Derive the equations necessary to expand Illustration 6.4-1 to include the thermodynamic state variables internal energy, Gibbs energy, and Helmholtz energy.

Illustration 6.4-1

Making of a Thermodynamic Properties Chart As an introduction to the problem of constructing a chart or table of the thermodynamic properties of a real fluid, develop a thermodynamic properties chart for oxygen over the temperature range of −100^◦C to +150^◦C and a pressure range of 1 to 100 bar. In particular, calculate the compressibility factor, specific volume, molar enthalpy, and molar entropy as a function of temperature and pressure. Also, prepare a pressure-volume plot, a pressure-enthalpy plot (see Fig. 3.4-2), and a temperature-entropy plot (see Fig. 3.4-3) for oxygen. Data: For simplicity we will assume oxygen obeys the Peng-Robinson equation of state and has an ideal gas heat capacity given by 

Figure 3.4-3

Figure 3.4-2

Transcribed Image Text:

C₂ (₁ = 25.46 +1.519 x 10-2T - 0.7151 × 10-57² +1.311 × 10-⁹73 mol K We will choose the reference state of oxygen to be the ideal gas state at 25°C and 1 bar: HIG (T= 25°C, P = 1 bar) and SIG (T= 25°C, P = 1 bar) = 0 As will be explained shortly, the Peng-Robinson parameters for oxygen are R²T² C a(T) = 0.45724- -a (T) Pe RTC Pe b(T) = 0.07780- [a(T)]¹/2 = 1+ k1 + x²(₁- = - T Te