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Equation of State Problems
If so instructed by your teacher, print out a worksheet page for these problems.

Open the slide called Air Properties Definitions (with text) and read the definitions.
Beginner's Guide to Aerodynamics is a "textbook" of information prepared at NASA Glenn Research Center to help you better understand how airplanes work. Click Beginner's Guide Index to access the list of slides. Open the slide called Air Properties Definitions (with text) and read the definitions. Using the information shown at Equation of State Problems and additional given information, complete the problems designed to demonstrate your ability to determine and use the gas constant from the Equation of State.

Flying through thin air!

The Equation of State for a gas, which is shown in the Air Properties Definitions slide, is p = R r T, where p is the pressure of the gas, R is a constant, r is the density of the gas, and T is the absolute temperature of the gas. 

  1. To convert a Fahrenheit temperature to an absolute temperature, add 459.69 degrees. (The absolute temperature scale in English units is known as the Rankine scale and is expressed as oR.) Therefore our typical value of 59 oF is __________oR.
    (Note: Zero degrees Rankine (or Kelvin in metric units) is defined as absolute zero which is the hypothetical temperature at which all molecular activity ceases.)
  2. Now, let's algebraically solve the equation of state, p = R r T, for R.
    R = ___________.


  3. We are ready to calculate R, the gas constant for air, for typical values of pressure, density, and temperature. Using the values with English units displayed in the Air Properties Definitions slide, substitute into the equation for R, remembering to use the temperature from #1 above.
    R = ( ) / ( )( ). Compute R. _____________________.


  4. As we go up in altitude, the pressure, density, and temperature decrease. At an altitude of 36,089 ft, p = 472.68 lb/ft2, r = 7.06 x 10-4 slug-ft3, and T = 390 oR.
    How many miles high are we? _______________.


  5. What is the air temperature in oF at this altitude? _______________.
    That's cold! (That is why the walls of an airplane are cold.)


  6. Notice that the units of pressure at the 36,089 ft data set are in lb/ft2. To be consistent with our first calculation of R, we must convert to lb/in2. Therefore 472.68 lb/ft2 = _______________ lb/in2. Comparing this to the typical value of 14.7 lb/in2, we notice that we have only about one fifth as much air! That would make it difficult to breathe; therefore, airplanes are pressurized inside.


  7. Calculate R at 36,089 ft (using pressure from #6 above, and r and T in oR from #4.

    R = _______________. Compare this to the R in #3. WOW! R is constant!


  8. Now that we have found (and checked ) R, let's use it to determine the density r at an altitude of 65,620 ft where p = 0.80 lb/in2 and T = 390oR.
    Solve the equation of state algebraically for r. r = ( ) / ( )( ). Then substitute in R and the other parameters and compute r.
    r = ______________slug/ft3.

Related Pages:
Lesson Index
Aerodynamics Index


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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Thu, May 13 02:38:25 PM EDT 2021

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