And you can do it, too, it's easy
(it's so easy)
Like takin' candy
(like takin' candy)
from a baby.

("1-2-3," by Len Barry, J. Medora, D. White, 1965)

 

INTRO TO BOYLE'S LAW AND GAS "COMPRESIBILITY"

PTOA Readers and Students ... who are reading the PTOA Segments in the intended sequential order ...

just learned that the so-called "Gas Laws" are really common sense predictions about the behavior of a gas under a set of described conditions.

Each "Gas Law" predicts whether or not the gas Pressure, gas Temperature, and gas Volume will increase, decrease or remain constant.

In the recently completed PTOA Segment #152, PTOA Readers and Students easily predicted the behavior of a gas (air) when:

• The gas Pressure is held constant. In that case, an increase in the gas Temperature will cause a corresponding one-to-one increase in the gas's Volume ... and vice versa. That tidbit of common sense is called "Charles's Law."
• 

  The volume of air in this ball is constant, meaning the amount of air contained in the ball cannot change.

  The Volume is held constant. In that case, an increase in the gas Temperature will cause a corresponding one-to-one increase in the gas Pressure ... and vice versa. That tidbit of common sense is called "Gay-Lussac's Law."

 

PTOA Readers and Students also learned that "Volume" is a component of the PV Flowrate; therefore, changes in the Volume of a flowing gas will also change the Flowrate of that gas!

This PTOA Segment #153 continues to challenge PTOA Readers and Students to use their common sense and figure out:

What happens to a gas's Pressure and Volume when the gas's Temperature is held constant?

A dude named Boyle gets credited for the "gas law" describing those conditions.

PTOA Readers and Students will also learn the instructional jargon term "compressibility" and why gases are compressible but liquids are not.

Wow! Away we go to start covering all this gas-phase related stuff!

 

PREDICT GAS BEHAVIOR #3

PTOA Readers and Students can use their own common sense to predict how a gas's Pressure and the Volume will change when it's Temperature is held constant.

Smart PTOA Readers and Students ...who are reading the PTOA Segments in the intended sequential order ...

already observed a Volume that was capable of expanding and contracting ...

the inflated balloon that was featured in Charles's Law in PTOA Segment #152!

However, ...

to predict the gas Pressure/gas Volume relationship that Boyle observed, the container that contains the gas must have rigid walls. 

The kick ball used to illustrate the Gay-Lussac's Law in PTOA Segment #152 had rigid walls.

The problem is that ... to observe the gas Pressure/gas Volume relationship predicted by Boyle's Law the rigid walls of the container holding the gas must somehow also be able to expand and contract so that the container's Volume can be varied.

So the classic apparatus used to represent ...

"A Rigid-Walled Volume that Can Still Expand and Contract While Studying How Pressure Varies" is:

Ye Olde Piston Moving In and Out of a Cylinder!

PTOA Readers and Students that have experienced purchasing a gasoline-powered vehicle probably know about pistons and cylinders via trying to decide between an inline 4 cylinder versus a slant V-6 or V-8 cylinder engine.

Those PTOA Readers & Students who are less familiar with automobile engines can just think of a "cylinder" as a hollow tube with a bottom on one end and open on the other end.

An opened and emptied can of soup is shaped like a cylinder ... once the hanging lid is taken off!

 

So is a medical syringe.

The plunger of the syringe can change the Volume of vaccine as it is pushed down.

Likewise ...

A piston is a circular disk that glides into and out of the cylinder in successive strokes.

The piston "magically fits" into the cylinder so that it can glide in and out of the cylinder easily with each stroke...

yet the air that is entrapped within the cylinder before the first stroke cannot escape ... because the fit of the piston to the cylinder is so tight!

The air that is entrapped within the cylinder represents a specified amount and Volume of gas that is held captive and cannot escape.

The gas can be any kind of gas; Your Mentor has just chosen to use air in this case study of predictable gas behavior.

Once again, PTOA Readers and Students need to stop right here and use their common sense to predict:

What will happen to the Pressure that the enclosed gas exerts on the walls of the cylinder as the Volume of the gas is decreased by 1/2 ... which happens when the moving piston is extended half way into the cylinder?

Will the Pressure of the gas increase ... or decrease?

Then:

What will happen to the Pressure that the enclosed gas exerts on the interior walls of the cylinder as the Volume of the gas expands back to the original full Volume when the piston stroke is returned to the starting point? 

Imagine that you are a gas particle inside that cylinder being squashed into a smaller and smaller Volume by the invading piston ... just like being Princess Leia in the trash compactor of the Death Star. No doubt Princess Leia was feeling increased Pressure!

and then

Ahhhh! Relief at last! ...

The piston retracts again and there's suddenly more room for you in your air particle state and all the air particles around you.

Your Mentor is certain common sense prevailed and PTOA Readers and Students figured out that ...

when the Temperature is held constant ...

A decrease in gas Volume will increase the gas Pressure and vice versa ...

An increase in gas Volume will decrease the gas Pressure.

Voila!

PTOA Readers and Students just used their common sense to predict gas behavior that is described by Boyle's Law.

Actually, we'll give Boyle a bit more credit because Boyle's Law predicts the magnitude of the change within the gas Pressure/gas Volume relationship:

BOYLE'S GAS LAW:

When the Temperature is held constant ...

A gas Pressure will double when the gas Volume is halved (and vice versa). 

Otherwise stated ...

1/2 Original Volume = 2 * Original Pressure and/or

2*Original Pressure = 1/2 Original Volume

The above graphic of Boyle's Law shows that:

• When the Volume decreases from 6 to 3 Liters (on the Y axis) ...
• The Pressure increases from 50 to 100 kPa (on the X axis)

1/2 Volume = 2 X Pressure!

 

BOYLE'S LAW IS THE DEFINITION OF "COMPRESSING" 

When the piston extends into a cylinder full of gas, the gas is being compressed. Refer to condition (b) in the nearby graphic.

The word compressing means "cramming gas molecules into a smaller Volume."  The act of cramming a gas into a smaller volume (aka "Compressing a gas") increases the Pressure of the gas. (Who amongst the brilliant PTOA Readers and Students wishes to guess what the Rotating Equipment called a "Compressor" does?).

In the case of Boyle's Law, the gas Pressure increases because the gas molecules exert their Force on a dwindling amount of Surface Area as the Piston extends into the Cylinder. A Force spread over less Surface Area means an increase in Pressure is happening!

Once the piston retracts, the same amount of gas molecules will have more Volume to occupy. The gas molecules will spread out as far as they can from each other to occupy the entire Volume as is shown in the nearby graphic as condition (a).

With more Volume to share, the Force of the mass of gas molecules is spread out over an increased Surface Area, hence the gas Pressure decreases.

Otherwise stated, "decompression of a gas" results in less gas Pressure.

 

WHY GASES ARE COMPRESSIBLE AND LIQUIDS ARE NOT (NOR ARE SOLIDS). 

Imagine replacing the gas entrapped in the cylinder shown nearby with a liquid ... like water. The water molecules are attracted to each other much more that gas molecules are. Otherwise stated, there's not much room between liquid molecules that can be used to force those liquid molecules "more together."

Imagine that the Force of the extended Piston does not cause the water ... which has no way out ... to break the Cylinder apart.

Since liquids are not compressible, that means feel free to Imagine that the Piston will just sit on top of the water. Hence, the Force component of the Pressure that the Piston exerts is simply transferred through the water in all directions.

Note that the Volume of the water does not change hardly at all because the Piston cannot "compress" the liquid into a smaller Volume.

Hence the dissipated Force that the water exerts on the interior walls of the Cylinder will not noticeably increase, thus the measured Pressure will only negligibly increase ... if at all.

The PTOA Department of Redundancy Department reiterates:

The reason that gases are Compressible and liquids are not is because liquid molecules are more attracted to each other and naturally just want to hang around each other.

Gas molecules are not attracted to each other and will always fill up a container by moving as far apart from each other as they can.

Therefore:

Gases are Compressible because there is more empty space available between gas molecules that makes it possible to cram them together. Liquid molecules are already close together and thus Non-Compressible.

Accessing the below You Tube link will explain why:

• 

  This Reciprocating-Action PD Compressor "compresses" gases. The discharge gas has a higher Pressure.

  Gases are compressible.

• Liquids are hardly at all compressible.
• Solids are not at all compressible.

 

Thank you KClassScience Channel for demonstrating that the ability to compress a substance depends upon what physical state the substance is in.

KClassScienceChannel Compressibility You Tube

Conclusion: Whenever there's an interest in building up the Pressure in a substance via Compression, the first step is to make sure the substance is in the gaseous phase!

 

 

A GAS PRESSURE CAN INCREASE WITHOUT AN INCREASE IN TEMPERATURE!

Who amongst the brilliant PTOA Readers and Students figured out that the increase in Pressure observed by Boyle and predicted by our common sense is not due to molecular agitation ... because the Temperature is held constant?

The increase in Pressure we predicted was caused by the increased gas density!

The amount of mass did not change in the Cylinder no matter where the Piston was positioned during its stroke. 

Although the amount of gas mass (aka, gas molecules) did not vary, the Volume within the Cylinder was at maximum when the Piston was fully contracted and at the minimum when the Piston was full extended.

Hence, the increase in gas Pressure that Boyle observed, and we all predicted was simply created by cramming gas mass particles into a smaller Volume.

Hey! Cramming the same amount of mass into a smaller Volume means the density has increased because ...

Density = Mass / Volume.

All PTOA Readers and Students learned about density in PTOA Segment #145.

Conclusion: The increase in Pressure described by Boyle's Gas Law is due to increasing the density of the air enclosed in the cylinder!

 

SMART CONTROL BOARD OPERATORS ARE AWARE:
THERE'S ONLY 2 WAYS THE PV GAS PRESSURE INCREASES

In the last PTOA Segment (#152), PTOA Readers and Students learned that Process Operators and Control Board Operators must be alert when Pressure builds up unexpectedly.

PTOA Readers and Students learned that an unknown increase in the PV Temperature can cause an increase in the gas's PV Pressure; That's Gay-Lussac's common sense Gas Law.

PTOA Readers and Students just learned the second way the PV Pressure can build up in the gas phase ... even when there is no increase in the PV Temperature.

In that situation, the increase in gas Pressure can be caused by an increase in gas density.

What is the relevance of the above paragraphs with respect to the real world of industrial processing?

Picture yourself as a future Control Board Operator.

Harken!

Me thinks the PV Pressure is increasing in yon Vessel ... or Tower ... or Tank ...whatever!

 

When this situation happens, the Control Board Operator uses his/her/their training to assess which of these two types of root causes is behind the increase in Pressure.

• Is the PV Pressure of the enclosed process gas stream increasing due to an unknown source of heat? (The application of Gay-Lussac's law to industry) ...Or
• Is the density of the gas being increased via a changing mass or Volume? (Boyle's Law applied to industry).

 

Spoiler Alert #1: Very soon PTOA Readers and Students will learn that some kinds of Rotating Equipment will change the gas density to increase gas Pressure.

Spoiler Alert #2: If the Volume of the rigid gas container cannot change ...then the Control Board Operator should communicate with the Outside Operator and inquire if a valve is open that should be closed.

Because adding more mass into a rigid and unchanging Volume will also increase gas density, hence gas Pressure! (That's actually "Avogadro's  Number Gas Law" ...a logical extension of Boyle's Law)!

There you go! That's it! It's that simple!

One of these two phenomena are ongoing when the PV Pressure increases in a contained fluid!

TAKE HOME MESSAGES: Boyle's Gas Law is nothing but a common sense prediction of gas behavior between a gas Pressure and a gas Volume when the gas's Temperature is held constant.

Boyle's Gas Law states that when the Volume of a gas is cut in two, the Pressure of the gas doubles.

Boyle's Gas Law is typically studied with a piston and cylinder apparatus that allows changing the Volume of a rigidly walled container ... which allows the impact on Pressure to be observed.

The piston and cylinder apparatus allows the study of compression ... meaning the increase in Pressure that results in a gas when its mass is crammed into a smaller Volume.

Cramming a specified amount of gas mass into a smaller Volume is equivalent to increasing the gas's density (and vice versa). So an alternative conclusion from Boyle's Gas Law is a correspondence between increased gas Pressure and increased gas Density (when Temperature is held constant).

Compressibility is a characteristic of gases ...  not liquids nor solids.

Boyle's Gas Law and Gay-Lussac's Gas Law predict the only two ways gas Pressure can build up in industrial process equipment: 

The PV Pressure can be increased either by

• A PVTemperature increase.
• An increase in a gas's density by compressing

... meaning cramming gas mass into less Volume
or cramming more mass into a rigid, unchanged Volume.

©2017 PTOA Segment 0153
PTOA Process Variable Pressure Focus Study Area
PTOA Introduction to PV Pressure Focus Study

You need to login or register to bookmark/favorite this content.