Two uniform bars of length L1 and L2 with coefficient of linear expansion -1 and -2 are joined to form a longer rod of length L1-L2- The effective coefficient of linear expansion of composite bar is-

The correct option is B L_1α_1+L_2α_2L_1+L_2 Let us write, L'_1 = L_1 (1 + α_1 dt) nbsp; L'_2 = L_2 (1 + α_2 dt) nbsp; Adding these two equat ...

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Standard XII

Chemistry

Activation Energy

Two uniform b...

Question

Two uniform bars of length $L_{1}$ and $L_{2}$ with coefficient of linear expansion $α_{1}$ and $α_{2}$ are joined to form a longer rod of length $L_{1} + L_{2} .$ The effective coefficient of linear expansion of composite bar is:

\frac{L_{1} + L_{2}}{L_{1} α_{1} + L_{2} α_{2}}

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\frac{L_{1} α_{1} + L_{2} α_{2}}{L_{1} + L_{2}}

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\frac{L_{1} α_{1} - L_{2} α_{2}}{L_{1} + L_{2}}

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\frac{L_{1} - L_{2}}{L_{1} α_{1} - L_{2} α_{2}}

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Solution

The correct option is B $\frac{L_{1} α_{1} + L_{2} α_{2}}{L_{1} + L_{2}}$
Let us write,
$L_{1}^{'} = L_{1} (1 + α_{1} d t)$
$L_{2}^{'} = L_{2} (1 + α_{2} d t)$
Adding these two equations, we get,
$L_{1}^{'} + L_{2}^{'} = L_{1} + L_{2} + L_{1} α_{1} d t + L_{2} α_{2} d t$
= $(L_{1} + L_{2}) + (L_{1} α_{1} + L_{2} α_{2}) d t$
= $(L_{1} + L_{2}) [1 + (L_{1} α_{1} + L_{2} α_{2}) d t / (L_{1} + L_{2})]$
If $α$ = coefficient of linear expansion of the combined length , we can write,
$α$ = $(L_{1} α_{1} + L_{2} α_{2}) / (L_{1} + L_{2})$

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Two uniform bars of length L1 and L2 with coefficient of linear expansion α1 and α2 are joined to form a longer rod of length L1+L2. The effective coefficient of linear expansion of composite bar is:

Two uniform bars of length $L_{1}$ and $L_{2}$ with coefficient of linear expansion $α_{1}$ and $α_{2}$ are joined to form a longer rod of length $L_{1} + L_{2} .$ The effective coefficient of linear expansion of composite bar is: