Question

One end of a thermally insulated rod is kept at a temperature T₁ and the other at T₂. The rod is composed of two sections of length l₁ and l₂ and thermal conductivities K₁and K₂ respectively. The temperature at the interface of the two section is –

• A. $\frac{(K_{1}\mathcal{l}_{1}T_{1} + K_{2}\mathcal{l}_{2}T_{2})}{(K_{1}\mathcal{l}_{1} + K_{2}\mathcal{l}_{2})}$
• B. $\frac{(K_{2}\mathcal{l}_{2}T_{1} + K_{1}\mathcal{l}_{1}T_{2})}{(K_{1}\mathcal{l}_{1} + K_{2}\mathcal{l}_{2})}$
• C. $\frac{(K_{2}\mathcal{l}_{1}T_{1} + K_{1}\mathcal{l}_{2}T_{2})}{(K_{2}\mathcal{l}_{1} + K_{1}\mathcal{l}_{2})}$
• D. $\frac{(K_{1}\mathcal{l}_{2}T_{1} + K_{2}\mathcal{l}_{1}T_{2})}{(K_{1}\mathcal{l}_{2} + K_{2}\mathcal{l}_{1})}$

Answer 1

Answer: (D)

$\frac{(K_{1}\mathcal{l}_{2}T_{1} + K_{2}\mathcal{l}_{1}T_{2})}{(K_{1}\mathcal{l}_{2} + K_{2}\mathcal{l}_{1})}$

Answer 2

H₁ = H₂ \ $\frac{k_{1}A\lbrack T_{1}–T\rbrack}{\mathcal{l}_{1}}$ = $\frac{k_{2}A\lbrack T–T_{1}\rbrack}{\mathcal{l}_{2}}$