How to find Compressibility Factor Z

Brian Bernard
30 Aug 202009:29
EducationalLearning
32 Likes 10 Comments

TLDRIn this educational video, Dr. Bernard, an engineering professor, introduces three methods to solve ideal gas problems involving ammonia, focusing on calculating specific volume. The methods include the ideal gas law, the generalized compressibility chart, and steam tables. He emphasizes the importance of professional development alongside academic success for job interviews. The video demonstrates the process of solving the problem using each method, highlighting the accuracy of steam tables and the limitations of the ideal gas law as an approximation.

Takeaways
  • 😀 The video discusses three methods to solve ideal gas problems, specifically finding the specific volume of ammonia given its pressure and temperature.
  • 🔍 The first method uses the ideal gas law, a fundamental equation from introductory chemistry, which can be adapted to different units.
  • 📚 The second method involves using the generalized compressibility chart, which requires calculating reduced temperature and pressure to find the compressibility factor (z).
  • 🌡️ Unit conversions are crucial, especially converting Celsius to Kelvin for temperature and bar to Pascal for pressure, to ensure correct calculations.
  • 📉 The third method refers to using steam tables, which are reliable for determining properties of gases, even though ammonia is not steam.
  • 🧩 The ideal gas law is an approximation, and gases like helium, hydrogen, or oxygen can deviate from ideal behavior under certain conditions.
  • 📊 The compressibility chart provides a correction factor to the ideal gas law, accounting for deviations from ideal behavior.
  • 📖 Professional development opportunities, in addition to good grades, are emphasized as essential for landing and winning jobs in engineering.
  • 🔎 The video highlights the importance of meticulous attention to units when using the ideal gas law to avoid mistakes in calculations.
  • 📚 Steam tables are considered the most accurate source for solving gas problems, as they are based on meticulous experiments and provide the 'truth' in contrast to approximations.
  • 🤔 The video concludes by suggesting that if tables are available, they should be used for the most accurate results, followed by the ideal gas law for a quick approximation, and the compressibility chart for a more detailed analysis.
Q & A

  • What are the three methods discussed in the video for solving ideal gas problems involving ammonia?

    -The three methods discussed are: 1) Using the ideal gas law, 2) Using the generalized compressibility chart to find the compressibility factor z, and 3) Using the steam tables found in thermodynamics textbooks.

  • Why is it important to have high grades in engineering courses according to the video?

    -High grades in engineering courses help you land more job interviews, but to win the job, you need confidence and competence that comes from professional development opportunities outside of the classroom.

  • What is the significance of the ideal gas law in thermodynamics?

    -The ideal gas law is a fundamental equation in thermodynamics that describes the relationship between pressure, volume, temperature, and the amount of gas. It is used as a starting point for solving various gas-related problems.

  • Why is it necessary to convert Celsius to Kelvin and bar to pascal when using the ideal gas law?

    -Unit consistency is crucial when using the ideal gas law. Converting Celsius to Kelvin and bar to pascal ensures that all units are compatible with the standard units used in the law.

  • What is the role of the molar mass in the ideal gas law equation?

    -The molar mass is used to adjust the gas constant 'R' to the specific units of the problem. By dividing 'R-bar' by the molar mass, you get the correct 'R' value to use in the equation.

  • Why is meticulous attention to units important when solving problems with the ideal gas law?

    -Attention to units is critical to avoid mistakes in calculations. Incorrect unit handling can lead to wrong results, as the units must cancel out appropriately to yield the correct final units for the specific volume.

  • What is the generalized compressibility chart and how is it used?

    -The generalized compressibility chart is a tool used to find the compressibility factor 'z' for a substance, which indicates how closely the substance behaves like an ideal gas. It requires reduced temperature and pressure to find the 'z' value.

  • What are reduced temperature and pressure, and why are they needed in the compressibility chart?

    -Reduced temperature and pressure are dimensionless quantities obtained by dividing the actual temperature and pressure by the critical temperature and pressure of the substance. They are used to find the compressibility factor 'z' on the compressibility chart.

  • Why are the steam tables considered the most accurate method for solving ideal gas problems in the video?

    -Steam tables provide experimentally determined values that are considered more accurate than approximations made by the ideal gas law or the compressibility chart. They are based on meticulous experiments and are thus considered the 'truth' for engineers.

  • What is the conclusion of the video regarding the ideal gas law and the existence of an ideal gas?

    -The video concludes that there is no such thing as an ideal gas, as all gases deviate from ideal gas behavior under certain conditions. The ideal gas law is an approximation, and more complex gases like ammonia may only behave like ideal gases in very narrow ranges.

Outlines
00:00
🔍 Introduction to Solving Ammonia Gas Problems

This paragraph introduces the video's focus on solving ideal gas problems using ammonia as an example. The presenter outlines three methods to determine the specific volume of ammonia given its pressure and temperature. The methods include: 1) using the ideal gas law, 2) using the generalized compressibility chart to find the compressibility factor (z), and 3) consulting steam tables. The presenter emphasizes the importance of professional development alongside academic performance for engineering students. The ideal gas law is introduced with a focus on unit conversions, specifically converting Celsius to Kelvin and bar to Pascal. The molar mass of ammonia is noted as 17.03, and the importance of meticulous unit handling in thermodynamics is highlighted.

05:01
📚 Applying the Generalized Compressibility Chart

This paragraph delves into the second method of solving for ammonia's specific volume using the generalized compressibility chart. The chart is used to find the compressibility factor (z), which adjusts the ideal gas law to account for deviations from ideal gas behavior. The presenter explains the need to convert given temperature and pressure to reduced temperature and pressure, using critical temperature and pressure values for ammonia. The chart's complexity is noted, particularly in distinguishing between temperature and volume lines. The value of z is found to be approximately 0.93, and the presenter demonstrates how to use this value in the equation, emphasizing the importance of unit consistency. The paragraph concludes with a discussion on the reliability of steam tables, contrasting them with the ideal gas law and the compressibility chart, and suggesting that tables provide the most accurate results.

Mindmap
Keywords
💡Thermodynamics
Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In the video, thermodynamics is the overarching theme, as the script discusses methods to solve problems related to the behavior of gases, specifically ammonia, under various conditions of temperature and pressure.
💡Ideal Gas Law
The Ideal Gas Law is a fundamental principle in chemistry and physics that describes the behavior of an ideal gas in terms of its pressure, volume, temperature, and the number of moles of gas particles. The video script explains how to apply this law to calculate specific volume of ammonia, highlighting its importance in solving the given problem.
💡Specific Volume
Specific volume is a thermodynamic property that represents the volume occupied by a unit mass of a substance. In the context of the video, the goal is to find the specific volume of ammonia using different methods, which is a key step in solving the problem presented.
💡Generalized Compressibility Chart
The Generalized Compressibility Chart is a graphical tool used to estimate the compressibility factor (z) of a substance, which is a measure of how much the substance deviates from ideal gas behavior. The video script describes using this chart as one of the methods to find the specific volume of ammonia, emphasizing its role in providing a more accurate solution than the ideal gas law alone.
💡Compressibility Factor (z)
The compressibility factor (z) is a dimensionless quantity that indicates the deviation of a real gas from ideal gas behavior. In the script, z is used in conjunction with the Generalized Compressibility Chart to account for non-ideal behavior of ammonia, providing a more precise calculation of specific volume.
💡Critical Temperature and Pressure
Critical temperature and pressure are the temperature and pressure at which a substance can no longer be converted to a distinct gas phase. The script mentions these values for ammonia as necessary inputs for using the Generalized Compressibility Chart, underlining their importance in determining the compressibility factor.
💡Reduced Temperature and Pressure
Reduced temperature and pressure are dimensionless properties obtained by dividing the actual temperature and pressure of a substance by its critical temperature and pressure, respectively. In the video, these reduced properties are used to locate the compressibility factor on the Generalized Compressibility Chart.
💡Steam Tables
Steam tables, or more generally, thermodynamic property tables, provide a wealth of information about the properties of a substance at various temperatures and pressures. The video script refers to these tables as a reliable source for determining the specific volume of superheated ammonia, highlighting their accuracy based on experimental data.
💡Saturated and Superheated Gas
Saturated and superheated are terms used to describe the state of a gas. Saturated gas is at the point where it can condense into a liquid, while superheated gas is above the saturation temperature and will not condense. The script uses these concepts to determine which tables to consult for calculating the specific volume of ammonia.
💡Unit Conversion
Unit conversion is the process of changing the units of a physical quantity to another unit. In the script, unit conversions are necessary to ensure consistency and accuracy when applying the Ideal Gas Law and using the Generalized Compressibility Chart, such as converting Celsius to Kelvin for temperature and bar to Pascal for pressure.
💡Professional Development
Professional development refers to activities and experiences that contribute to one's professional growth and skills beyond formal education. The script mentions the importance of professional development in addition to academic grades for securing job interviews and employment, emphasizing its role in building confidence and competence in the workplace.
Highlights

The video teaches three methods to solve ideal gas problems with given pressure and temperature of ammonia to find specific volume.

The first method involves using the ideal gas law from introductory chemistry.

The second method uses the generalized compressibility chart to find the compressibility factor z.

The third method relies on steam tables in thermodynamics textbooks.

Professional development opportunities are crucial for job interviews and securing a job, beyond just academic grades.

Different versions of the ideal gas law are used based on the units available.

Unit conversions are necessary for temperature (Celsius to Kelvin) and pressure (bar to Pascal).

The molar mass of ammonia is 17.03, used to adjust the gas constant in the ideal gas law.

Attention to units is critical to avoid mistakes in ideal gas law calculations.

The compressibility factor z is a scaling factor showing how close a substance behaves to an ideal gas.

Reduced temperature and pressure are needed to use the generalized compressibility chart.

Critical temperature and pressure values for ammonia are 406 Kelvin and 112.8 bar.

The generalized compressibility chart provides a correction factor for deviations from ideal gas behavior.

Steam tables are used to find specific volume directly for superheated gases.

Saturated tables are used when only temperature or pressure is given, not both.

The steam table provides the most accurate answer as it is based on experimental data.

The ideal gas law is an approximation and not all gases behave ideally under all conditions.

The generalized compressibility chart offers a better approximation than the ideal gas law but requires more work.

There is no such thing as an ideal gas; all gases deviate from ideal behavior under certain conditions.

Transcripts

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ThermodynamicsIdeal Gas LawAmmoniaCompressibility ChartSteam TablesEngineeringChemistryUnit ConversionProfessional DevelopmentEducational Video