A rigid
tank contains 90 L of xenon
gas at 385^{o}C and 2.3
MPa. The xenon gas has
a total enthalpy of 1350 kJ. Assuming the xenon behaves as an ideal gas, determine its specific internal energy. 


Read : 
Given the temperature,
pressure and volume of xenon
in an ideal gas state,
we can calculate the mass of xenon in the system using the Ideal Gas
EOS. This
allows us to convert the enthalpy into specific enthalpy. We can use the definition of enthalpy or
specific enthalpy to relate U to H
and PV and then
eliminate PV using the Ideal Gas EOS again. The units may get tricky. 










Diagram: 


















Given: 
V = 
90 
L 



P = 
2.3 
MPa 

T = 
385 
^{o}C 



H = 
1350 
kJ 










Find: 
U = 
??? 
kJ/kg 
















Assumptions: 
1  Equilibrium
conditions exist inside the tank. 





2  Xenon is an ideal
gas at this T and P. 













Equations
/ Data / Solve: 


















Since xenon behaves as an ideal gas, the definition of
specific enthalpy can
be modified as follows: 






















Eqn 1 

Eqn 2 

Eqn 3 











But : 

Eqn 4 





Eqn 5 











For ideal gases : 

Eqn 6 


Eqn 7 











Molecular weight of xenon : 
( NIST WebBook ) 
MW 
131.29 
g / mol 












Universal
Gas Constant values : 


R 
0.08205 
atm L/gmol K 






R 
8.314 
J/mol K or
Pa m^{3}/mol K 











Note: To convert ^{o}C to K, add 273.15 to ^{o}C. 

T 
658.15 
K 

















m 
4.9667 
kg 







RT / MW 
41.7 
kJ/kg 







H 
271.8 
kJ/kg 

















U 
230.1 
kJ/kg 

Verify: 



















Answers : 
U 
230 
kJ/kg 

(Rounded to 3 significant
digits.) 











