# The coefficient of volume expansion of glycerine is 49 \times 10^{-5} K^{-1}. What is the...

## Question:

The coefficient of volume expansion of glycerine is {eq}49 \times 10^{-5} {/eq} K{eq}^{-1} {/eq}. What is the fractional change in its density for a 30{eq}^{\circ} {/eq}C rise in temperature?

## Thermal Expansion

When a liquid is heated then its volume is increased. As the mass remains the same we can say that the density of the liquid decreases.The density change in liquids is given as

$$\Delta \rho = -\rho_o \gamma \Delta T $$

Negative sign shows that the density of a solid decrease due to the rise in temperature.

- {eq}\gamma {/eq} is the coefficient of volume expansion.

- {eq}\rho_o {/eq} is the initial density

## Answer and Explanation:

Given:

- The coefficient of volume expansion of glycerine is {eq}49 \times 10^{-5} {/eq} K{eq}^{-1} {/eq}.

- There is a {eq}\Delta T = 30^{\circ} {/eq}C rise in temperature.

The volume expansion of glycerine we calculate the the fractional change in its density given by

{eq}\begin{align*} \Delta \rho & = - \rho_o \gamma \Delta T \\ \frac{\Delta \rho }{\rho_o} & = - \gamma \Delta T \\ & = 49 \times 10^{-5} \times 30 \\ & = 0.0147\Rightarrow(Answer) \end{align*} {/eq}

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Chapter 16 / Lesson 3