- #1

CAF123

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## Homework Statement

The resistance of a wire is given by ##R = R_0 (1 + at + bt^2)##, where ##t## is the temperature in degrees celcius measured on the ideal gas scale and so ##R_0## is the resistance at the ice point. The constants ##a## and ##b## are 3.8 x 10

^{-3}K

^{-1}and -3.0 x 10

^{-6}K

^{-2}respectively. Calculate the temperature on the resistance scale at a temperature of 70

^{o}C on the ideal gas scale.

## Homework Equations

Relationship between thermometric variable ##X## and temperature ##T##

## The Attempt at a Solution

The given eqn for R is the relationship between the thermometric variable (R) and t. Consider a system where the thermometric variable ##X## varies linearly with the temperature ##T##. Then ##X = pT##, for some constant ##p## fixed upon determining the temperature at a particular point. It is given that at ##R_0##, T = 273.15K, (ice point) so then p = R

_{0}/273.15K, so ##R = \frac{R_0}{273.15K}{T}. ## When T = 70

^{o}C, on this scale, R= 1.26R

_{o}.

So the temperature on the resistance scale at a temperature of 70

^{o}C on the ideal scale is found by $$1.26R_0 = R_0 (1 + at + bt^2)$$, cancelling and solving gives two values of t, neither of which agree with the answer. Physically, I don't see any sense in there being two solutions so I was wondering if there is an error in my method, particularly in considering the linear scale.

Many thanks,