Baby's good to me, you know
She's happy as can be, you know
She said so
I'm in love with her and I feel fine

("I Feel Fine," the Beatles, 1964)

THE PV PRESSURE - PV TEMPERATURE RELATIONSHIP

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order are already aware that this PTOA Segment #157 is the first in a series which focusses on the relationship between the PV Pressure and a different process variable … in this case the PV Temperature.

When the stuff we're talking about is a gas held in a rigid-walled container …

PTOA Readers and Students have already predicted that an increase in the PV Temperature will cause a corresponding increase in the PV Pressure  ... and vice versa.

Yes, indeedo!

Gay Lussac's common sense "Gas Law" was recently featured in PTOA Segment #152 ... so let's not waste paragraphs repeating all that information!

However, the PV Pressure - PV Temperature relationship is very different when the container is holding a liquid that is being heated up to its Boiling Point Temperature.

THIS PTOA Segment #157 begins with focusing on what happens when water is heated in a container …just as it would be to make a cup of tea at three different worldwide locations:

 

The three worldwide locations are:

 

• 

  This graph shows how an INCREASE IN ALTITUDE (Y axis) correlates to a DECREASE IN ATMOSPHERIC PRESSURE (X axis).

  At sea level in New York City, where the P_atm = 14.7 psia (29.92 in Hg = 101.3 kPa = 1 Atm).

• Way up high at the summit of Mt. Sagarmatha (aka Mt Everest) which is located at an altitude of  29,029 feet (8848 m) and where the  P_atm = 4.89 psia (aka 9.96 in Hg =33.7 kPa = 0.333 Atm).
• In the vicinity of Lake Baikal in Russia during the winter when the cold dry air creates the "Siberian High" ... a perennial increase in the P_atm to 15.23 psia (aka 31 in Hg = 105 kPa = 1.03 Atm).

 

 

For each of the above case studies ...

The Atmospheric Pressure (P_atm) above the surface of the water will represent the PV Pressure  ...and the increasing Temperature of the heated water will represent the PV Temperature.

MAKING A CUP OF TEA  AT WORLDWIDE LOCATIONS

The below graphic illustrates how Altitude (aka "Feet Above Sea Level"), Atmospheric Pressure (aka P_atm), and the Boiling Point Temperature of Water are related.

This graphic was prominently featured in PTOA Segment #149 which explained why P_atm at sea level is 101.3 kPa = 14.7 psia  ... and how it decreases with increasing Altitude.

But why exactly does a change in P_atm change the Boiling Point Temperature of Water?

And since it apparently can change ...

What exactly is meant by "Boiling Point Temperature" of a Liquid?

 

Case Study 1:Boiling Water at Sea Level 

Sitting at an altitude of just 10 feet above sea level, New York City is essentially at sea level.

Therefore, the air pressure that surrounds and lingers above the liquid's surface as it is being heated to a boil in NYC is 101.3 kPa (aka 14.7 psia = 29.92 in Hg = 1 Atm).

Before the first water particles on the surface of the water can change their physical state and move into the vapor/gas phase, their pressure must exceed that of the P_atm that is pressing down upon them.

Ergo ...

As the water particles absorb the heat that is transferred into them via conduction and convection, their Temperature increases ...

until they have finally absorbed sufficient energy to break their liquid-state bonds ...

and begin to change their physical state into that of a vapor/gas.

The Temperature of the water when vaporization starts happening will be the Boiling Point Temperature of water at sea level ... 100 °C = 212 °F

So the Boiling Point Temperature is the Temperature that the liquid particles attain when the liquid has sufficient thermal energy to do these two things:

• Get excited and agitated enough to break up the liquid-liquid bonds.
• Have sufficient "chutzpah" to press up and through the air particles that are at the liquid's surface and thereby become part of the composition of the gas phase that lingers above the liquid's surface.

 

Case Study 2: Boiling Water at High Altitude

Now assume that the pot of water being boiled for tea is located at the top of Mt. Sagarmatha (aka Mt. Everest in the nearby graphic).

As the nearby chart shows, the highest altitude of Mt. Sagarmatha is 29,028 feet (8848 meters).

The chart also shows that P_atm at this high altitude has decreased significantly from the 101.3 kPa (14.7 psia) measured at sea level to just 32 kPa (aka 4.64 psia = 9.4 in Hg = 0.32 Atm).

OMG!

The P_atm at the top of Mt Sagarmatha is slightly less than one-third of what it is at sea level!

Another way to look at it is:

 

 

On a barometer, the length of the column of mercury ...

(aka "head of mercury," H) ...

that is used to measure P_atm would be just 9.96 in Hg high compared to the 29.92 in Hg head observed at sea level (don't remember that? Go to PTOA Segment # 149).

Ergo ...

The water particles in the teapot have significantly less P_atm pressing down upon them and squishing them together while they are absorbing thermal energy from whatever source is supplying heat.

Therefore ...

The water particles do not need to absorb as much heat to get excited and start breaking up the water bonds and ...

now in their newly vapor state ...

the water vapor particles can push through the air pressure that is pressing down upon them.

 

Thus, the particles of water vapor can mix and mingle with the air particles hovering above the liquid level at a much lower Boiling Point Temperature.

As the chart shows, the Boiling Point Temperature of water on top of Mount Sagarmatha (aka Mt. Everest) is just 70 °C  (aka 158 °F).

Aha! A pattern is emerging!

The Boiling Point Temperature of a liquid (in this case water) decreases as the Pressure above the liquid level in the container decreases!

The above conclusion pertains to all liquids ... not just water!

 

Case Study 3: Boiling Water where P_atm is High

The "Siberian High" is a mass of cold, dry air that hangs around Lake Baikal in Russia from September through April.

During this time interval, the P_atm is typically 15.23 psia (aka 31 in Hg = 105 kPa = 1.03 Atm).

Wow!

A barometer measuring P_atm at sea level is 29.92 in Hg! So the taller mercury head of 31 in Hg that would be measured at Lake Baikal during a "Siberian High" is a noteworthy increase in P_atm!

Your Mentor predicts that all smart PTOA Readers and Students can deduce how this significantly higher P_atm will impact the Boiling Point Temperature of Water.

Water particles being boiled for tea during the "Siberian High" have a significantly greater pressure above them that must be overcome before they can get sufficiently excited to start changing into the vapor/gas state.

The water particles will need to absorb significantly more thermal energy before they can start to vaporize and join the gas phase that is lingering above the liquid level.

In fact, the water in the teapot where the P_atm is 15.23 psia (aka 31 in Hg = 105 kPA = 1.03 Atm)  will not begin to boil until 221 °F (aka 105 °C).

Aha! The pattern that emerged above still applies!

The Boiling Point Temperature of a liquid (in this case water) increases as the Pressure above the liquid level in the container increases!

And once again, the important addendum ...

The above conclusion pertains to ALL liquids, not just water!

 

WHAT IS OBSERVED IN NATURE
IS LIKEWISE OBSERVED IN PROCESS INDUSTRY

The Pressures that are created in the process industries via mechanical means are much greater and much lower than the Atmospheric Pressure (P_atm) that is measured with a barometer at different altitudes on the Earth's surface.

Yet, the above relationship that was observed to naturally exist between the PV Pressure (represented as P_atm) and the PV Temperature (represented as the Boiling Point Temperature of water) universally applies to Pressures that are created by mechanical means:

 

The higher the PV Pressure in the Vessels and Towers and Tanks that are used in the process industries to contain liquids ... 

the greater the Boiler Point Temperature that will be required to convert the contained liquids into gases .. and vice versa!

 

 

REAL WORLD EXAMPLES
OF THE PV PRESSURE - PV TEMPERATURE RELATIONSHIP
APPLIED IN THE PROCESS INDUSTRIES

PV Pressure and Water Tube Package Boilers

PTOA Readers and Students learned all about boilers in PTOA Segments #24 and #25.

The Operating Pressure (PV Pressure) of a water tube boiler that is sized to generate 4 million pounds of steam per hour could easily be 2321 psi (aka 16.2 MEGAPascal = 158 Atm = 160 Bar).

On any scale of measurement ... that's a high pressure! A lot more pressure than P_atm at any altitude on Earth!

So who amongst the brilliant PTOA Readers and Students would be surprised to learn that the water in this boiler will not be able to boil and start turning into steam until the Operating Temperature (PV Temperature) is around 1022 °F (550 °C).

Wow!

That's a lot higher Boiling Point Temperature than the 212 °F (100 °C) observed at the sea level P_atm = 14.7 psia!

 

 

PV Pressure and Atmospheric Crude Towers

PTOA Readers and Students were first introduced to the (Atmospheric) Crude Tower Distillation process way back in PTOA Segment # 34 which focused on shell and tube heat exchanger trains.

Much more recently, PTOA Segment #154 explained how the hydrocarbons n-hexane and n-heptane can be separated from each other by taking advantage of their different Boiling Point Temperatures.

The binary example of separating n-hexane from n-heptane by Boiling Point Temperature can be extrapolated to separate the stew of hydrocarbons that are in the Crude Tower feedstock.

 

In the future PTOA Separating Systems Focus Study Area, PTOA Readers and Students will learn that each tray in the Atmospheric Distillation Tower has a distinct relationship between the liquid hydrocarbon stew that is on each tray and the combination of vapors/gases that linger above the tray.

 

 

 

When the Control Board Operator changes the Operating Pressure of the Tower, the composition of the gas and liquid phases will change over a 24 hour interval.

If the Operating Pressure is increased (PV Pressure ↑)  and a corresponding increase in Temperature is not supplied by a heat source ...

the liquid layer on each tray will not be able to maintain the level of excitement and agitation that was needed to convert the same amount of liquid into gas as it could do before the PV Pressure was changed.

Thus, a greater percentage of the hydrocarbons with higher Boiling Point Temperatures will remain on the tray in the liquid phase.

So ...over the 24 hour interval, the composition of the gas phase that lingers above each tray will changed into a gas with a lighter density and the liquid level on each tray will become a liquid with a heavier density.

 

Of course the opposite happens when the Operating Pressure of the Crude Tower is decreased.

In that case the liquid components with the lowest Boiling Point Temperatures on each tray will have an easier time getting excited and agitated enough to change into the gas phase.

In 24 hours the gas phase will have a heavier density and the liquid on each tray will become a liquid with a lighter density.

Hey!

Don't stress out if you did not follow what happens on each tray of a Crude Distillation Tower. The subject matter will be repeated in the future PTOA Separating Systems Focus Study Area.

TAKE HOME MESSAGES: PTOA Readers and Students already know that a gas contained in a rigid-walled container exhibits a one-to-one linear relationship between the PV Pressure and the PV Temperature:

If the PV Temperature increases, so does the PV Pressure of the gas ... and vice versa.

When a rigid container has a liquid level, the PV Pressure of the gas that hovers over the liquid level will impact the Boiling Point Temperature of the liquid:

The higher the PV Pressure above the liquid level, the higher the Boiling Point Temperature that will be needed to turn the liquid into a vapor/gas ... and vice versa. 

A Boiling Point Temperature is the temperature of a liquid that signifies the liquid has sufficient thermal energy to perform these two functions:

• Break the liquid-liquid bonds between the particles of liquid.
• Generate enough pressure so that the newly formed vapor/gas particles can push into and mix in with the gas that lingers above the liquid level.

 

©2017 PTOA Segment 0157
PTOA Process Variable Pressure Focus Study Area
PTOA PV Pressure Interrelationship with PV Temperature

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