Question 3.98E: Reconsider Prob. 3.97. Solve the problem using EES (or other......
Reconsider Prob. 3.97. Solve the problem using EES (or other) software. Again using the EES, compare the temperature of water for the three cases at constant specific volume over the pressure range of 0.1 MPa to 1 MPa in 0.1 MPa increments. Plot the percent error involved in the ideal-gas approximation against pressure, and discuss the results.
EES Problem 3.97 is reconsidered. The problem is to be solved using EES (or other) software. The temperature of water is to be compared for the three cases at constant specific volume over the pressure range of 0.1 MPa to 1 MPa in 0.1 MPa increments. The %error involved in the ideal gas approximation is to be plotted against pressure.
Analysis The problem is solved using EES, and the solution is given below.
Function vanderWaals(T,v,M,R_u,T_cr,P_cr) v_bar=v*M "Conversion from m^3/kg to m^3/kmol" "The constants for the van der Waals equation of state are given by equation 3-24" a=27*R_u^2*T_cr^2/(64*P_cr) b=R_u*T_cr/(8*P_cr) "The van der Waals equation of state gives the pressure as" vanderWaals:=R_u*T/(v_bar-b)-a/v_bar**2 End
| m=2.841[kg] Vol=1 [m^3] {P=6*convert(MPa,kPa)} T_cr=T_CRIT(Steam_iapws) P_cr=P_CRIT(Steam_iapws) v=Vol/m P_table=P; P_vdW=P;P_idealgas=P T_table=temperature(Steam_iapws,P=P_table,v=v) “EES data for steam as a real gas” {P_table=pressure(Steam_iapws, T=T_table,v=v)} {T_sat=temperature(Steam_iapws,P=P_table,v=v)} MM=MOLARMASS(water) R_u=8.314 [kJ/kmol-K] “Universal gas constant” R=R_u/MM “Particular gas constant” P_idealgas=R*T_idealgas/v “Ideal gas equation” “The value of P_vdW is found from van der Waals equation of state Function” P_vdW=vanderWaals(T_vdW,v,MM,R_u,T_cr,P_cr) Error_idealgas=Abs(T_table-T_idealgas)/T_table*Convert(, %) Error_vdW=Abs(T_table-T_vdW)/T_table*Convert(, %) |
| \mathrm{P} [kPa] | \mathrm{T}_\text{ideal gas} [K] | \mathrm{T} _\text{table} [K] | \mathrm{T} _\text{vdw} [K] | \mathrm{Error} _\text{ideal gas} [K] |
| 100 | 76.27 | 372.8 | 86.35 | 79.54 |
| 200 | 152.5 | 393.4 | 162.3 | 61.22 |
| 300 | 228.8 | 406.7 | 238.2 | 43.74 |
| 400 | 305.1 | 416.8 | 314.1 | 26.8 |
| 500 | 381.4 | 425 | 390 | 10.27 |
| 600 | 457.6 | 473 | 465.9 | 3.249 |
| 700 | 533.9 | 545.3 | 541.8 | 2.087 |
| 800 | 610.2 | 619.1 | 617.7 | 1.442 |
| 900 | 686.4 | 693.7 | 693.6 | 1.041 |
| 1000 | 762.7 | 768.6 | 769.5 | 0.7725 |