It's the flow of energy from where there is a higher concentration of energy (steam boiler), to where there is a lesser concentration (cooling tower) that generates the electricity. The greater the difference in concentration (temperatures) the greater the flow that can be harnessed.
In this thought experiment, we have an imaginary machine that can generate electricity on the very small temperature gradient (difference) between the inside of the room and the outdoors. The air conditioner would have the same effect of a hole in a bucket of water, it would divert energy from flowing through the generator to the outside. Assuming there is no further filling of the heat reservoir, the airconditioner would pump out the heat and shorten the time that the system would operate.
No, here is how this problem is solved. There are two possibilities. If we are talking how an air conditioner works, it pulls air from
outside to the room. in this case, the heat from the air would generate electricity, which the air conditioner would use to pull air from outside, then cool it, then throw it inside the room where it would displace the natural temperatured air that was there - no longer hot because it's heat was removed to produce electricity. Conversely, if you assume that the air involved is only the air in the room, then the problem is more tricky but the solution is the same. The air cools down from the heat being converted into electricity, and this energy can be used to either heat the air again or to cool it down. The conservation of energy is not violated here because the process of removing the heat from the air to convert it into electricity also has a cooling effect. Once the energy is turned into eletricity, it makes no difference where it came from but what it can do. Therefore, the second law of thermodynamics is not violated here. The problem is deeply flawed in that it ignores how air conditioners work. Since it removes air from outside, the air would be cooled by the energy generated by the electricity from the heat of the air inside the room, and then it would displace that air. As stated, the problem is trickier but also easily solved. It is a simple logical problem.
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