Work obtainable from two finite reservoirs

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Homework Help Overview

The problem involves a Carnot engine operating between two finite size reservoirs, specifically a hot reservoir at 100°C and a cold reservoir at 0°C. The objective is to determine the maximum work obtainable from these two reservoirs.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to relate the work done by the engine to the second law of thermodynamics and is seeking guidance on how to express the heat removed from the hot reservoir. Some participants suggest considering infinitesimal heat transfers and the relationship between the heat exchanged and the temperatures of the reservoirs.

Discussion Status

The discussion is ongoing, with participants providing insights into the thermodynamic principles involved. There is a recognition of the need to visualize the Carnot cycle through a PV graph, which may help clarify the problem further.

Contextual Notes

The original poster mentions a lack of recent experience with thermodynamics, indicating a potential gap in foundational knowledge that may affect their understanding of the problem.

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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