( 2 ) A cylinder equipped with a set of stops for the piston is initially filled

Question

( 2 ) A cylinder equipped with a set of stops for the piston is initially filled with 5 kg saturated liquid-vapor mixture of water at 125 kPa. Initially, 3 kg of the 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 300 kPa. Heat transfer continuous until the total volume increases by 20%. Determine
(a) the initial and final temperature,
(b) the work done during this process, and
(c) 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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