Question

The resistance R of a platinum wire at temperature t°C, measured on the gas
scale is given by
R. R. (1 + aT +bT)
Where a = 3.8 x 10-³°C!
b = -5.6 x 10^7C.
What temperature will the platinum thermometer indicate when the
temperature on the gas scale is 200°C?

Answer 1

$R=R_0(1+aT+bT^2);$

$a=3.8\sdot 10^{-3}(1/^oC);$

$b=-5.6\sdot10^{-7}(1/^oC^2);$

$\dfrac{R}{R_0}=1+3.8\sdot10^{-3}(1/^oC)\sdot 200^oC-5.6\sdot10^{-7}(1/^oC^2)\sdot(200^oC)^2=$

$=1.7376;$

The temperature dependence of the resistance for most metals is close to linear for a wide range of temperatures and is described by the formula:

$R=R_0(1+\alpha\Delta T)$ , $\alpha-$ is the temperature coefficient of electrical resistance

$\alpha=0.003927(1/^oC);$

$1+\alpha\Delta T=\dfrac{R}{R_0}\implies \Delta T=\dfrac{\dfrac{R}{R_0}-1}{\alpha};$

$\Delta T=\dfrac{1.7376-1}{0.003927}=187.8^oC;$

Answer: $\Delta T=187.8^oC.$