Need some help with my home work.

Which of the following controllers anticipates the future from the slope of errors over time? a)-proportional b)-on/off c)-integral d)-derivative.

An engine runs on the ideal diesel cycle. the cycle has a compression ratio of 20 and a cutoff ratio of 2. the highest temperature in the cycle is 1200 k. if the heat into the system is 300 kj/kg of working fluid and using variable specific heats determine the work produced per mass of working fluid

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.