Work obtainable from two finite reservoirs

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SUMMARY

The discussion focuses on calculating the maximum work obtainable from a Carnot engine operating between two finite reservoirs: a hot reservoir (mass MH at 100°C) and a cold reservoir (mass ML at 0°C). Participants emphasize the importance of understanding the relationship between heat transfer and temperature ratios as dictated by the second law of thermodynamics. Key insights include expressing the heat removed from the hot reservoir in terms of the heat added to the cold reservoir and the current temperatures of both reservoirs. A graphical representation of the Carnot cycle is recommended for clarity.

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vandergale
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The problem is as follows:

A Carnot engine operates between two finite size reservoirs, one a body of water of mass MH at 100°C and the other a body of water of mass ML at 0°C. Find the maximum work obtainable from the two reservoirs.

The Attempt at a Solution



I haven't done thermodynamics in a while and am trying to relearn a lot of this stuff. I first tried expressing the work done by the engine in terms of the 2nd law. I know I can write the efficiency of the engine with the ratio of the two temperatures, but I'm not sure how to find the heat removed from the hot reservoir. If someone could point me in the right direction I would be grateful.
 
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Hello, vandergale. Welcome to PF!

Consider an infinitesimal step during the process. Corresponding to an amount of heat |dQH| removed from the warmer reservoir, there will be a certain amount of heat |dQC| added to the cooler reservoir. Can you express |dQC| in terms of |dQH| and the current temperatures TH and TC of the two reservoirs?
 
Start out by drawing a PV graph of what the reversible Carnot cycle with these reservoirs looks like. Label some schematic temperature points on this graph. You need to get the "lay of the land."
 
Sorry I haven't checked back, thanks you guys, its much clearer now.
 

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