6.85. The temperature dependence of the second virial coefficient B is shown for nitrogen on Fig. 3.10. Qualitatively, the shape of B(T) is the same for all gases; quantitatively, the temperature for which B = 0 corresponds to a reduced temperature of about T, = 2.7 for many gases. Use these observations to show by Eqs. (6.54) through (6.56) that the residual properties GR. Hand * are negative for most gases at modest pressures and normal temperatures. What can you say about the signs of VR and CK? Vapor Iconsty T Liquia Const 3 | Const # Solid pinbrigos Consta Liquid/Vapor Triple-point line Salid/Vapor $ Figure 6.3: TS diagram. Equation (3.38), the two-term virial equation, gives Z-I = BP/RT. Substitution in Eq. (6.49) reduces it to: GR BP (6.54) RT RT RT) B By Eq. (6.44). -T =-T RT 1 dB TdT --[*/AM).--06) ] - ) dB HR RT or PB R (6.55) Substitution of Eqs. (6.54) and (6.55) into Eq. (6.47) yields: SR R RIT (6.56)