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

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 (A) α1+α2 (B) 2 α1+α2 (C) α1+2 α2 (D) None of these

Tardigrade Admin · Accepted Answer

V=V0(1+&gamma; Δ θ) L3=L0(1+α1 Δ θ) L02(1+α2 Δ θ)2 =L03(1+α1 Δ θ)(1+α2 Δ θ)2 Since L03=V0 text and L3=V Hence 1+&gamma; Δ θ=(1+α1 Δ θ)(1+α2 Δ θ)2 ≅(1+α1 Δ θ)(1+2 α2 Δ θ) ≅(1+α1 Δ θ+2 α2 Δ θ) ⇒ &gamma; α1+2 α2

Q. 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

$α_{1} + α_{2}$

$2 α_{1} + α_{2}$

$α_{1} + 2 α_{2}$

None of these

Q. 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

α1​+α2​

2α1​+α2​

α1​+2α2​

None of these

V=V0​(1+γΔθ) L3=L0​(1+α1​Δθ)L02​(1+α2​Δθ)2 =L03​(1+α1​Δθ)(1+α2​Δθ)2 Since L03​=V0​ and L3=V Hence 1+γΔθ=(1+α1​Δθ)(1+α2​Δθ)2 ≅(1+α1​Δθ)(1+2α2​Δθ) ≅(1+α1​Δθ+2α2​Δθ) ⇒γα1​+2α2​

Q. 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

$α_{1} + α_{2}$

$2 α_{1} + α_{2}$

$α_{1} + 2 α_{2}$