At a tee junction in the piping of a chemical plant, 5 kg/s of methane enters on one side at P₁ = 1 MPa, T₁ = 400 K, and 1 kg/s of methane enters on the other as a saturated liquid at P₂ = 1 MPa. The two streams are mixed and exit from the junction at P₃ = 1 MPa. Assuming steady-state, neglecting the kinetic and potential energies of the flow streams, and treating the mixer as adiabatic, determine the temperature of the discharge stream (T₃). This will require both an energy balance and a mass balance.