Quick thermo problem[just an uncertainty]

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Homework Help Overview

The discussion revolves around the properties of a semi-conducting thermistor and the relationship between its resistance and temperature, specifically focusing on the calibration constants B and R_0 in the equation R(T)=R_0 exp[B/T].

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the units of the calibration constants and question the requirements for the argument of an exponential function to be unitless. There is an attempt to eliminate dimensional analysis as a method for solving the problem.

Discussion Status

The discussion has progressed with some participants confirming the understanding that the argument of the exponential must be unitless, leading to conclusions about the units of B and R_0. However, the conversation does not reach a definitive consensus on the interpretation of these units.

Contextual Notes

Participants note that this problem is part of an introductory chapter in a second thermodynamics course, indicating a learning context that may influence their reasoning and approaches.

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Homework Statement


A semi-conducting thermistor has a resistance that veries with temperature as follows:
[tex]R(T)=R_0 exp[\frac{B}{T}][/tex]
What are the SI units of the calibration constants [tex]B[/tex] and [tex]R_0[/tex]

This is just the intro chapter to my second thermodynamics course. Anyway, I'm not sure how to start off. I mean I've eliminated dimensional analysis as a way of going about things. I can see its almost an exponential decay formula. All I need is a clue or something :)
 
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Mathematically, what must be the units of any argument to an exponential function? (I assume you meant R0eB/T.)
 
Ok the units of the exponential function must be unitless. So B is temperature so that it cancels with T. And that leaves [tex]R_0[/tex] to be Resistance in ohms! Right? Thank u.
 
Right! :wink:
 

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