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Q5.3-16CQ

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Found in: Page 187

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# When a glass bottle full of vinegar warms up, both the vinegar and the glass expand, but vinegar expands significantly more with temperature than glass. The bottle will break if it was filled to its tightly capped lid. Explain why, and also explain how a pocket of air above the vinegar would prevent the break. (This is the function of the air above liquids in glass containers.)

A pocket of air above the vinegar would prevent the bottle to break because gases (air) are compressible in nature.

Thus, the air gets compressed and allows the liquid to expand without breaking the glass bottle.

See the step by step solution

## Step 1: Definition of Vinegar

A watery solution of acetic acid and trace compounds, which may contain flavorings, is vinegar.

## Step 2: Determining the coefficient of different matter

The volume expansion coefficient of liquid ($\gamma$), is three times of linear expansion coefficient ($\propto$) and double that of the area expansion coefficient ($\beta$).

$\gamma =3\alpha \phantom{\rule{0ex}{0ex}}\beta =2\alpha$

When the temperature rises, matter (solid, liquid, and gas) expands. However, matter does not expand in the same way. It differs depending on the various states of matter.

For a given temperature expansion coefficient of different matter varies as follows

Gas > Liquid > solid

## Step 3: Explaining the bottle would not break if there was a pocket of air above the vinegar.

With a rise in temperature, vinegar expands more than the bottle, hence the volume of vinegar expands more than the volume of the glass bottle.

If the bottle is filled to the securely shut lid, the bottle will break owing to the large rise in the volume of vinegar.

A pocket of air above the vinegar would prevent the bottle to break because gases (air) are compressible in nature. Thus, air gets compressed and allows the liquid to expand without breaking the glass bottle.