Question 7.13: Problem: Calculate the pressure of nitrogen that has a speci...

Problem: Calculate the pressure of nitrogen that has a specific volume ν = 0.025 m³ / kg and a temperature of 252 K using (a) the ideal gas equation and (b) the van der Waals equation of state.

Find: Pressure of nitrogen P.

Known: Specific volume ν = 0.025 m³ / kg, temperature T = 252 K.

Governing Equations:

Ideal gas equation                    P\bar{ν}=R_uT

van der Waals equation                    \left\lgroup P+\frac{a}{\bar{\nu }^2}\right\rgroup (\bar{\nu}-b)=R_uT

Properties: For nitrogen, the critical temperature T_C = 126.2 K (Table 7.1), critical pressure P_C = 3.39 MPa (Table 7.1) and molar mass M = 28.013 kg / kmol (Appendix 1), van der Waals constants a = 137 kPa m^6\ / kmol^2 and b = 0.0386 m³ / kmol (Table 7.5).