Thermistor's temperature problem

[matt_crouch]

Homework Statement

A thermistor's temperature dependence is given by R=R₀e^b/t
where R is in ohms T is in Kelvins R₀ and B are constants to be found.

a) If R =7360 at the ice point and 153 at steam point find R₀ and B

Homework Equations

The Attempt at a Solution

I took logs so

LnR=R₀B/T
rearranged so
(LnR)T/B=R₀

then get simultaneous equations but the constant i am trying to find so for this example B are just going to cancel?

(Ln153)x373.15/B = (Ln7360)x273.15/B

Thanks in advance

 

[OmCheeto]

Homework Statement

A thermistor's temperature dependence is given by R=R₀e^b/t
where R is in ohms T is in Kelvins R₀ and B are constants to be found.

a) If R =7360 at the ice point and 153 at steam point find R₀ and B

Homework Equations

The Attempt at a Solution

I took logs so

LnR=R₀B/T

Shouldn't that be LnR=LnR₀ + B/T ?

 

[kerimek]

Your approach is correct. By taking the natural logarithm of both sides of the equation, you are able to eliminate the exponential term and create a linear relationship between LnR and 1/T. This allows you to use the two data points (ice point and steam point) to solve for the two unknown constants R0 and B. The fact that B cancels out in this particular problem is not a problem, it just means that the two data points happen to align perfectly with the equation and it is not necessary to solve for B. However, if you had more than two data points, you would need to use the value of B to find the best fit line and solve for R0.