First slide

Thermal expansion

Question

The value of coefficient of volume expansion of glycerin is $5 \times 10^{- 4} K^{- 1}$ . The fractional change in the density of glycerin for a rise of $40^{0} C$ in its temperature is

Moderate

A

0.0010
B

0.015
C

0.020
D

0.025

Solution

$d_{f} = \frac{d_{1}}{(1 + γ ∆ T)}$
Fractional change = $\frac{d_{1} - d_{f}}{d_{1}} = 1 - \frac{d_{f}}{d_{i}}$
= $1 - {(1 + γ ∆ T)}^{- 1} = 1 - (1 - γ ∆ T)$
${(1 + x)}^{n} = 1 + nx = γ ∆ T$
= 5 $\times 10^{- 4} \times 40 = 0.020$

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