As steam is slowly injected into a turbine, the angular acceleration of the rotor is observed to increase linearly with the time t. Knowing that the rotor starts from rest at t = 0 and that after 10 s the rotor has completed 20 revolutions, write the equations of motion for the rotor and determine (a) the angular velocity at t = 20 s, (b) the time required for the rotor to complete its first 40 revolutions.

Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kpa and 17°c. this system uses a regenerator as well as reheating and intercooling – the intercooler returns the air to the inlet temperature. the pressure ratio across each compressor is 4 ; 300 kj/kg of heat are added to the air in each combustion chamber; and the regenerator operates perfectly while increasing the temperature of the cold air by 20°c. determine the system’s thermal efficiency. assume isentropic operations for all compressor and the turbine stages and use constant specific heats at room temperature. (0.378)