JEE PYQ: Properties Of Matter Question 8
Question 8 - 2020 (05 Sep 2020 Shift 2)
Two different wires having lengths $L_1$ and $L_2$, and respective temperature coefficient of linear expansion $\alpha_1$ and $\alpha_2$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is:
(1) $\frac{\alpha_1 L_1 + \alpha_2 L_2}{L_1 + L_2}$
(2) $2\sqrt{\alpha_1 \alpha_2}$
(3) $\frac{\alpha_1 + \alpha_2}{2}$
(4) $4\frac{\alpha_1 \alpha_2}{\alpha_1 + \alpha_2} \cdot \frac{L_2 L_1}{(L_2 + L_1)^2}$
Show Answer
Answer: (1)
Solution
At $T + \Delta T$°C: $(L_1 + L_2)(1 + \alpha_{eq}\Delta T) = L_1(1 + \alpha_1 \Delta T) + L_2(1 + \alpha_2 \Delta T)$
$\Rightarrow \alpha_{eq} = \frac{\alpha_1 L_1 + \alpha_2 L_2}{L_1 + L_2}$
BETA
