Gas Cooling: Part 4

Reading the Fire

Before returning to discussion of the science underlying gas cooling as a fire control technique, I wanted to share a video of an industrial fire in Maidencreek Township, Pennsylvania that provides an excellent illustration of smoke and air track indicators. Watch the first minute (1:00) of the video and answer the following questions:

  • Consider how you would read the smoke and air track indicators (particularly the level of the neutral plane and velocity) if this was a single family dwelling. How is air track indicators are different in a large building (with multiple ventilation openings) such as was the case in this incident?
  • What stage of development (incipient, growth, fully developed, or decay) and burning regime (fuel or ventilation controlled) is this fire in?
  • Watch the remainder of the video and examine the effectiveness of the master stream application? Are the streams effective? Why or why not? What could be done to increase the effectiveness of application?

For additional information on reading the fire, see the following posts:

Gas Laws

Paraphrasing Albert Einstein, British science writer Simon Singh stated that, “Science has nothing to do with common sense. Common sense is a set of prejudices” (Capps, 2010, p. 115). One of the challenges faced by firefighters engaging with the science of their craft is the common sense understanding of the fire environment and firefighting practices. This post continues examination of gas cooling as a fire control technique, by peeling off a few more layers and digging deeper into the underlying science related to the behavior of gases.

Readers who have worked through Gas Cooling Part 1, Part 2, and Part 3 have a reasonable idea how a small volume of water can reduce the temperature of the upper layer in a compartment and also reduce the volume of the upper layer (raising the level of the lower boundary of the layer). In addition, readers are likely to also understand the limitations of the simple explanation provided in prior posts.

In Water and Other Extinguishing Agents (Särdqvist,2002), Dr. Stefan Särdqvist provides a fairly detailed explanation of volume changes during smoke cooling and examines how the percentage of water vaporizing in the upper layer influences these changes. Understanding Stefan’s explanation requires a good understanding of the ideal gas law and a willingness to work through the math.

Gas Laws

The introduction to the gas laws and overview of Charles’s Law was provided in Gas Cooling: Part 3. This content has been repeated in this post, to save you from going back to the previous post.

While gases have different characteristics and properties, the behavior of gases can be described in general terms using the ideal gas law. This physical law describes the relationship between absolute temperature, volume, and pressure of a given amount of an ideal gas.

Figure 1. Temperature, Volume, Pressure & Amount

The concept of an ideal gas is based on the following assumptions:

  • Gases consist of molecules in random motion
  • The volume of the molecules is negligible in comparison to the total volume occupied by the gas
  • Intermolecular forces (i.e., attractive forces between molecules) are negligible
  • Pressure is the result of gas molecules colliding with the walls of its container

The ideal gas law is actually a synthesis of several other physical laws that each describes a single characteristic of the behavior of gases in a closed system (enclosed in some type of container).

Charles’s Law: In the 1780s, French scientist Jacques Charles studied the effect of temperature on a sample of gas at a constant pressure. Charles found that as the gas was heated, the volume increased. As the gas was cooled, the volume decreased. This finding gave rise to Charles’s Law which states that at a constant pressure the volume of a given amount (mass or number of molecules) of an ideal gas increases or decreases in direct proportion with its absolute (thermodynamic) temperature. The symbol  is used to express a proportional relationship (much the same as = is used to express equality), so this relationship can be expressed as:

Where:

V=Volume

T=Temperature

When two values (such as volume and temperature in Charles’s Law) are proportional, one is a consistent multiple of the other. For example If one value was consistently eight times the other, the values would also be proportional. In the case of Charles’s Law when the absolute temperature of a gas doubles, the pressure doubles. Figure 2 illustrates the relationship between absolute temperature in Kelvins (K) and volume in cubic millimeters (mm3).

Figure 2. Charles’s Law

This relationship can also be stated using the following equation:

Where

V=Volume

T=Temperature

Subscript of 1 refers to initial conditions

Subscript of 2 refers to final conditions

Gay-Lussac’s Law: When Jacques Charles discovered the relationship between temperature and volume, he also discovered a similar relationship between temperature and pressure. However, Charles never published this discovery. Charles’s work on temperature and pressure was recreated by French chemist Joseph-Louis Gay-Lussac. Gay Lussac’s Law states that if the volume of an ideal gas is held constant, the pressure of a given amount (mass or number of molecules) of an ideal gas increases or decreases proportionally with its absolute temperature. As with Charles’s Law, Gay-Lussac’s law can be expressed mathematically as:

Where

V=Volume

P=Pressure

Figure 3. Gay-Lussac’s Law

Boyle’s Law: in the 1660s, Irish physicist Robert Boyle studied the relationship of pressure and volume of gases. Boyle discovered that as pressure on a gas was increased, its volume decreased. Boyle’s Law states that if the temperature of an ideal gas is held constant, the pressure and volume of a given amount (mass or number of molecules) of an ideal gas are inversely proportional, as pressure increases, the volume occupied by the gas decreases. Boyle’s Law can be expressed mathematically as:

Where:

V=Volume

P=Pressure

Figure 4. Boyle’s Law

General Gas Law: The General Gas Law simply integrates Charles’s, Gay-Lussac’s, and Boyle’s Laws to state that the volume of an ideal gas is proportional to the amount (number of molecules) and absolute temperature and inversely proportional to pressure. The General Gas Law can be expressed mathematically as:

Where:

V=Volume

n=Mole (mol)

T=Temperature

P=Pressure

The General Gas Law defines the amount of gas in terms of the number of molecules, measured in moles (which has nothing to do with the animal having the same name).

Mole: While related to Avogadro’s Law, the term mole as a unit of measure was conceived by German chemist Wilhelm Ostwald in 1893. Unlike liters or grams, a mole is not a unit of volume or mass, but a counting unit. A mole is defined as the quantity of anything that has the same number of particles found in 12 grams of carbon-12. As atoms and molecules are extremely small, a mole is a large number of molecules. Specifically a mole contains 602,510,000,000,000,000,000,000 (more commonly written 6.0251 x 1023 in scientific notation) molecules of a substance. The number of moles of a substance is denoted by the letter n. In SI units, a kilogram mole (Kmol) is often used instead of the mole. A Kmol is 1000 mol or 6.0251 x 1026 molecules of a substance.

It may seem that using the mole to measure an amount of a substance makes this more complicated. After all, why not use a measure of volume such as liters or cubic meters or mass such as grams or kilograms? Chemical formula (such as H2O for water) describes the makeup of a chemical compound in terms of the numbers of atoms of each element comprising a single molecule of the substance.

While not a unit of mass, moles can be related to mass (just as you can determine the mass of a dozen eggs of a given size, by multiplying the mass of one of the eggs by 12).

Molar Mass: The molar mass of a compound is the mass of 1.0 moles of the substance in grams. Molar mass is determined by the sum of the standard atomic weights of the atoms which form the compound multiplied by the molar mass constant (Mu) of 1 g/mol. Figure 5 illustrates how the molar mass of water is calculated.

Figure 5. Molar Mass of Water

Molar mass can also be calculated for mixtures of substances. When dealing with mixtures, the molar mass of each constituent is calculated and applied proportionately on the basis of the percentage of that substance in the mixture. For example air is comprised of 78% Nitrogen, 21% Oxygen, and 1% of other gases such as Argon (Ar) and Carbon Dioxide (CO2). Nitrogen (N2) and Oxygen (O2) molecules are each comprised of two atoms (and are referred to as diatomic molecules). This means that the molar mass of Nitrogen and Oxygen molecules is twice the atomic mass.

Figure 6. Molar Mass of Air

Hopefully how the concepts of the mole and molar mass can be applied will become clear after examining the expansion of water when turned to steam and application of the gas laws to integrate steam expansion and changes in volume of the upper layer during gas cooling under a variety of circumstances.

Avogadro’s Law: In 1811, Italian physicist and mathematician Amedeo Avogadro published a theory regarding the relationship of the number of molecules in a gas if temperature, pressure, and volume are held constant. Avogadro’s Law states that samples of ideal gasses, at the same absolute temperature, pressure and volume, contain the same number of molecules regardless of their chemical nature and physical properties. More specifically, at a temperature of 273 K (0oC) and absolute pressure of 101300 Pa, 22.41 L (0.001 m3) of an ideal gas contains 6.0251 x 1023 molecules (1.0 mol)

Ideal Gas Law: This gas law integrates Avogadro’s law with the Combined Gas Law. If the number of molecules in a specific volume of an ideal gas at a consistent temperature and pressure (273 K and 101300 Pa) is always the same, then the proportional relationship between pressure, volume, temperature, and amount can be defined as having a constant value (Universal Gas Constant).

Where:

P=Pressure (Pa)

V= Volume (m3)

T=Temperature (K)

n=Moles

Ru=Universal Gas Constant (8.3145 J/mol K)

Universal Gas Constant (Ru): This physical constant identifies the internal kinetic energy per mole of an ideal gas for each Kelvin of temperature (J/mol K). As it is universal this constant is the same for all gases that demonstrate the properties of an ideal gas.

If the pressure, volume, and temperature of an ideal gas can be observed and Avogadro’s Law is accepted as being true (making the amount of gas also known), the value of the Universal Gas Constant can be determined empirically (based on observation) by solving the ideal gas law equation for Ru.

Where:

V=Volume

Ru=Universal Gas Constant

n=Moles

T=Temperature

P=Pressure

Figure 7 illustrates each of the gas laws and how they are integrated into the Ideal Gas Law.

Figure 7. Gas Laws

Application-Steam Expansion

As stated in Gas Cooling: Part 3, the 5th Edition of the Essentials of Firefighting (IFSTA, 2008) states that the volume of water expands 1700 times when it is converted to steam at 100o C (212o F). However, this information is presented as a fact to be memorized and no explanation is provided as to why this is the case or that if temperature is increased further, that the volume of steam will continue to expand. In the previous post, I asked the reader to accept this assumption with assurance that an explanation would follow. Application of the ideal gas law to expansion of steam provides an excellent opportunity to exercise your understanding of the gas laws and other scientific concepts presented in this post.

What we know:

  • Molecular Mass of Water: 18 g/mol
  • Boiling Point of Water at Atmospheric Pressure: 100o C (373.15 K)
  • Density of Water at 20o C (293.15 K): 1000000 g/m3
  • Atmospheric Pressure: 101325 Pa
  • Ideal Gas Constant (Ru): 8.3145 J/mol K

What we need to find out:

  1. What is the volume of 1 mole of steam
  2. What is the density (mass per unit volume) of steam at 100o C
  3. What is the ratio between the density of water and the density of steam at 100o C

The volume of 1 mole of pure steam can be calculated by solving the ideal gas equation for V.

As 1 mole of water (in the liquid or gaseous phase) contains the same number of molecules, it’s molar mass will be the same. 1 mole of water has a mass of 18 grams. Density is calculated by dividing mass by volume, so the density of steam at 100o C can be calculated as follows:

Dividing the density of water by the density of steam at 100o C determines the expansion ratio when a specific mass of water is vaporized into steam at this temperature.

This means that if a specific mass of water is vaporized into steam at 100o C, its volume will expand 1700 times. So the 5th Edition of the Essentials of Firefighting (IFSTA, 2008) is correct, but now you know why. However, what would happen if the steam continued to absorb energy from the upper layer and its temperature increased from 100o C to 300o C, the mass of the steam would remain the same, but what would happen to the volume? You can use the Ideal Gas Law to solve this question as well.

The Next Step

Just as the Ideal Gas Law can be used to determine the expiation ratio of steam, it can also be used to calculate contraction of the upper layer as it is cooled. The next post will examine how Dr. Stefan Särdqvist integrates these two calculations to determine changes in the volume of the upper layer under a variety of conditions.

New Book

Greg Gorbett and Jim Phar of Eastern Kentucky University (EKU) have written a textbook titled Fire Dynamics focused on meeting the Fire and Emergency Services Higher Education (FESHE) curriculum requirements for Fire Behavior and Combustion. I just received my copy and at first glance it appears to be an excellent work (as I would expect from these outstanding fire service educators). One useful feature of the text is a basic review of math, chemistry, and physics as it relates to the content of the course. I will be dong a more detailed review of the book in a subsequent post, but wanted to give readers of the CFBT-US Blog a heads up that it had been released.

Ed Hartin, MS, EFO, MIFireE, CFO

References

International Fire Service Training Association (IFSTA). (2008). Essentials of firefighting (5th ed). Stillwater, OK: Fire Protection Publications.

Särdqvist, S. (2002) Water and other extinguishing agents. Karlstad, Sweden: Räddnings Verket

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One Response to “Gas Cooling: Part 4”

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