In a two-fluid heat exchanger of a methane cooling system, 4 kg/s of methane at T₁ = 350 K, P₁ = 0.5 MPa enters the tubes, emerging at T₂ = 225 K with negligible loss in pressure (P₁ = P₂). Refrigerant R134a flows on the outside of the tubes, entering as a liquid–vapor mixture having quality x₃ = 0.4 at T₃ = 200 K and emerging as a saturated vapor at the same pressure (P₄ = P₃). Assuming steady-state, neglecting the kinetic and potential energies of the flow streams, and assuming that the heat exchanger is adiabatic (no heat transfer to the environment, but of course much heat transfer taking place internally), determine the required mass flow rate ṀR134a of the refrigerant (kg/s).