KELVIN scale-Can't make sense of the last step of this solution

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Homework Help Overview

The discussion revolves around the transition between logarithmic expressions related to temperature differences on the Kelvin scale, specifically addressing the relationship between two temperatures denoted as T_c and T_H.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the mathematical steps involved in manipulating logarithmic expressions and question the reasoning behind dropping subscripts in the context of temperature measurements.

Discussion Status

There is an ongoing exploration of the mathematical relationships and assumptions regarding temperature measurements. Some participants are seeking clarification on the implications of treating one temperature as fixed, while others are attempting to unpack the algebraic steps taken in the solution.

Contextual Notes

Participants are discussing the implications of using different temperature measurements and the assumptions that come with treating one of the temperatures as a constant in the context of the problem.

Saladsamurai
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I do not understand how they went from [itex]\ln T_c-\lnT_H=\theta_c-\theta_H[/itex]
to
[itex]\theta=\ln T+C[/itex]

Why did the subscripts drop out? What just happened?
 
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exp means e^thethac if that is thetha

so you get e^(thethac-thethah) is Tc/Th.

If you ln both sides, you'll get ln(Tc/Th) = lnTc-lnTh and on the other side lne^(thethac-thethah) = (thethac-thethah)lne. lne is one.

Thus

lnTc-lnTh = thethac-thethah
 
"C" and "H" just represent different measurements of the temperature. Since you take TH to be a fixed temperature, that just leaves one temperature- you don't need the "C" to distinguish it form "H".
 
I am sorry Halls, I don't quite follow. What do you mean I take TH to be fixed?
 

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