Thermal Properties of Matter

JEE Main level, single correct, medium

18 of 126

Question 18 of 126

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω8 \Omega and 10Ω10 \Omega respectively. After inserting in a hot bath of temperature 400∘C400^{\circ} \mathrm{C}, the resistance of platinum wire is :

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Answer: (C) 16Ω16 \Omega

Given R0=8Ω,R100=10ΩR_0=8 \Omega, R_{100}=10 \Omega
∴R100=R0(1+αΔT)\therefore \mathrm{R}_{100}=\mathrm{R}_0(1+\alpha \Delta \mathrm{T})
Also, R400=R0(1+αΔT1)R_{400}=R_0\left(1+\alpha \Delta \mathrm{T}^1\right)
$\begin{aligned}
& \therefore 10=8(1+\alpha \times 100) \Rightarrow 100 \alpha=\frac{1}{4} \\
& \therefore \mathrm{R}_{400}=8(1+400 \alpha)=8(1+1)=16 \Omega
\end{aligned}$

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