Boyles Law

bzoomImage

Boyle's law

boil = Boyle
lawyer = law
P1V1=P2V2 = Boyles Law equation

Volume

size of boil = volume

Pressure

scuba diving = pressure

Boyle's Law

States of Matter

Most matter on Earth exists in one of three states: solid, liquid, or gas. There are many other states of matter, of them, only plasma exists naturally on Earth. While plasma is the most common state of matter in the universe, it is much less common and usually temporary on Earth.states-of-matter

Matter in the solid state maintains a fixed volume and shape. The component atoms, ions, and molecules are close together and fixed into place. There is relatively low energy in this state of matter, and very little molecular movement. The molecules still vibrate some, but generally do not move from place to place.

Matter in the liquid state also maintains a fixed volume, but the shape can adapt to fit the liquid's container. The molecules are still fairly close together, but not as close as in the solid form. Liquid molecules vibrate and slide past each other. This property is what allows liquids to flow and change shape.

Matter in the gaseous state does not have a fixed volume or shape. It is capable of adapting both to fit its container and conditions. The molecules are neither close together nor fixed in place. Gas molecules vibrate and move freely at high speeds. If not contained, a gas can dissipate completely.

Behavior of Contained Gases

When gases are contained, the walls of their containers prohibit them from dissipating. As the highly active molecules move around in an enclosed space, they constantly hit and bounce off the walls of their container. Each time a gas molecule bounces, it imparts a force on the wall. The force of each molecule is typically quite small, but the sheer number of collisions can have a very large cumulative effect. For example, all of the molecules of air or helium inside a balloon exert enough pressure, or continuous physical force, to keep the balloon inflated.

The pressure a gas exerts on its container can change if one or more of three things occur.

  1. Temperature Changes – As the temperature changes, so does the amount of molecular movement. If the temperature increases, the gas molecules move faster, creating more pressure. If it decreases, the molecules move slower and reduce pressure. If the temperature decreases enough, the gas will condensate, or change to a liquid state. If a big enough temperature drop occurs quickly enough, the gas can even skip the liquid phase and change directly to a solid. This is called deposition.
  2. Number of Molecules Changes – If more molecules are added, there will be more collisions with the container, resulting in an increase in pressure. A decrease in molecules results in a decrease in pressure, as there are fewer collisions occurring.
  3. Volume Changes – If the volume of the container is decreased, the molecules have less distance to travel between collisions, resulting in more collisions and an increase in pressure. If the volume is increased, then gas molecules have farther to go and the number of collisions and pressure decreases.

The Law

boylesBoyle's Law deals with the third variable, the relationship between volume and pressure when temperature and the number of gas molecules remains the same.  According to Boyle's Law, so long as nothing else changes, the volume of a given mass of gas is inversely proportional to the pressure it is under. This relationship is linear, so if the pressure on a gas doubles, its volume will be halved.

This law can be expressed mathematically as P1V1=P2V2, where P1 and V1 are the first pressure and volume, and P2 and V2 are the new pressure and volume after a change. It can be alternatively expressed as PV = C, where the product of the pressure and volume equals a constant (C).

This relationship between pressure and volume results from the influence volume has on the rate at which gas molecules collide with the container walls. As stated under variable 3 above, if the volume decreases, the molecules encounter the walls of the container more often, resulting in more pressure. Conversely, if the volume decreases, the rate of collisions and therefore pressure increases.

Summary

There are many possible states of matter in the universe, but on Earth, matter typically exists only as solids, liquids, or gases. Solids have the least molecular movement these three states, and typically maintain a rigid shape and volume. Liquids have somewhat more molecular movement. The molecules are able to slide past one another, but are still fairly closely packed together. This means that liquids maintain their volume, but not necessarily their shape. Gases maintain neither volume nor shape. Their molecules move too fast and too far. If not contained, gases can and often do dissipate completely. When contained, gases exert pressure on the walls of their containers based on the rate at which the molecules collide with the walls. Assuming that temperature and the number of molecules inside a container remain the same, Boyle's Law states that pressure and volume are inversely proportional to each other. If the volume of a container is halved, the pressure on the gas is doubled. If the volume were tripled, the pressure would be reduced to a third. Boyle's Law can be expressed mathematically either as PV=C or as P1V1=P2V2.

Boyle’s Law script

1. Zoom: Lawyer with boil on his nose

Hot Spot: boil = Boyle’s, lawyer = law, P1V1=P2V2 = Boyle’s Law equation

Learning: Boyle’s Law, shown in our CoursePic by the lawyer, is a gas law that describes the relationship between pressure and volume. Pressure is the amount of force exerted on one unit of area. The equation P1V1=P2V2represents Boyle’s Law, indicating the inversely proportional connection between pressure and volume in a closed system where temperature and number of molecules are both constant. While Boyle’s Law applies to gas, we’ll represent it visually through the large boil on Harold’s nose. With 760 mmHg (millimeters of mercury), Harold is at sea level and hardly bothered by the boil.

Story: Harold Boyle is a lawyer. As legal representation goes, he’s the best money can buy in D.C., but it’s hard not to be distracted by the giant boil on the tip of his nose. Just the same, he pulls in enough money to have a comfortable office right around sea level on the Potomac. Harold certainly isn’t bothered by his boil as he texts a new client on his way to the office.

2. Zoom: Lawyer with boil on mountaintop

Hot Spot:size of boil = volume

Learning: Let’s use the boil to represent this relationship. Assume the pressure at Devil’s Tower is 380 mmHg, or half of that in Washington, D.C.. The higher he climbs, the lower the pressure. Lower pressure means higher volume, so if P1V1=P2V2, Harold’s boil would double in size.

Story: But this case is a special case, leading Harold to the top of Devil’s Tower in Wyoming to file a legal brief. While the temperature there is the same as it was in D.C., Harold’s not dealing with the new topography well. As the pressure decreases on his way up the mountain, Harold notices that his boil doubles in size. He’s embarrassed, but hoping that his legal track record will speak for itself.

3. Zoom: Lawyer with boil scuba diving

Hot Spot: scuba diving = pressure 

Learning: On the other hand, let’s put Harold in a situation where the pressure doubles from the original 760 to 1520 mmHg. Under these high-pressure circumstances, if temperature and the number of molecules are the same, Harold’s boil would now shrink to half its original size. 

Story: Fortunately, Harold’s client also has a boil and takes to his new attorney at once. He invites Harold scuba diving to talk over the particulars of the case. The water pressure has the fortunate result of shrinking Harold’s boil, but he struggles with the force of the overlying water. His client, an experienced diver, is having a great time. Then again, he hasn’t descended as low as Harold, so the pressure on him is less.

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