For a multicomponent mixture containing any number of species, prove that M ¯ i = M + ( ∂ M ___ ∂ x i ) T, P − ∑ k x k ( ∂ M ___ ∂ x k ) T, P where the summation is over all species. Show that for a binary mixture this result reduces to Eqs. (10.15) and (10.16).

Two flowing streams of argon gas are adiabatically mixed to form a single flow/stream. one stream is 1.5 kg/s at 400 kpa and 200 c while the second stream is 2kg/s at 500 kpa and 100 ? . it is stated that the exit state of the mixed single flow of argon gas is 150 c and 300 kpa. assuming there is no work output or input during the mixing process, does this process violate either the first or the second law or both? explain and state all your assumptions.

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

Aplate clutch has a single pair of mating friction surfaces 250-mm od by 175-mm id. the mean value of the coefficient of friction is 0.30, and the actuating force is 4 kn. a) find the maximum pressure and the torque capacity using the uniform-wear model. b) find the maximum pressure and the torque capacity using the uniform-pressure model.