1. Tardigrade
  2. Question
  3. Physics
  4. A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the rim and the iron ring are 5.243 m and 5.231 m respectively at 27° C. The αl of iron is 1.2 × 10-5 K -1 . To what temperature should the ring be heated so as to fit the rim of the wheel?

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Q. A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the rim and the iron ring are $5.243 m$ and $5.231 m$ respectively at $27^{\circ} C$. The $\alpha_{l}$ of iron is $1.2 \times 10^{-5} K ^{-1} .$ To what temperature should the ring be heated so as to fit the rim of the wheel?

Thermal Properties of Matter

Solution:

$ L=L_{0}\left(1+\alpha_{l} \Delta T\right)$
$\Delta T=\left(\frac{L}{L_{0}}-1\right) \frac{1}{\alpha_{l}}$
$=\left(\frac{5.243}{5.231}-1\right) \times \frac{1}{1.2 \times 10^{-5}}=191^{\circ} C$
$\Rightarrow T_{2}=\Delta T+T_{1}=(191+27)=218^{\circ} C$