It's just common sense
think about it, bout it
think about it, bout it
think about, about it

("Common Sense," by Ne-Yo Smith, 2009)

 

THE COMMON SENSE GAS LAWS THAT ARE NEVER TAUGHT WELL TO STUDENTS

Let's get something cleared up right away.

The (Common Sense) "Gas Laws" that will be featured in the next few PTOA Segments existed since the birth of the Universe.  These "secrets of the how the Universe works" just happened to be whispered into the ears of dudes named Charles, and Boyles, and Gay-Lussac, and Dalton .... scientists who just happened to be alive and alert enough to pick up what the Universe was puttin' down.

While progressing through this PTOA Segment #152, PTOA Readers and Students will begin to deduce on their own how those interrelationships work via understanding what's going on at the molecular level.

Your Mentor is going to go out on a limb and assume that your introduction to "The Gas Laws" was poorly executed.

When PTOA Readers & Students were in middle school science class or high school chemistry class they were briefly introduced to "Boyle's Law" and "Charles's Law" and maybe even Gay-Lussac's Law and "Dalton's Law" and finally the vague mention of "The Ideal Gas Law" that had the strange and mysterious expression:

PV = nRT

And then your instructor heaved a sigh of relief to be done with the chapter on "Gas Laws" (or whatever the chapter was called in your earth science or chemistry textbook).

Ever after, you continued through life confused about how these "laws" applied to the real world.

The duo purposes of this PTOA Segment are:

• To illustrate how the PV Pressure is an integral part of the "Gas Laws."
• To illustrate how the so-called "Gas Laws" are merely common sense that anyone can use to predict the behavior of gases.

 

A COUPLE QUICK REVIEWS

Reminder of What the Word "Gas" Means

Way, way back in PTOA Segment #3 (entitled "Do You Know What I Mean?") PTOA Readers and Students learned that:

• Both liquids and gases fall into the broad category of "Fluids."
• The term "gas" is supposed to mean "a 100% gaseous substance made up of the same type of gas molecules." However, ...
• In the Process Industry World, the descriptor "gas" is interchangeably used to mean both a mixture of gases and a pure gas. In other words, any substance that is in the gas phase. The Process Industry World does not get hung up on nuances.

 

This PTOA Segment #152 is all about gases ... not liquids.

 

Absolute Temperature Scale Reminder 

All PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order learned about Absolute Temperature and the Absolute Temperature Scales (Kelvin and Rankin) way back in PTOA Segment #96.

So PTOA Readers and Students already know that when the Temperature declines to the theoretical temperature of -273.15 °C (aka -459.67 °F) ...

... which are also known respectively as Absolute Zero and 0 °Kelvin and 0 °Rankin ...

the molecules that make up any mass are at a dead stand still and thus not capable of transferring any heat.

Why do we care at this juncture? ...

The Temperature Expression in Gas Law Calculations Must Be Represented as an Absolute Temperature

The "Gas Laws" are one of the few applications of the Absolute Temperature scales in process industry.

Me thinks an application exercise will help the above statement make sense:

When was the last time you inflated a balloon?

Maybe you self-inflated the balloon with air blown into the balloon innards from your mouth ...

or maybe you inflated the balloon with helium from a helium cylinder.

More than likely those were the only two economical gas choices to choose from for balloon inflation.

Let's say you inflated the balloon with air at a room temperature of 70 °F (21 °C) until it was 8 inches (20.32 cm) in diameter ... which of course means a 4-inch radius (10.16 cm).

At the molecular level, this is what was happening:

The particles of air inside the inflated balloon are excited at 70 °F (aka 21 °C = 294.2 °K = 529.7 °R) and start knocking into each other.

Because the balloon skin is a defined yet flexible boundary ... the air particles smack into the inside interior skin of the balloon and then ricochet off the interior wall skin and smack into more particles.

The balloon eventually becomes inflated to a starting Volume.

If we wanted to we could calculate the Volume of the air enclosed in the balloon using the mathematical expression below:

Volume of Any Spherical Shaped Object Like A Balloon =

Volume_(sphere) = (4/3) *(3.14) * (Radius)³

Notice how the Volume of the balloon is determined by the radius ... and therefore diameter ... of the balloon!

Spoiler Alert: PTOA Readers and Students will soon learn that Volume is directly related to the PV Flowrate. Ergo ... the content in this PTOA Segment devoted to "Volume" is directly applicable to the PV Flowrate.

 

CASE STUDY 1: PREDICTING GAS BEHAVIOR

All PTOA Readers and Students need to stop at this point and use their common sense to first ponder and then predict what might happen to the diameter ... and hence Volume ... of the balloon given the below two scenarios:

First Scenario:

The inflated balloon is exposed to a much colder Temperature ... like maybe it is suddenly put into the refrigerator.

Use your common sense and Imagine what would happen to the molecular activity of the air particles.

Would they zoom around and collide with each other more or less frequently in a refrigerator versus a room temperature of 70 °F (21 °C)?

And how would the diameter and shape of the colder balloon change compared to the balloon at 70 °F (21 °C)?

Second Scenario:

The inflated balloon is exposed to a hotter temperature. Maybe it is taken outside on a 104 °F day (40 °C) ... or maybe it is held near a candle flame.

Use your common sense and Imagine what the air particles inside the balloon would do if they were excited by a hotter environmental temperature.

Would they be crashing into each other and the interior skin of the balloon with greater or less frequency than at the lower room temperature?

And how would the diameter and shape of the hotter balloon change when compared to the balloon at 70 °F (21 °C)?

Your Mentor is pretty certain that all the smart PTOA Readers and Students accurately predicted that ...

The Volume of the air-filled balloon ...

• Decreases when exposed to a lower Temperature and
• Increases when exposed to a higher gas Temperature.

Voila! You just predicted Charles's Law by using common sense!

When a specified amount of gas is enclosed within a specified but elastic Volume and the surrounding environment is held at a constant Pressure ...

(which was atmospheric pressure in our example) ...

An increase in Absolute Temperature will result in a predictable increase in gas Volume and ...

A decrease in Absolute Temperature will result in a predictable decrease in gas Volume.

In summary ...

There is a directly linear, predictable relationship between the volume of a specified amount of gas and a changing Temperature when the gas is held at a constant Pressure.

The relationship between the Volume and (Absolute)Temperature of the gas is so linear that it can be graphed as a straight line with a constant slope.

In fact ... when the Pressure is held constant ...

the relationship between the Volume of a gas and the Temperature of a gas is so predictable one can assume ...at constant Pressure:

If the Absolute Temperature of a specified amount of gas doubles, then its volume will double.

Like ...Duh!

But Hey! This observation of gas behavior was big news back in the 1780s-early 1800s.

 

Why "Gas Laws" are "Gas Laws" and not "Fluid Laws"

Let's take a few paragraphs to ponder what would happen if the balloon were filled with water instead of air?

How would the Volume of a water balloon change as the ambient Temperature around the balloon were raised or lowered from 70 °F (21 °C) ?

Stop and think about how the Volume of the water balloon might change if the balloon were put into a refrigerator.

Stop and think about how the Volume of the water-filled balloon might change if the balloon was held near a candle flame or taken outside on a 104 °F (21 °C) day.

Smart PTOA Readers and Students are thinking ... is this a trick question?

Because the Volume of a water balloon won't  change much at all when exposed to a higher Temperature or lower Temperature.

In fact the Volume of a liquid won't change much at all until the surrounding Temperature causes the liquid to start changing into the gas phase.

That's because liquid molecules are held much more closely together than gas molecules and they just are not as easily excited by changes in Temperatures.

Ergo,

The "Gas Laws" predict only Gas behavior ...

specifically the interrelationships between the Pressure, Volume, and (Absolute) Temperature that the gas is experiencing.

The "Gas Laws" are simply not "Fluid Laws" because the molecular bonding of gas molecules is totally different than the much closer bonding of liquid molecules.

 

CASE STUDY #2: PREDICTING GAS BEHAVIOR

Let's Imagine the balloon is now made out of non-stretchy material ... so it's more rigid ... like a hollow kick ball.

In other words ... The Volume of the container is fixed.

Once again, the kick ball is filled with a specified amount of air at 70 °F (aka 21 °C = 294.2 °K = 529.7 °R).

Air molecules don't care what kind of container they are in ...rigid or stretchy walled ...they will always get excited when exposed to a hotter (Absolute) Temperature and vice versa.

Since the interior walls of the kickball are rigid ...

the increased molecular activity caused by an increased (Absolute) Temperature results in an increase of agitated molecular activity on the  the interior surface of the kickball ...

just as happened in the balloon ...

... but since the Volume of the kickball cannot expand because of the rigidity of the container ...

there is more force exerted on each square inch of the interior surface of the kick ball  ...

and you know what that means ...

The increased (Absolute) Temperature will cause an increase in Pressure created by the increased force of air on the  interior walls of the kick ball!

So PTOA Readers and Students need to stop right here and predict ...

What will happen to the Pressure exerted on the interior walls of the kickball when:

• The Temperature of the enclosed gas (air) is increased?
• The Temperature of the enclosed gas (air) is decreased?

 

Your Mentor knows that smart PTOA Readers and Students used their common sense to predict that the Pressure of a gas confined within a fixed Volume will increase with increased Temperature and decrease with decreased Temperature.

Congratulations! Using your common sense, you just predicted the behavior of a gas that a dude named Gay-Lussac gets credit for.

For a specified amount of gas held within a constant Volume, there is a one-to-one correspondence between the change in Absolute Temperature of the enclosed gas and the Pressure that the gas exerts on the interior of the fixed-Volume container.

Here's the graph of the Gay-Lussac Law relationship:

Oh no, Fred's confused!

Fred ...

just pretend that you are a particle of air inside the kick ball ...

and then let's say the air in the kick ball experiences an increase in (Absolute) Temperature from:

32 °F (aka 0 °C = 492 °R = 273°deg K)

to:

212 °F (aka 100 °C = 672 °R = 373 °K)

The % difference in Absolute Temperature experienced by the air in the kick ball can be quantified thus:

[(672 °R - 492 °R) / (492 °R)] * 100  = 36.6%

or if you prefer to work in Kelvin Scale:

[(373 ° K - 273 °K)/ (273°K)]  * 100 =  36.6%

Well ..

The Pressure exerted on the rigid interior walls of the kick ball also increases by 36.6%!

(unless the kick ball explodes due to the increase in Pressure!)

Wow Fred! You were really zinging around hitting the interior wall of that kickball with over 1/3rd more force!

Fred ... R U O K?

Likewise, the Pressure inside the kickball would reduce by a predictable amount if the Absolute Temperature were decreased.

Got it, Fred?

Whew! This is enough common sense for now!

 

But Guess What?  Another Spoiler Alert!

PTOA Readers and Students just learned one of the two ways that the PV Pressure can build up in the gaseous phase of a process fluid that is stored in any vessel, tower or other type of container.

So Gay-Lussac's common sense Gas Law contains directly applicable process industry information that will be revisited in the future PTOA Troubleshooting Focus Study Area!

Here's a preview:

There you are ... the future Process Industry Control Board Operator ... and you notice a process stream Pressure unexpectedly increasing in a vessel or tower!

And you say to yourself ...

"Lo and behold!

Could it be that there is an unknown source of heat entering that rigid-walled vessel containing that process gas stream ...

ergo causing the molecular activity of the gas stream to increase rapidly ...

thereby increasing the PV Pressure?"

Okay ... maybe your thought stream will not be quite that analytical at that precise moment ... but more like the nearby thought cloud.

In the next PTOA Segment, PTOA Readers and Students will learn the only other way that the PV Pressure of a gas can build up unexpectedly in a process industry vessel, tower, or container.

The next two PTOA Segments feature the last three common sense "Gas Laws."

TAKE HOME MESSAGES: The so-called "Gas Laws" are actually common sense, predictable behaviors of gases that illustrate the interrelationships of Pressure, Volume, and Temperature for a specified amount of gas.

The Gas Laws apply to gases only ... not liquids; the molecular bonding of liquids is stronger than gases and therefore liquids are not as significantly impacted by changes in Temperature.

The Gas Laws are one of the few uses of Absolute Temperature (°R or °K) in the process industries.

Gas Volume is dependent upon the diameter (and therefore radius) of the container that is storing the gas. The Volume of both gases and liquids are directly related to their PV Flowrate.

Charles's Law assumes the PV Pressure is constant, then logically predicts what will happen to the Volume of a fixed amount of gas when the gas is exposed to a change in Temperature.

A useful conclusion of Charles's Law is:

If the Absolute Temperature of a specified amount of gas doubles, then the Volume of the gas will likewise double.

Gay-Lussac's Gas Law assumes the Volume of the gas is fixed, then predicts the impact that a Temperature change will cause on the PV Pressure that the enclosed gas exerts on the container. Gay-Lussac's Gas Law states:

For a specified amount of gas held within a constant Volume, there is a one-to-one correspondence between the change in Absolute Temperature of the enclosed gas and the Pressure that the gas exerts on the interior of the fixed-Volume container.

Gay-Lussac's Gas Law serves as a warning to all Process Operators regarding what happens when a gas enclosed in a container is exposed to an unexpected temperature increase.

©2017 PTOA Segment 0152
PTOA Process Variable Pressure Focus Study Area
PTOA Introduction to PV Pressure Focus Study

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