First slide

Temperature and heat-thermal properties of matter

Question

The resistance of a resistance thermometer has values $2.7 Ω$ and $3.7 Ω$ at $0^{0} C$ and $100^{0} C$ respectively. The temperature at which the resistance is $3.1 Ω$ is

Moderate

A

$30^{0} C$
B

$40^{0} C$
C

$60^{0} C$
D

$70^{0} C$

Solution

$R_{t}, R_{0,} R_{100}, a r e r e s i s \tan c e s o f w i r e a t t^{0} C, 0^{0} C, 100^{0} C t h e n t e m p e r a t u r e i s t = (\frac{R_{t} - R_{0}}{R_{100} - R_{0}}) \times 100 s u b s t i t u t e t h e g i v e n v a l u e s i n a b o v e e q u a t i o n t = (\frac{3.1 - 2.7}{3.7 - 2.7}) \times 100 \Rightarrow t = \frac{0.4}{1} \times 100 \Rightarrow t = 40^{0} C$

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