Heat Engines 1: 40%, 28.6% 2: step 1, step 2, c = WitW2+W, 3: 3791 cycles Q1 4: 86 minutes, 183400 J, decreases 5: 28.8% In a (TH - To) 6: 6= 22.8%, 26.8% to100 TH - To) + Ta In a1: In a heat engine we ultimately care about the efficiency of the entire cycle. That is, what percentage of the heat which flows into your system is converted to work. However, you could certainly ask that same question for an individual step in a cycle. Specifically, determine the efficiency of an isobaric process which takes a system from a volume V to a volume of where o > 1. You will not need to know the actual value of o. In the end, it will cancel out of all expressions. a: Do this calculation if the gas is monatomic. b: Do this calculation if the gas is diatomic. These results will certainly differ. This implies that when we build REAL engines, their efficiency depends upon what the "working substance" is inside the engine. 2a: An engine operates using the following cycle. Step one is isothermal and step three is adiabatic. In which step(s) does heat flow from the hot reservoir into your system? Explain. b: In which step(s) does heat flow from your system into the cold reservoir? Explain. c: Determine a general expression for the efficiency of the engine using labels like Q1 for the heat flow during step one, W1 for work done during step one, etc. 3 2 3: An ideal Carnot engine operates between 500 C and 100 C. Assume that there is a heat flow of 250 J per cycle from the hot reservoir. How many cycles are necessary for the engine to lift a 500 kg rock to a height of 100 m above its starting point? 4a: An ideal Carnot engine operates between thermal reserviors at 0 'C and 100 .C. The 0 'C reservoir is a mixture of 1.5 kg of ice and some water. The engine is running at 200 revolutions/minute or equivalently 200 cycles/minute and the heat flow from the hot reservoir is 40 J/cycle. How much time is required for the heat transferred to the cold reservoir to melt all the ice? Use Ly = 3.34 x 105 J/kg b: How much work did the engine do during that time? c: What happens to the efficiency of the engine after that time? Explain