Tank A is insulated, has a volume of 600 liters, and contains steam at 1.4 MPa a
ID: 2995599 • Letter: T
Question
Tank A is insulated, has a volume of 600 liters, and contains steam at 1.4 MPa and 300 degrees Celsius. Tank B is not insulated, has a volume of 300 liters and contains steam at 200 kPa and 200 degrees Celsius. A valve connecting the two tanks is then opened and steam flows from tank A to B until the temperature in tank A reaches 250 degrees Celsius. The valve is then closed. During this process, heat is transferred from tank B to the surroundings at 25 degrees Celsius so that the temperature in tank B is maintained at 200 degrees Celsius. If it can be assumed that the steam remaining in tank A has undergone a reversible, adiabatic process, find:
a) the final pressure in each tank;
b) the final mass in tank B; and
c) the net entropy change in the system and surroundings for this process.
Explanation / Answer
From steam properties at 1.4 MPa and 300 deg C we get v = 0.182 m^3/kg, u = 2790 kJ/kg, h = 3040 kJ/kg, s = 6.96 kJ/kg-K
From steam properties at 200 kPa and 200 deg C we get v = 1.08 m^3/kg, u = 2650 kJ/kg, h = 2870 kJ/kg, s = 7.51 kJ/kg-K
Since steam in A undergoes reversible adabatic process, entropy s remains constant.
From steam properties at 250 deg C and s = 6.96 kJ/kg-K we get P = 940 kPa, v = 0.248 m^3/kg, u = 2710 kJ/kg, h = 2950 kJ/kg
Initial Mass in A = V/v = 0.6 / 0.182 = 3.297 kg
Initial mass in B = 0.3 / 1.08 = 0.278 kg
Final mass in A = 0.6 / 0.248 = 2.419 kg
Mass transfer = 3.297 - 2.419 = 0.878 kg
Final mass in B = 0.278 + 0.878 = 1.156 kg
Final specific volume in B = V/m = 0.3 / 1.156 = 0.26 m^3/kg
From steam properties at 200 deg C and v = 0.26 m^3/kg, we get P = 803 kPa, u = 2630 kJ/kg, h = 2840 kJ/kg, s = 6.81 kJ/kg-K
c)
For tank A+B,
Q - W = (1.156*2630 + 2.419*2710) - (3.297*2790 + 0.278*2650)
Q - 0 = -339.56 kJ
Entropy change of surroundings = -Q / T_surr
= 339.56 / (25 + 273)
= 1.139 kJ/K
Entropy change of system = (1.156*6.81 + 2.419*6.96) - (3.297*6.96 + 0.278*7.51)
= -0.3263 kJ/K
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