SATHEE: Properties Of Solids And Liquids Question 115

Properties Of Solids And Liquids Question 115

Question: The coefficient of linear expansion of crystal in one direction is $α_{1}$ and that in every direction perpendicular to it is $α_{2}$ . The coefficient of cubical expansion is

Options:

A) $α_{1} + α_{2}$

B) $2 α_{1} + α_{2}$

C) $α_{1} + 2 α_{2}$

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

$V = V_{0} (1 + γ Δ θ)$

$L^{3} = L_{0} (1 + α_{1} Δ θ) L_{0}^{2} {(1 + α_{2} Δ θ)}^{2}$

$= L_{0}^{3} (1 + α_{1} Δ θ) {(1 + α_{2} Δ θ)}^{2}$

Since $L_{0}^{3} = V_{0}$ and $L^{3} = V$

Hence $1 + γ Δ θ = (1 + α_{1} Δ θ) {(1 + α_{2} Δ θ)}^{2}$

$\tilde{=} (1 + α_{1} Δ θ) (1 + 2 α_{2} Δ θ)$

$\tilde{=} (1 + α_{1} Δ θ + 2 α_{2} Δ θ)$

therefore g = a1 + 2a2

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Properties Of Solids And Liquids Question 115

Question: The coefficient of linear expansion of crystal in one direction is α1 and that in every direction perpendicular to it is α2 . The coefficient of cubical expansion is

Options:

Answer:

Solution:

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Question: The coefficient of linear expansion of crystal in one direction is $α_{1}$ and that in every direction perpendicular to it is $α_{2}$ . The coefficient of cubical expansion is