AERO9660 Advanced Propulsion
Assignment No2 2022.
van der Waal’s equation may be expressed as: 𝑅𝑅�𝑇𝑇 𝑎𝑎
𝑃𝑃 = 𝑣𝑣̅ − 𝑏𝑏 − 𝑣𝑣̅2 . At the critical point: �𝜕𝜕2𝑃𝑃� = 0 ,
Copyright By PowCoder代写 加微信 powcoder
For hydrogen, the critical points are:
�𝜕𝜕𝑃𝑃� =0.
𝜕𝜕𝑣𝑣̅ 𝑇𝑇 �
Use this fact to derive expressions for 𝑎𝑎, 𝑏𝑏 in terms of 𝑣𝑣�𝑐𝑐, as well as 𝑅𝑅 and 𝑇𝑇.
p o i n t t o g e t 𝑣𝑣� , 𝑎𝑎 , a n d 𝑏𝑏 i n t e r m s o f 𝑅𝑅� , 𝑇𝑇 , a n d 𝑃𝑃 . 𝑐𝑐𝑐𝑐𝑐𝑐
Then insert these expressions for a and b into van der Waal’s equation at the critical
iii) Therefore find 𝑎𝑎 in �𝑃𝑃𝑎𝑎 �𝑚𝑚3�2� and 𝑏𝑏 in 𝑚𝑚3 . 𝑘𝑘𝑚𝑚𝑘𝑘𝑘𝑘2 𝑘𝑘𝑚𝑚𝑘𝑘𝑘𝑘
𝑇𝑇𝑐𝑐 = 33.3𝐾𝐾 , 𝑃𝑃𝑐𝑐 = 1.30𝑀𝑀𝑃𝑃𝑎𝑎 .
iv) For hydrogen, plot pressure (in 𝑃𝑃𝑎𝑎) against molar specific volume (in 𝑚𝑚3/𝑘𝑘𝑚𝑚𝑘𝑘𝑘𝑘) over
the range: 0 ≤ 𝑃𝑃 ≤ 2.5 × 106𝑃𝑃𝑎𝑎 0 ≤ 𝑣𝑣̅ ≤ 1.5𝑚𝑚3/𝑘𝑘𝑚𝑚𝑘𝑘𝑘𝑘
for isotherms of 15𝐾𝐾, 18𝐾𝐾, 21𝐾𝐾, 24𝐾𝐾, 27𝐾𝐾, 30𝐾𝐾, 𝑇𝑇𝑐𝑐 = 33.3𝐾𝐾, 36𝐾𝐾 and 39𝐾𝐾.
The Redlich-Kwong equation of state may be expressed as:
w h e r e :
Now you see why we need these other equations of state.
𝑃𝑃 = 𝑣𝑣̅ − 𝑏𝑏 − 𝑣𝑣̅(𝑣𝑣̅ + 𝑏𝑏)𝑇𝑇(0.5) ,
𝑎𝑎 = 0 . 4 2 7 4 8 𝑅𝑅� 2 𝑇𝑇 𝑐𝑐 2 . 5 , 𝑃𝑃𝑐𝑐
𝑏𝑏 = 0 . 0 8 6 6 4 𝑅𝑅� 𝑇𝑇 𝑐𝑐 . 2 𝑃𝑃𝑐𝑐
Find𝑎𝑎in𝑃𝑃𝑎𝑎� 𝑚𝑚3 � 𝐾𝐾0.5 and𝑏𝑏in 𝑚𝑚3 giventhat𝑇𝑇𝑐𝑐 =33.3𝐾𝐾and𝑃𝑃𝑐𝑐 =1.3𝑀𝑀𝑃𝑃𝑎𝑎. 𝑘𝑘𝑚𝑚𝑘𝑘𝑘𝑘 𝑘𝑘𝑚𝑚𝑘𝑘𝑘𝑘
Calculate the density of hydrogen if 𝑃𝑃 = 700𝑏𝑏𝑎𝑎𝑏𝑏 and 𝑇𝑇 = 400𝐾𝐾 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.
If 𝑅𝑅 = 4.124𝑘𝑘𝑘𝑘/𝑘𝑘𝑘𝑘𝐾𝐾, use the ideal gas equation to find the specific volume of hydrogen
if 𝑃𝑃 = 700𝑏𝑏𝑎𝑎𝑏𝑏 and 𝑇𝑇 = 400𝐾𝐾.
Predict the density of hydrogen if 𝑍𝑍 = 1.40 .
𝑃𝑃𝑣𝑣 = 𝑍𝑍 𝑅𝑅𝑇𝑇
𝑣𝑣 = 𝑍𝑍𝑅𝑅𝑇𝑇 = 1 . 𝑃𝑃𝜌𝜌
The partition function that accounts for the vibrational component of energy storage in a
molecule is:
�𝑐𝑐���=𝑅𝑅 𝑥𝑥2𝑒𝑒𝑥𝑥 . 𝑝𝑝𝑣𝑣 (𝑒𝑒𝑥𝑥 −1)2
show that:
𝑍𝑍𝑣𝑣= 1𝜃𝜃, 1 − 𝑒𝑒 − 𝑇𝑇𝑣𝑣
where 𝜃𝜃𝑣𝑣 is the characteristic vibrational temperature of the molecule and 𝑇𝑇 is the absolute temperature.
Given that the component of the molar specific internal energy due to the vibrational
�𝑢𝑢��=𝑅𝑅�𝑇𝑇2�𝜕𝜕(ln𝑍𝑍)� , 𝑣𝑣 � 𝜕𝜕𝑇𝑇 𝑥𝑥 𝑟𝑟 𝒱𝒱
𝑢𝑢���=𝑅𝑅𝑇𝑇(𝑒𝑒 −1), 𝑣𝑣 𝜃𝜃𝑥𝑥
𝑥𝑥 = 𝑇𝑇𝑣𝑣 .
component of energy storage is:
show that:
�𝑐𝑐��� �= 𝑑𝑑�𝑢𝑢���� , 𝚤𝚤𝚤𝚤𝚤𝚤
Marks will be deducted for a lack of working.
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com