Heat And Thermodynamics Ques 9
9 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 ${ }^{\circ} \mathrm{C}$, if this thermometer in the contact with the object reads $x_0 / 2$ ?
(2019 Main, 11 Jan II)
(a) 35
(b) 60
(c) 40
(d) 25
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Answer:
Correct Answer: 9.( d )
Solution:
Formula:
- (d) By principle of thermometry for any liner temperature scale,
$ \frac{T-T_{\text {LFP }}}{T_{\mathrm{UFP}}-T_{\mathrm{LFP}}}=\mathrm{a} \text { (constant) } $
where, $T=$ temperature measured
$T_{\mathrm{LFP}}=$ temperature of melting ice or lower fixed point.
$T_{\mathrm{UFP}}=$ temperature of boling water or upper fixed point.
If, $T=$ temperature of given object.
Then we have,
$ \frac{T-0^{\circ} \mathrm{C}}{100^{\circ} \mathrm{C}-0^{\circ} \mathrm{C}}=\frac{\frac{x_0}{2}-\frac{x_0}{3}}{x_0-\frac{x_0}{3}} \text { or } \frac{T}{100}=\frac{1}{4} \text { or } T=25^{\circ} \mathrm{C} $
BETA
