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)

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 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 a gas Volume can often infer a change in the gas's flowrate.

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 ...

In the featured Boyle's Gas Law case study, the Volume must be in a container that has rigid walls ...

kind of like the kick ball that was featured in the explanation of Gay-Lussac's Law in PTOA Segment #152 .

Except ... to observe the Volume/Pressure 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 ... sort of!

 

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 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 ... like being Princess Leia in the trash compactor of the Death Star. No doubt Princess Leia was feeling 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 in gas Pressure that can be expected with a change in gas Volume (while, of course ... the gas Temperature is held constant).

A gas Pressure will double when the gas Volume is halved (and the temperature is held constant).

aka ...

1/2 Original Volume = 2 * Original Pressure

The above graphic of Boyle's Law shows that:

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

1/2 Volume = 2 X Pressure!

 

DEFINITION OF "COMPRESSING" 

When the piston extends into the cylinder, it is in the act of compressing the gas. Refer to (b) in the nearby graphic.

 

The word compressing means "cramming gas particles into a smaller Volume for the purpose building up gas Pressure."

Once the piston retracts, the same amount of gas mass particles have more room to occupy and fill up.

Refer to (a) in the nearby graphic.

More surface area to bang into translates into less Force per unit of Area ... hence, less Pressure and less compression.

 

ONLY GASES ARE COMPRESSIBLE 

Imagine replacing the gas entrapped in the cylinder shown below with a liquid ... like water.

Once the piston stroke extends into the cylinder ...

Well ...

the piston will get wet, but the force that the water exerts on the interior walls of the cylinder won't noticeably change ...

So that means the Pressure of the water won't change.

That's because the water particles are much closer together in their liquid state ... so there's not much room to compress them to become even closer together. No Pressure will build up.

Accessing the below You Tube link will explain why:

• 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 trapped gas having less Volume available to occupy.

In nerdy terms ...

PTOA Segment #142 explained that

Pressure = Force / Area

and ...

Force = mass * acceleration

so ...

Pressure = (mass * acceleration) / Area 

The amount of mass does not change in the cylinder no matter where the stroke of the piston is.

However, the amount of Area on the cylinder walls available for the gas to bump into and ricochet off us is much less when the stroke of the piston is fully extended into the cylinder.

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 we predicted was 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 they 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 ... this time in the absence of a Temperature increase:

An increase in gas Pressure can be caused by a decrease in Volume ...

aka an increase in gas density.

That's the gist of the just-now-learned "Boyle's Law."

 

 

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 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? ...Or
• Is the density of the gas being increased via a changing Volume?

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 Temperature increase
• A 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

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