Air at a temperature of 150C passes through a heat exchanger at a velocity of 30 m/s where its temperature is raised to 8000C. It then enters a turbine with the same velocity of 30 m/s and expands until the temperature falls to 6500C. On leaving the turbine, the air is taken at a velocity of 60 m/s to a nozzle where it expands until the temperature falls to 5000C. If the air flow rate is 2 kg/s, calculate the following.

(i) Rate of heat transfer to the air in the heat exchanger,

(ii) Power output from the turbine assuming no heat loss, and

(iii) Velocity at exit from the nozzle, assuming no heat loss.

Take the enthalpy of air as h =cpt, where cp is the specific heat equal to 1.005kJ/kg K and t is the temperature.

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg. a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?