Heat Engine Efficiency: How Ice Water Affects Performance

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Mixing ice water with hot water can bring the two reservoirs closer to the same temperature, which impacts the mechanical and thermodynamic efficiency of a heat engine. The Carnot efficiency, defined by the temperature difference between the hot and cold reservoirs, will decrease if the temperatures are too similar. This reduction in temperature difference results in lower ideal efficiency, as the Carnot efficiency is maximized when the temperature difference is greatest. Understanding the expression for Carnot efficiency is crucial for analyzing these changes. Overall, the efficiency of a heat engine is significantly influenced by the temperature of its reservoirs.
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Consider mixing ice water with the hot water and vice versa so that the two reservoirs are closer to the same temperature. What will happen to the mechanical/thermodynamic efficiency and ideal Carnot efficiency of a heat engine?
 
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Is this a homework question? Are you familiar with the expression for the Carnot efficiency of an engine?
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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