Two rods A and B of identical dimensions are at temperature 30,^oC . If a heated upto 180,^oC and B

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^oC$. If a heated upto $180\,^oC$ and $B$ upto $T\,^oC$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$, then the value of $T$ is........$^oC$

A

$230$

B

$270$

C

$200$

D

$250$

(JEE MAIN-2019)

Solution

$\Delta {\ell _1} = \Delta {\ell _2}$

$\ell {\alpha _1}\Delta {T_1} = \ell {\alpha _2}\Delta {T_2}$

$\frac{{\alpha { _1}}}{{{\alpha _2}}} = \frac{{\Delta {T_1}}}{{\Delta {T_2}}}\,\,;\,\,\frac{4}{3} = \frac{{T – 30}}{{180 – 30}}$

$T = {203^ \circ }C$

Standard 11

Physics

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