(A) For a linear scale,the temperature $T$ can be related to the reading $x$ by the formula:$T = \frac{x - x_{ice}}{x_{steam} - x_{ice}} \times 100^\c

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(A) For a linear scale,the temperature $T$ can be related to the reading $x$ by the formula:$T = \frac{x - x_{ice}}{x_{steam} - x_{ice}} \times 100^\circ C$Given:$x_{steam} = x_0$$x_{ice} = x_0/3$$x = x_0/2$Substituting these values into the formula:$T = \frac{x_0/2 - x_0/3}{x_0 - x_0/3} \times 100^\circ C$$T = \frac{(3x_0 - 2x_0)/6}{(3x_0 - x_0)/3} \times 100^\circ C$$T = \frac{x_0/6}{2x_0/3} \times 100^\circ C$$T = \frac{x_0}{6} \times \frac{3}{2x_0} \times 100^\circ C$$T = \frac{1}{4} \times 100^\circ C = 25^\circ C$

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Temperature and Temperature scales

Difficult

$A$ thermometer graduated according to a linear scale reads a value $x_0$ when in contact with boiling water,and $x_0/3$ when in contact with ice. What is the temperature of an object in ${}^oC$,if this thermometer in contact with the object reads $x_0/2$?

JEE MAIN 2019 All JEE MAIN

A
$25$
B
$60$
C
$40$
D
$35$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Temperature and Temperature scales

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$A$ thermometer graduated according to a linear scale reads a value $x_0$ when in contact with boiling water,and $x_0/3$ when in contact with ice. What is the temperature of an object in ${}^oC$,if this thermometer in contact with the object reads $x_0/2$?

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The melting point of ice and the boiling point of water are marked as $20^o X$ and $150^o X$ respectively on a thermometer. What will be the temperature of $60^o C$ on this scale?

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