The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400^{\circ} \mathrm{C}$, the resistance of platinum wire is:
JEE MAIN 2024, Diffcult
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$\text { Given } \mathrm{R}_0=8 \Omega, \mathrm{R}_{100}=10 \Omega$
$\therefore \mathrm{R}_{100}=\mathrm{R}_0(1+\alpha \Delta \mathrm{T})$
$\text { Also, } \mathrm{R}_{400}=\mathrm{R}_0\left(1+\alpha \Delta \mathrm{T}^1\right)$
$\therefore 10=8(1+\alpha \times 100) \Rightarrow 100 \alpha=\frac{1}{4}$
$\therefore \mathrm{R}_{400}=8(1+400 \alpha)=8(1+1)=16 \Omega$
Hence option $(2)$
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