Question

A piston-cylinder assembly contains 5kg of water that undergoes a series of processes to form a thermodynamic cycle. Process 1à2: Constant pressure cooling from p1=20bar and T1=360°C to saturated vapor Process 2à3: Constant volume cooling to p3=5 bar Process 3à4: Constant pressure heating Process 4à1: Polytropic process following Pv =constant back to the initial state Kinetic and potential energy effects are negligible. Calculate the net work for the cycle in kJ.

Answer 1

`W_(net) = - 1223 kJ`

Step-by-step explanation:

State 1:

`P_1 = 20 bar\\T_1 = 360^(0)C\\ h_1 = 3159.3 kJ/kg\\S_1 = 6.9917 kJ/kg`

State 2:

`P_2 = 20 bar\\x_2 = 1 \\ h_2 = 2799.5 kJ/kg\\u_2 = 2600.3 kJ/kg\\v_2 = 0.09963m^3/kg`

State 3:

`P_2 = 5 bar\\v_2 = v_3 \\v_3 = v_f + x_3 (v_g - v_f)\\0.09963 = (1.0926 * 10^(-3)) +x_3 (0.3749 - (1.0926 * 10^(-3)))\\x_3 = 0.263`

`u_(3) = u_f + x_3 ( u_g - u_f)\\u_(3) = 639.68 + 0.263 (2561.2 - 639.68)\\u_(3) = 1146.2 kJ/kg`

State 4:

`P_(4) = 5 bar\\T_4 = 360^0 C\\h_4 = 3188.4 kJ/kg\\S_4 = 7.660 kJ/kg-K\\Q_(12) = h_2 - h_1 = 2799.5-3159.3 = -359 kJ/kg\\Q_(23) = u_3 - h_2 =1146.2-2006.3 = -1454.1 kJ/kg\\Q_(34) = h_4 - h_3 = 3188.4-1196.04 = 1992.36 kJ/kg\\Q_(41) = T(S_1 - S_4) = (360 + 273) (6.9917 - 7.660) = -423.04 kJ/kg`

Calculate the network done for the cycle

`W_(net) = m( Q_(12) + Q_(23) + Q_(34) + Q_(41))\\W_(net) = 5( -359.8 - 1454.1 + 1992.36 - 423.04)\\W_(net) = -1223 kJ`