The density of a substance at 0° C is 10 g / cc and at 100° C, its density is 9.7 g / cc. The coefficient of linear expansion of the substance is

Question

The density of a substance at 0° C is 10 g / cc and at 100° C, its density is 9.7 g / cc. The coefficient of linear expansion of the substance is (A) 10-4 (B) 10-2 (C) 10-3 (D) 102

Tardigrade Admin · Accepted Answer

Coefficient of volume expansion is three times the coefficient of linear expansion.
The coefficient of volume expansion is given by

γ = \frac{Δ ρ}{ρ _{1} \times Δ T}

where

ρ_{1}

is density,

T

is temperature.

γ = \frac{ρ _{1} - ρ _{2}}{ρ _{1} ( T _{2} - T _{1} )}

= \frac{10 - 9.7}{10 ( 100 - 0 )} = 3 \times 1 0^{- 4}

Coefficient of linear expansion is

α = \frac{γ}{3} = \frac{3 \times 1 0 ^{- 4}}{3} = 1 0^{- 4}

Q. The density of a substance at $0^{\circ} C$ is $10 g / cc$ and at $10 0^{\circ} C$ , its density is $9.7 g / cc$ . The coefficient of linear expansion of the substance is

$1 0^{- 4}$

$1 0^{- 2}$

$1 0^{- 3}$

$1 0^{2}$

Q. The density of a substance at 0∘C is 10g/cc and at 100∘C, its density is 9.7g/cc. The coefficient of linear expansion of the substance is

10−4

10−2

10−3

102

Q. The density of a substance at $0^{\circ} C$ is $10 g / cc$ and at $10 0^{\circ} C$ , its density is $9.7 g / cc$ . The coefficient of linear expansion of the substance is

$1 0^{- 4}$

$1 0^{- 2}$

$1 0^{- 3}$

$1 0^{2}$