AERO9660 Advanced Propulsion Assignment No2 2022. Q1 van der Waal’s equation may be expressed as: = 2 . At the critical point: 2 2 = 0 , and: = 0 . i) Use this fact to derive expressions for , in terms of , as well as and . ii) Then insert these expressions for a and b into van der Waal’s equation at the critical point to get , , and in terms of , , and . For hydrogen, the critical points are: = 33.3 , = 1.30 . iii) Therefore find in 3 2 2 and in 3 . iv) For hydrogen, plot pressure (in ) against molar specific volume (in 3/) over the range: 0 ≤ ≤ 2.5 × 106 0 ≤ ≤ 1.53/ for isotherms of 15, 18, 21, 24, 27, 30, = 33.3, 36 and 39. ( /35) Q2 The Redlich-Kwong equation of state may be expressed as: = ( + )(0.5) , where: = 0.42748 22.5 , and: = 0.08664 . i) Find in 3 2 0.5 and in 3 given that = 33.3 and = 1.3 . ii) Calculate the density of hydrogen if = 700 and = 400 using the Redlich- Kwong equation of state. This is basically the conditions you would find in a typical hydrogen tank on board an aircraft of a car. iii) If = 4.124/, use the ideal gas equation to find the specific volume of hydrogen if = 700 and = 400. iv) Predict the density of hydrogen if = 1.40 . = = = 1 . Now you see why we need these other equations of state. ( /35) Q3 The partition function that accounts for the vibrational component of energy storage in a molecule is: = 11 , where is the characteristic vibrational temperature of the molecule and is the absolute temperature. Given that the component of the molar specific internal energy due to the vibrational component of energy storage is: = 2 (ln) , show that: = ( 1) , where: = . Then as: = , show that: = 2( 1)2 . Marks will be deducted for a lack of working. ( /30)
