Example Problem with Complete Solution

3A-1 : Enthalpy and Internal Energy for Ideal Gases 2 pts
A rigid tank contains 90 L of xenon gas at 385oC 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.
Given: V = 90 L P = 2.3 MPa
T = 385 oC 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 m3/mol K
Note:  To convert oC to K, add 273.15 to oC. T 658.15 K
m 4.9667 kg
RT / MW 41.7 kJ/kg
H 271.8 kJ/kg
U 230.1 kJ/kg
Answers : U 230 kJ/kg (Rounded to 3 significant digits.)