It is required to design a two-stage spur gear unit with 20° full-depth involute teeth. The (20] input shaft rotates at 1440 pm and receives 10 kW power from an electric motor. The speed of the output shaft should be approximately 180 rpm. The gears are made up of plain carbon steel C45 and the service factor may be taken as 1.5. Find the dimension of the gears and recommend surface hardness in terms of BHN.