What Is the Maximum Efficiency of a Heat Engine Using Lake Water Temperatures?

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Homework Help Overview

The problem involves calculating the maximum possible efficiency of a heat engine that utilizes lake water at specific temperatures as a heat source and sink. The temperatures given are 18.5°C for the heat source and 4.3°C for the heat sink located 0.100 km below the surface.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to determine the heat capacity of water at the specified temperatures, noting a lack of data in their textbook. Some participants question the relevance of temperature differences and pressure effects on water properties. Others discuss the equations related to heat transfer and efficiency, expressing confusion over the calculations presented.

Discussion Status

Participants are exploring various aspects of the problem, including the correct application of formulas and the significance of temperature values. There is a recognition that the original poster's approach may not align with the requirements of the problem, and some guidance has been offered regarding the Carnot efficiency concept.

Contextual Notes

There is mention of potential constraints related to the specific heat capacity values available in textbooks and the implications of significant digits in calculations. Additionally, the discussion highlights the need to focus on efficiency rather than work output.

mikefitz
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Homework Statement



Calculate the maximum possible efficiency of a heat engine that uses surface lake water at 18.5°C as a source of heat and rejects waste heat to the water 0.100 km below the surface where the temperature is 4.3°C.

Homework Equations



e=1-Qc/Qh
Q=cm(deltaT)

The Attempt at a Solution



I order to calculate the max efficiency I need the heat capacity of water at 18.5°C and 4.3°C. My book only provides 15C and 0C - how am I to solve this problem?
 
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What is different about water at 0C?
Pressure might make some difference, but they don't seem to be asking that.

Here is some more info
http://en.wikipedia.org/wiki/Specific_heat_capacity
Are residual temperature effects important when you round your answer to significant digits?
 
from my book

Qc/Qh = W/Qh - 1

262.54999/294.15 = (W/294.15)-1

1.89=W/294.15

W=556.699 J

Why is this wrong?
 
mikefitz said:
from my book

Qc/Qh = W/Qh - 1

262.54999/294.15 = (W/294.15)-1

1.89=W/294.15

W=556.699 J

Why is this wrong?

Partly because you were not asked to calculate work. You were asked to calculate efficiency. Furthermore, you are not changing the temperature of an object by absorbing or emitting heat. Your Q = cmΔT equation is not what you need here. You are extracting heat form a "hot" reservior, using some of the energy to do work, and delivering the remaining heat to a "cold" reservoir. The maximum efficiency with which this can be done (most work done) is by the Carnot Cycle. That efficiency can be expressed in terms of the reservoir temperatures. You do not need anything else.
 
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