1. (Steam lift) A simple example of a heat engine is a lift. Consider a sealed piston, lled with water vapor (\"gas\") and pushing up a platform, to move a load. The cross-section area of the piston is 0.10m2 and it Operates between heights 3m and 5m. Here you will break down its energy usage. Neglect the mass of the piston but do not neglect ambient pressure from the atmosphere. To keep numbers simple, use pambient = IOOkPa and g = 10m/s2. (a) Find the state of the gas (10, V) at the following four instants: (b) (d) A. Piston is at lowest point (h = 3m), with 1000kg load. B. Piston is at highest point (h = 5m), with 1000kg load. C. Piston is at highest point (h = 5m), load removed. D. Piston is at lowest point (h = 3m), load removed. Draw the rectangular cycle (ABCDA) on a pV diagram (with 19 vertical). Is the cycle clockwise or counter-clockwise? What is its area? *Optional: pressure is naturally constant during steps AB and CD since there is a constant force on the piston. Explain how constant-volume steps BC and DA could be realized in practice. How much mechanical work is done by the gas in each of the four steps? Compare the net work with the area in (b). How much net work is done on the load, and on the atmosphere? Some steps (DA and AB) require input of heat energy, for example from a ame, while other steps release heat. What is the net amount of heat absorbed after a full cycle? (Hint: your answer should not depend on details of the cycle, nor on the nature of the gas!)