Answer :
To determine the specific exergy of the system, we need to first determine the exergy of the system and then divide by the mass of hydrogen in the tank. The exergy of the system is given by:
E = U - U0 - T0(S - S0) + P0(V - V0)
where U is the internal energy, U0 is the internal energy at the dead state, T0 is the temperature at the dead state, S is the entropy, S0 is the entropy at the dead state, P0 is the pressure at the dead state, V is the volume, and V0 is the specific volume at the dead state.
We can find the internal energy of H2 using the ideal gas equation:
U = (3 lbm)(102.4 Btu/lbm-mol)/(2 lbm-mol)(8314 J/kmol-K)(343 K)
U = 42,548 J
The specific volume of H2 can also be determined using the ideal gas equation:
V = (8314 J/kmol-K)(343 K)/(1.2 MPa)(10^6 Pa/MPa)(2 lbm-mol/3 lbm)(0.453592 kg/lbm)
V = 0.0387 m^3/kg
Using steam tables, we can find the entropy of H2 at 70°C and 1.2 MPa:
S = 130.71 J/kg-K
The entropy at the dead state can be approximated as the entropy of an ideal gas at 101.325 kPa and 20°C:
S0 = (29.27 J/mol-K)(2 lbm-mol/3 lbm)(0.453592 kg/lbm)
S0 = 10.46 J/kg-K
The exergy of the system is then:
E = 42,548 J - (3 kg)(101.325 kPa)(0.0387 m^3/kg) - (293 K)(130.71 J/kg-K - 10.46 J/kg-K) + (101.325 kPa)(0.0387 m^3/kg - 0.0804 m^3/kg)
E = 33,383 J
Finally, the specific exergy is:
e = E/m
e = 33,383 J/3 lbm
e = 11,128 J/lbm
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