You received a promotion to production engineer at a foodprocessing factory.

A particularly critical process involves the mixing of ingredients with warm water in a large insulated vat. The vat's drain is kept open, so water must be continuously added to maintain the proper mix.

The water comes from a hot water source at 38.0°C at 3.10 kg/s and a cold water source at 15.0°C at 2.50 kg/s. The local environment is at 0.101 MPa and 20.0°C.

To keep control of this process, you need to know the temperature of the mixed water in the tub and the second law availability efficiency of the tub as a mixing-type heat exchanger.

Write and solve a thermodynamics problem that provides the answers to these questions.