Two Carnot cycles are placed between two reservoirs as shown in the figure. The heat flows in and out of the intermediate reservoir are equal so there is no accumulation of heat in that reservoir. Is the total output of the two cycles (w₁+w₂) independent of the temperature of the center reservoir, or does it depend on its temperature? This problem involves no calculation or derivation, but does require a justification for your decision. W₁ W₂ 1000 K TR=? 300 K

a) A suction pump. Consider a pipe that is inserted vertically into water. By suction, the pipe is evacuated of air. How high will the water rise? b) A water turbine is designed to extract kinetic energy from the hor- izontal flow of water and convert it into rotation of the turbine. You may assume that the height of the fluid does not change as it flows through the turbine, and that the fluid is incompressible. If the velocity is lowered from 100 m/s to 70 m/s as the fluid flows through the turbine, what is the change in pressure? c) Is the pressure higher upstream or downstream? d) The fluid in (b) is replaced by air to make a wind turbine. What is the change in pressure now for the identical change in velocity to (b)?

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2.  Which of the following is/are true of angular momentum?a)  torque is time derivative of angular momentumb)  angular momentum is conserved in a system that has no losses (like friction)c)  angular momentum is a vector quantityd)  a-c are all correct