First slide

Thermal expansion

Question

The coefficient of volume expansion of glycerine is 49 x $10^{- 5} /^{0} C$ . What is the fractional change in its density (approx.) for 30°C rise in temperature?

Moderate

A

$1.5 \times 10^{- 2}$
B

$2.5 \times 10^{- 2}$
C

$2.0 \times 10^{- 2}$
D

$2.8 \times 10^{- 2}$

Solution

Coefficient of volume expansion of glycerine.
$γ = 49 \times 10^{- 5} /^{0} C$
Rise in temperature, $∆$ T = 30°C
As $γ = \frac{1}{∆ T} (\frac{∆ V}{V}) \Rightarrow \frac{∆ V}{V} = γ \times ∆ T$
$or \frac{∆ V}{V} = (49 \times 10^{- 5}) \times 30 = 0.0147$
Since mass remains constant,
Fractional change in density = fractional change in volume = 0.0147 = 1.5 x $10^{- 2}$

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