1. (a) Calculate a numerical value for the isothermal compressibility kT = -+ (), for air for summer in Albuquerque under the conditions of 0.83 atm and 311 K (100 °F), assuming ideal gas behavior. (b) The speed of sound is related to the isothermal compressibility via 1 Vsound p KT where the adiabatic exponenty = 7/5. Evaluate this expression to find the speed of sound in air (in meters per second, or in mph). It is helpful to note that the mass density p = (kg/mole) and molar density, i.e. the number of moles per cubic meter, which is the ratio n/V. You can use the ideal gas law PV = nRT to write the ratio n/V in terms of your known pressure P and known temperature T. The gas constant R = 8.314 J/(mole-Kelvin) or alternatively R = 0.08206 (liter-atm)/(mole- K). Standard temperature and pressure are 0 degrees C (273.15 K) and 1 atm (1.013×105 N/m²). A good estimate of M for air can be found by taking 20% of the molecular weight of oxygen and adding this to 80% of the molecular weight of nitrogen. M4 is the product of the molecular weight M %3D
1. (a) Calculate a numerical value for the isothermal compressibility kT = -+ (), for air for summer in Albuquerque under the conditions of 0.83 atm and 311 K (100 °F), assuming ideal gas behavior. (b) The speed of sound is related to the isothermal compressibility via 1 Vsound p KT where the adiabatic exponenty = 7/5. Evaluate this expression to find the speed of sound in air (in meters per second, or in mph). It is helpful to note that the mass density p = (kg/mole) and molar density, i.e. the number of moles per cubic meter, which is the ratio n/V. You can use the ideal gas law PV = nRT to write the ratio n/V in terms of your known pressure P and known temperature T. The gas constant R = 8.314 J/(mole-Kelvin) or alternatively R = 0.08206 (liter-atm)/(mole- K). Standard temperature and pressure are 0 degrees C (273.15 K) and 1 atm (1.013×105 N/m²). A good estimate of M for air can be found by taking 20% of the molecular weight of oxygen and adding this to 80% of the molecular weight of nitrogen. M4 is the product of the molecular weight M %3D
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Transcribed Image Text:1. (a) Calculate a numerical value for the isothermal compressibility kT =
-+ (), for air for summer in Albuquerque under the conditions of 0.83 atm
and 311 K (100 °F), assuming ideal gas behavior. (b) The speed of sound is
related to the isothermal compressibility via
1
Vsound
p KT
where the adiabatic exponenty = 7/5. Evaluate this expression to find the
speed of sound in air (in meters per second, or in mph). It is helpful to note
that the mass density p =
(kg/mole) and molar density, i.e. the number of moles per cubic meter, which is
the ratio n/V. You can use the ideal gas law PV = nRT to write the ratio n/V
in terms of your known pressure P and known temperature T. The gas constant
R = 8.314 J/(mole-Kelvin) or alternatively R = 0.08206 (liter-atm)/(mole-
K). Standard temperature and pressure are 0 degrees C (273.15 K) and 1 atm
(1.013×105 N/m²). A good estimate of M for air can be found by taking 20% of
the molecular weight of oxygen and adding this to 80% of the molecular weight
of nitrogen.
M4 is the product of the molecular weight M
%3D
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