4-126 A mass of 5 kg of saturated liquid-vapor mixture of water is contained in

Question

4-126
A mass of 5 kg of saturated liquid-vapor mixture of water is contained in a piston-cylinder device at 125kPa. Initially, 2kg of water is in the liquid phase and the rest is in the vapor phase. Heat is now transferred to the water, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 300kPa. Heat transfer continue until the total volume increased by 20%. Determine a) The initial and final temperature, b) the mass of the liquid water when the piston first starts moving, and c) work done during the process. Also, show the process on a P-v diagram

Explanation / Answer

I will be using the software Engineering Equation Solver (EES). It contains all of the steam tables built-in to the software. I am using these every time I refer to a function such as: T[1] = Temperature(Steam, P=P[1], x=x[1]) If you are doing this the old fashioned way, it will involve a maze of paper tables to solve every problem indicated by a steam table function. "---------Begin EES Code------------" "Data" "State 1 is the initial condition State 2 is the condition once the piston begins to move State 3 is the final condition" m = 5 [kg] m1liq = 2[kg] P[1] = 125 [kPa] P[2] = 300 [kPa] r_v = 1.2 "the volume ratio of the expansion" "Strategy" "Deduce the initial quality" x[1] = (m - m1liq)/m "Look up all trivial properties to find of the initial steam" vspec[1] = volume(Steam, P=P[1], x=x[1]) "Caution, volume funciton in EES means specific volume" T[1] = Temperature(Steam, P=P[1], x=x[1]) u[1] = IntEnergy(Steam, P=P[1], x=x[1]) "Constant volume constraint between states 1 and 2" vspec[1] = vspec[2] "Look up all properties to find of the steam at state 2" T[2] = Temperature(Steam, P=P[2], v=vspec[2]) u[2] = IntEnergy(Steam, P=P[2], v=vspec[2]) x[2] = quality(Steam, P=P[2], v=vspec[2]) "Meaning of volume ratio of the expansion, and constraint of a constant pressure expansion" vspec[3] = r_v*vspec[2] P[2] = P[3] "Look up all properties to find of the steam at state 2" T[3] = Temperature(Steam, P=P[3], v=vspec[3]) u[3] = IntEnergy(Steam, P=P[3], v=vspec[3]) x[3] = quality(Steam, P=P[3], v=vspec[3]) "Find the bulk volume at all states" duplicate i=1,3 V[i] = vspec[i]*m end "Now to answer objectives" "A: the initial and final temperatures, just look them up in the table T[1] = 106 [C] T[3] = 374.3 [C] " "B: The mass of liquid water when the piston first starts moving Observe that x[2] = 100. This is an error code for superheated vapor, thus quality is a meaningless number. Superheated vapor means the mass of the liquid water is zero. " "C: The work done during this process Work is only done during the constant pressure portion of the process. It can be easily found by the isobaric work formula." W_out = P[2]*(V[3] - V[2]) "Result: W_out=247.9 [kJ]" "D: The total heat added" Q_in = m*(u[3] - u[2]) "Q_in=832 [kJ]" "---------End EES Code------------" Just for the record, here is the complete table: State 1: P[1] = 125 [kPa] x[1] = 0.6 T[1] = 106 [C] u[1] = 1685 [kJ/kg] vspec[1] =0.8262 [m^3/kg] V[1] = 4.131 [m^3] State 2: P[2] = 300 [kPa] x[2] = 100 T[2] = 268.9 [C] u[2] = 2758[kJ/kg] vspec[2] =0.8262 [m^3/kg] V[2] = 4.131 [m^3] State 3: P[3] = 300 [kPa] x[3] = 100 T[3] = 374.3 [C] u[3] = 2924[kJ/kg] vspec[3] =0.9914 [m^3/kg] V[3] = 4.957 [m^3]

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