Since the tank is insulated, the first law becomes
210UWUUW=Δ+=−+
We need the internal energy at the final state, where and It is not clear from the problem statement whether the final state is in the two-phase region or the superheated vapor region. To answer this question, consult Table A-10 for saturated steam. Note that the specific volume of saturated vapor at 1903210.2045m/kgvv==o2190C.T=oC is 0.15654 m3/kg. Since v2 is greater than this, the final state must be superheated vapor, as shown in the figure above. To find the internal energy at the final state, we need to double interpolate in Table A-12. The table below reproduces selected values from Table A-12 at 0.8 and 1.0 MPa. Interpolated values are highlighted in bold.
0.8 MPa
1.0 MPa
T oC
v m3/kg
u kJ/kg
T oC
v m3/kg
u kJ/kg
170
0.2402
2577
180
0.194
2584
190
0.2539
2613
190
0.2000
2603
200
0.2608
2631
200
0.2060
2622
A second interpolation between v and u gives 220.25390.2000261326030.20002603vu−−=−− 220.25390.200026132603kJ26030.20450.20002603kguu−−=→=−−
Substituting values in the first law,
()21Wmuu=−()()kJ1.3 kg26032298kg=−397 kJ=