Q. 95.0( 2 Votes )

A resistance thermometer reads R = 20.0Ω, 27.5Ω, and 50.0Ω 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 Rθ = Rθ (I + αθ + βθ2), find the values of Rθ, α and β. Here θ represents the temperature on the Celsius scale.

Answer :


Explanation:


Given:


Rθ1= Resistance at 0°C=20.0Ω


Rθ2= Resistance at 100°C=27.5Ω


Rθ3= Resistance at 420°C=50.0Ω


R0 = ?, α=?, β=?


Formula used



The values for 3 resistance ( are given at 3 temperatures (,


So, at temperature 0° C,


, (eqn. 1)


At 100° C,


, (eqn. 2)


At 420° C,


, (eqn. 1)


Solving this three equation simultaneously for three unknowns,


From eqn. 1, we get,


(Ans.)


Putting R0 in eqn.2 and eqn.3, and substituting given values, we get,


Eqn.2 as , and


Eqn.3 as


Now, from eqn.2 after re arranging, we get,


, (eqn.4)


Putting this value in eqn. 3, we get



Or,



Or,


(Ans.)


Putting the value of in eqn.4 , we get



(Ans.)


Hence, the required values are


(Ans.)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Henry's Law & effect of temperature on solubilityHenry's Law & effect of temperature on solubilityHenry's Law & effect of temperature on solubility43 mins
Work done in Thermodynamic ProcessWork done in Thermodynamic ProcessWork done in Thermodynamic Process43 mins
Human Evolution | An Important ConceptHuman Evolution | An Important ConceptHuman Evolution | An Important Concept40 mins
Rapid Quiz challenge - Cell Structure & Cell DivisionRapid Quiz challenge - Cell Structure & Cell DivisionRapid Quiz challenge - Cell Structure & Cell Division52 mins
Different high order thinking questions based on DNA structureDifferent high order thinking questions based on DNA structureDifferent high order thinking questions based on DNA structure39 mins
Everything About Genetic DisordersEverything About Genetic DisordersEverything About Genetic Disorders55 mins
Meselson and Stahl experimentMeselson and Stahl experimentMeselson and Stahl experiment49 mins
Human EvolutionHuman EvolutionHuman Evolution38 mins
Interactive Quiz | Biotechnology - 03Interactive Quiz | Biotechnology - 03Interactive Quiz | Biotechnology - 0342 mins
Interactive Quiz on Human EvolutionInteractive Quiz on Human EvolutionInteractive Quiz on Human Evolution33 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :