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Equation of State Answers

  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 518.69oR


  2. Now, let's algebraically solve the equation of state, p = R r T, for R.
    R = p/rT.

  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. R = 11.95 lb-ft2/slug-in2-oR.

  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? 6.84 miles high.

     
  5. What is the air temperature in oF at this altitude? -70 oF
    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 = 3.28 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 ~ 11.91. 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 = 1.72 x 10-4 slug/ft3

 


Related Pages:
Standards
Activity
Worksheet
Lesson Index
Aerodynamics Index

 

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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Thu, Jun 12 04:46:38 PM EDT 2014

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