
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.
 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 ^{o}R.) Therefore our typical value
of 59 ^{o}F is __________^{o}R.
(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.)
 Now, let's algebraically
solve the equation of state, p = R r T, for R.
R = ___________.
 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. _____________________.
 As we go up in
altitude, the pressure, density, and temperature decrease. At an altitude
of 36,089 ft, p = 472.68 lb/ft^{2}, r = 7.06 x 10^{4}
slugft^{3}, and T = 390 ^{o}R.
How many miles high are we? _______________.
 What is the air
temperature in ^{o}F at this altitude? _______________.
That's cold! (That is why the walls of an airplane are cold.)
 Notice that the
units of pressure at the 36,089 ft data set are in lb/ft^{2}.
To be consistent with our first calculation of R, we must convert to
lb/in^{2}. Therefore 472.68 lb/ft^{2} = _______________
lb/in^{2}. Comparing this to the typical value of 14.7 lb/in^{2},
we notice that we have only about one fifth as much air! That would
make it difficult to breathe; therefore, airplanes are pressurized inside.
 Calculate R at
36,089 ft (using pressure from #6 above, and r and T in ^{o}R
from #4.
R = _______________.
Compare this to the R in #3. WOW! R is constant!
 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/in^{2} and T = 390^{o}R.
Solve the equation of state algebraically for r. r = ( ) / ( )( ). Then
substitute in R and the other parameters and compute r.
r = ______________slug/ft^{3}.
