The volume of a metal sphere increases by 0.15 when its temperature is raised by 24° C. The coefficient of linear expansion of metal is:

Question

The volume of a metal sphere increases by 0.15 when its temperature is raised by 24° C. The coefficient of linear expansion of metal is: (A) 2.5 × 10-5 / ° C (B) 2.0 × 10-5 / ° C (C) 1.5 × 10-5 / ° C (D) 1.2 × 10-5 / ° C

Tardigrade Admin · Accepted Answer

Linear expansion coefficient α=(&gamma;/3)=(1/3) .(Δ V/V Δ t) ⇒ α=(1/3) ⋅ (0.15/100 × 24) ⇒ α=2 × 10-5 / ° C

Q. The volume of a metal sphere increases by $0.15$ when its temperature is raised by $2 4^{\circ} C$ . The coefficient of linear expansion of metal is:

$2.5 \times 1 0^{- 5} /^{\circ} C$

$2.0 \times 1 0^{- 5} /^{\circ} C$

$1.5 \times 1 0^{- 5} /^{\circ} C$

$1.2 \times 1 0^{- 5} /^{\circ} C$

Linear expansion coefficient $α = \frac{γ}{3} = \frac{1}{3} . \frac{Δ V}{V Δ t}$
$\Rightarrow α = \frac{1}{3} \cdot \frac{0.15}{100 \times 24}$
$\Rightarrow α = 2 \times 1 0^{- 5} /^{\circ} C$

Q. The volume of a metal sphere increases by 0.15 when its temperature is raised by 24∘C. The coefficient of linear expansion of metal is:

2.5×10−5/∘C

2.0×10−5/∘C

1.5×10−5/∘C

1.2×10−5/∘C