4.100
a) Since the tank contains saturated vapor at the final state, T = Tsat @ 800 kPa = 31.11 °C.
b) The initial mass in the tank = V/v1 = 0.2 m3/0.03182 m3/kg = 6.29 kg. The final mass = V/v2 = 0.2 m3/0/0255 m3/kg = 7.84 kg. The mass that enters is just the difference between these two = 1.55 kg. c) The energy balance becomes: Q = -mihI + m2u2 - m1u1 = -(1.55 kg)(356.52 kJ/kg) + (7.84 kg)(243.78 kj/kg)-(6.29 kg)(163.05 kJ/kg) = 333 kJ.

4.104
a) Again the cylinder contains saturated vapor at the end so T = Tsat @ 300 kPa = 133.6 °C.
b) The combination of the energy balance and the mass balance gives: -W = -(m2 - m1)hi +m2u2 - m1u1. Since by definition, enthalpy = u + Pv, you can combine the work term with the u terms and make the energy balance: 0 = -(m2 - m1)hI + m2h2 - m1h1. (Remember that mI = m2 - m1). You have all the variables you need to solve for m2 and therefore mi. So m2 = (hi - h1)/(hi - h2)* m1 = (3167.7 - 2292.51)/(3167.7 - 2725.3)*(10 kg) = 19.78 kg. So mI = 19.78 - 10 kg = 9.78 kg.

4.109
First find the masses using the volume divided by specific volumes. So m1 = 0.2 m3/0/12547 m3/kg = 1.594 kg and m2 = 0.2 m3/0/17568 m3/kg = 1.138 kg. From the mass balance, me = m1 - m2 = 0.456 kg. The energy balance is Q = mehe + m2u2 - m1u1. Remember that he = (h1 + h2)/2. So Q = (0.456 kg)(3245.55 kJ/kg) + (1.138 kg)(3116.2 kJ/kg) - (1.594 kg)(2772.6 kJ/kg) = 606.7 kJ.

4.111
a) The energy balance is 0 = mehe + m2u2 - m1u1. Since m2 = ½ m1 and me = ½ m1, we can write: 0 = ½ m1he + ½ m1u2 - m1u1. Divide through by m1 and multiply by 2: 0 = he + u2 - 2 u1. Then put in the ideal gas expression for h and u: 0 = CpTe + CvT2 - 2 CvT1. Divide through by Cv: 0 = kTe + T2 - 2 T1. Finally, Te = (T1 + T2)/2 and 0 = ½ k(T1 + T2) + T2 - T1. The k for helium is 1.667. Solve for T2 using absolute T's gives T2 = 225 K. b) Use the ideal gas law to solve for P. P1V/P2V = m1RT1/m2RT2 . So P2 = P1*(m2T2)/(m1T1) = ½ (25/353)2000 kPa = 687 kPa. See you never even had to solve for mass!
4.130
This is not an unsteady flow process. It's a simple mCDT problem. So: a) First find the mass flow rate of the turkeys = 200 turkeys/hr)(7.5 kg/turkey) = 1500 kg/hr = 0.4167 kg/s. Then Q = mC(T2-T1) = (0.4167 kg/s)(3.28 kJ/kg°C)(14 - 4) = 13.7 kW.
b) The chiller gains heat from the surroundings at a rate of 350 kJ/hr = 0.10 kW. This is added to the turkey so Q = 13.8 kW. This is the total rate of heat gain by the water. Since the temperature of the water cannot exceed 2.5 °C, m = Q/(CDT = 13.8 kW/(4.18 kJ/kg-°C)(2.5 °C) = 1.32 kg/s.