A thermometer graduated according to a linear | vedclass

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Question

(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}} 	imes 100^\c

Vedclass · Accepted Answer

$25$

Vedclass · Answer

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

$A$ 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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