First slide

Thermal expansion

Question

The density of a substance at 0°C is l0 g/cc and at l00°C, its density is 9.7 g/cc. The coefficient of linear expansion of the substance is

Moderate

A

$10^{2}$
B

$10^{- 2}$
C

$10^{- 3}$
D

$10^{- 4}$

Solution

The coefficient of volume expansion is given by
$γ = \frac{∆ ρ}{ρ_{1} \times ∆ T}$
where $ρ_{1}$ is density, T is temperature
$γ = \frac{ρ_{1} - ρ_{2}}{ρ_{1} (T_{2} - T_{1})}$
= $\frac{10 - 9.7}{10 (100 - 0)} = 3 \times 10^{- 4}$
Coeffiicient of linear expansion is
$α = \frac{γ}{3} = \frac{3 \times 10^{- 4}}{3} = 10^{- 4}$

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