A resistance thermometer reads `R=20.0Omega, 27.5 Omega,` and `50.0 Omega` at the ice point `(0^@C)`, the steam point `(100^@C)` and the zinc point `(420^@C)` respectively. Assuming that the resistance varies with temperature as `R_Theta=R_0(1+alphaTheta+betaTheta^2)` , find the values of `R_0`, `alpha` and `beta`. Here `Theta` represents the temperature on Celsius scale.

Explanation

`R at ice point (R_0) =20Omega`
`R` at steam point `(R_100)=27.5Omega`
`R at zinc point (R_420)=50 Omega`
`R_theta = R _0 (1 + alpha theta+beta theta^2)`
`rArr R_100 =R_0+R_0 alpha theta+ R_0 beta theta^2`
`rArr (R_100-R_0)/R_0 = alpha theta +beta theta^2`
`rArr 27.5-20/20=alpha theta+ beta theta^2`
`rArr 7.5/20= alpha100+beta 10000 ........(i)`
Again `R_420= R_0(1+alpha theta+beta theta^2)`
`rArr 50-R_0/20 = alpha theta+ beta theta^2`
`50-20/20 = 420alpha +176400 beta`
`rArr 3/2=420 alpha+176400 beta .............(ii)`
After solving (i) and (ii), we get
`alpha =3.8 xx 10^(-3)/^0C`,
`beta = -5.6 xx 10^(-7)/^0C`