In order to produce power, a plant absorbs heat at a rate of 1 mw from a combustion chamber maintained at 900 k and utilizes a nearby 109 gallon lake as a freshwater lake as heat sink. (for parts b-f, assume that sink is maintained at 20'c) new epa regulations state that the temperature of the lake cannot change by more than 10' c over a 24 hr period. ignoring environmental factors, at what rate can the plant reject heat? should the plant be worried about the epa regulation? is it safe to treat the lake as a sink with constant temperature, why? what is the maximum theoretical efficiency of the plant? what is the corresponding maximum power output? what is the thermal efficiency of the plant, when 290 kw of power is being produced? an ambitious engineer claims that the new improvements that he is proposing will increase the power output from 290 kw to 400 kw. is this possible? why? what can be done to increase the maximum theoretical efficiency of the plant by 25%? explain and show mathematically.