slow" process. The pressure is reduced at a rate slow enough that heat from the environment is able to keep the jar and its contents at nearly room temperature. Such a transformation that takes place without a change in temperature is said to be isothermal.
The air rushing from your mouth will be quite cool despite coming from the core of your body, which is normally quite hot (around 37 ℃). During a "fast" process like the ones just described, pressure and volume are changing so rapidly that heat doesn't have enough time to get into or out of the gas to keep the temperature constant. Such a transformation that takes place without any flow of heat is said to be adiabatic.
volume-temperature (constant pressure)
Increasing the temperature of bread dough increases its volume.
While there the dough expands again, but his time it's not due to the action of microorganisms (they all die around the boiling point of water). This time it's the heat, or rather the temperature. The temperature inside a bread oven is roughly 50% greater (in absolute terms) than the temperature outside. And similarly, the baked bread that comes out of a bread oven is also roughly 50% greater than the room temperature dough that goes in. This domestic example illustrates quite nicely a fundamental property of gases.
The volume of a gas is directly proportional to its temperature when pressure is constant. Symbolically…
V ∝ T (P constant)
While no doubt known and understood informally by billions of bakers since the dawn of civilization, the precise mathematical relationship was first discovered by the French physicistGuillaume Amontons (1663–1705) in 1699. The experiment was repeated much later by JacquesCharles (1746–1823) in 1787 and much, much later by Joseph Gay-Lussac (1778–1850) in 1802.
More specifically, an increase in one results in a proportional increase in the other and a decrease in one results in a proportional decrease in the other. For example…
Doubling the absolute temperature of the air in an engine cylinder will double its volume.
Halving the absolute temperature of the air in a bag of potato chips will cause it to shrink to one half its original volume.
The absolute temperature of a bread oven is one and a half times that of room temperature.
Therefore, the loaf of baked bread that comes out of an oven has 50% more volume than the ball of dough that went into it.
There's a symmetry at work here somewhere. A symmetry is a change in one quantity that leaves another, more fundamental quantity unchanged. It's something like multiplying both the numerator and denominator of a fraction by the same thing. pressure-temperature (constant volume)
absolute temperature.
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