Question

A plarinum resistance thermometer is condtructed which resds `,0^0` at ice point and `100^0` at steam point. Let t`p denote temoerature on this scale and let t denote the temperature on a metcury on a mercury themomenter scale. The resistance of the platinum coil vares with `t` as `R_1 = R_0 (1+alphat + betat^2)`. Derive an expression for the resistance as a function of `T_p`.

Answer 1

Let `R_(t_p)` denote the residtance of the coil at the platinum scale temperature `t_p`. Then
`t_p = (R_(T_p) - R_0)/(R_100 - R_0) xx 100`
or, `R_(t_p) = t_p/100 ( R_100 - R_0) + R_0`
= t_p/100 [R_0 {1+alpha xx 100 + beta xx (100)^2} - R_0] + R_0`
= t_p/100 [ alpha xx 100 + beta xx (100)^2] R_0 + R_0`
R_0 [ 1+ {1+{alpha xx 100 + beta xx (100)^2} t_p/100]`
`= R_0 [ 1+alphat_p + beta xx (100) t_p]`.
Only numerical values of `alpha and beta` are to be used.