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A platinum resistance thermometer is con...

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

Text Solution

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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.
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