Liquid water at 100 kPa and 10oC is heated by mixing it with an unknown amount of

Question:

Liquid water at 100 kPa and 10oC is heated by mixing it with an unknown amount of steam at 100 kPa and 200oC. Liquid water enters the chamber at 1 kg/s and the chamber loses heat at a rate of 500 kJ/min with the ambient conditions at 25oC. If the mixture leaves at 100 kPa and 50oC, determine.
(a) The mass flow rate of steam.
(b) The rate of entropy generation in the system and its immediate surroundings.