Newton's Law of Cooling - "k" constant

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The discussion revolves around Newton's Law of Cooling and the relationship of the cooling constant "k" with varying volumes of water in a beaker. The original poster, Ben, seeks to understand the expected trend of "k" as volume increases and requests mathematical explanations to support this. Participants suggest that "k" may be related to the area of heat flux, prompting further inquiry into how to determine "k" for different physical systems. The conversation emphasizes the need for empirical data and graphical representation of results to clarify the relationship. Understanding the behavior of "k" is essential for accurately applying Newton's Law of Cooling in practical scenarios.
Ben Evans
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Hi,

I have been exploring Newtons Law of Cooling. What relationship should i expect to see from the cooling constant "k". I have plotted the "k" values for each equation that i have developed (based off of different volumes of water in the same sized beaker). So, when the "k" vs volume graph is plotted, what trend should i see as the volume increases?? and why is this trend occurring. Any Mathematical working using Newtons formula showing to show this trend would be greatly appreciated.

Cheers,
Ben
 
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Ben Evans said:
Hi,

I have been exploring Newtons Law of Cooling. What relationship should i expect to see from the cooling constant "k". I have plotted the "k" values for each equation that i have developed (based off of different volumes of water in the same sized beaker). So, when the "k" vs volume graph is plotted, what trend should i see as the volume increases?? and why is this trend occurring. Any Mathematical working using Newtons formula showing to show this trend would be greatly appreciated.

Cheers,
Ben
Please show us a graph of your results so far.
 

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