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A resistance thermometer reads `R=20.0Omega, 27.5 Omega, and 50.0 Omega` at the 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=(1+alphaTheta+betaTheta^2)` , find the values of `R_0`, alpha and beta. Here Theta represents the temperature on Celsius scale. |
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Answer» `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` |
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