Please help! 8 kg of steam is contained in a piston-cylinder assembly with a pad

Question

Please help!

8 kg of steam is contained in a piston-cylinder assembly with a paddle wheel, as shown in the figure. The paddle wheel draws a power of 6.5 kW, which is perfectly transmitted to the steam inside the piston-cylinder assembly. In a process that takes 38.4 seconds, the piston-cylinder undergoes an expansion from 100 bar to 1 bar. Moreover, in the process, 178.7 kJ of heat is given off (transferred from the steam to the surroundings). If the pressure-volume relationship for the steam is PV" = constant, what is the change in the internal energy of the steam? The initial volume is 0.009 m3. For this process, n=1.0. Give your answer in kJ. If the answer is negative, do not forget to add the negative sign. Your answer must be correct within +/- 1. Assumptions: The system is closed and there is no change in the kinetic or potential energy of the system. FOR EVERY ATTEMPT, THE VALUES CHANGE.

Explanation / Answer

total energy supplied to the system is=6.5*38.4=249.6KJ

178.7KJ is given off

net inflow=249.6-178.7=70.9KJ

work done by the cylinder piston=p1v1ln(p1/p2)=10^7*9*10^-3ln(100)=414.46KJ

change in internal energy=70.9-414.46=-343.56KJ

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