The nonequilibrium grand ensemble method previously reported is rigorously implemented for a nonequilibrium dilute gas mixture sheared in plane Couette how geometry and analytic results are presented for the nonequilibrium thermodynamic quantities of the sheared gas. The calortropy is shown to contain all the constitutive information of the system. The notions of temperature and pressure for the nonequilibrium gas are examined on the basis of the calortropy calculated from the nonequilibrium grand partition function. The shear rate dependence of the nonlinear shear and first normal stress coefficients is calculated numerically and also by means of an iterative method. The first iterative solutions are found to give a qualitatively correct behavior for all Peclet numbers.