Thermal Properties of Matter

JEE Main level, single correct, medium

109 of 126

Question 109 of 126

One end of a thermally insulated rod is kept at a temperature T1T_1 and the other at T2T_2. The rod is composed of two sections of lengths ℓ1\ell_1 and ℓ2\ell_2 and thermal conductivities k1k_1 and k2k_2 respectively. The temperature at the interface of the two sections is

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Answer: (C) (k1ℓ2T1+k2ℓ1T2)/(k1ℓ2+k2ℓ1)\left(\mathrm{k}_1 \ell_2 \mathrm{T}_1+\mathrm{k}_2 \ell_1 \mathrm{T}_2\right) /\left(\mathrm{k}_1 \ell_2+\mathrm{k}_2 \ell_1\right)

(T1−T)k1ℓ1=(T−T2)k2ℓ2\frac{\left(\mathrm{T}_1-\mathrm{T}\right) \mathrm{k}_1}{\ell_1}=\frac{\left(\mathrm{T}-\mathrm{T}_2\right) \mathrm{k}_2}{\ell_2}
 T=T1k1ℓ2+T2k2ℓ1k1ℓ2+k2ℓ1\mathrm{~T}=\frac{\mathrm{T}_1 \mathrm{k}_1 \ell_2+\mathrm{T}_2 \mathrm{k}_2 \ell_1}{\mathrm{k}_1 \ell_2+\mathrm{k}_2 \ell_1}

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