Quick thermo problem[just an uncertainty]

[K29]

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 :)

 

[Doc Al]

Mathematically, what must be the units of any argument to an exponential function? (I assume you meant R₀e^B/T.)

 

[K29]

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.

 

[Doc Al]

Right!

 

[rwisz]

The calibration constants B and R_0 in the given equation have different units. B has units of Kelvin (K), while R_0 has units of Ohms (Ω). This can be seen by rearranging the equation to solve for each constant:

B = R(T) * T/ln(R(T)/R_0)
R_0 = R(T) * exp(B/T)

It is important to note that the units of the thermistor's resistance, R(T), will also depend on the units used for temperature (K or °C). This equation is commonly used in thermistor calibration to determine the resistance at a specific temperature.