Question

A volume of 100 m3 of a non-ideal gas is contained at 150°C and 50 bar. The gas is

then compressed isothermally to a pressure of 300 bar in a well-designed compressor. What is the volume of the compressed gas, how much work is done to compress it, and how much heat must be removed to maintain the temperature at 150°C during compression? You may apply the principle of corresponding states. The critical properties of the non-ideal gas are Tc = 304 K and Pc = 7.4 MPa.

Answer 1

From principle of corresponding states, equation becomes (p_r + 3/nu_r^2) (3 nu_r - 1) = 8 T_r - (1) where p_r = p/p_c: nu_r = v/v_c and T_r = T/T_c since, RT_c/P_c V_c = 8/3 Rightarrow v_c = 3 RT_c/8 p_c given T_c = 304 k and p_c = 7.4 Mpa Therefore V_c = 3 times 8.314 times 304/8 times 7.4 times 10^6 [Because R = 8.314 J k^-1 mol^1] Therefore v_c = 1.28 times 10^-4 m^3 For p = 300 bar, p_r = 300 times 10^5/7.4 times 10^6 [Because 1 bar = 1 times 10^5 p] p_r = 4.05 For T = 105 degree c = 273 + 105 = 378 k T_r = 378/304 = 1.24 putting values of p_r and T_r in equation (1) (4.05 + 3/nu_r^2) (3 nu_r - 1) = 8 times 1.24 12.15 v_r + 9/nu_r - 4.05 - 3/nu_r^2 = 9.92 12.15 nu_r^3 + 9 nu_r - 3 = 13.97 nu_r^2 12.15 nu_r^3 - 13.97 nu_r^2 + 9 nu_r - 3 = 0