# Why does my height not vary with temperature? Has the ruler dilated?

Sep 24, 2015

Are you certain that it does not? On the dilation question... maybe.

#### Explanation:

Most physical objects change size (at least a little) with temperature. How much they change depends on a property we call the coefficient of thermal expansion. In most cases, objects get a little larger when heated and smaller when cooled.

It's not unusual for a person's height to change by about half an inch over the course of a day for a variety of reasons. Mostly it just has to do with compression of the spine. If the change due to temperature differences is smaller than this, it might be difficult to measure.

The volume of the human body is about 65 liters. Your body can tolerate temperatures in the range of about 95ºF to 105ºF. The former is nearing hypothermia and the latter is a very high fever. Let's calculate how much 65 liters of water would expand when heated from 95ºF to 105ºF.

The expansion coefficient for water near 98.6ºF is $\beta = 0.000385$.

$\Delta V = {V}_{0} \beta \Delta T$
$\Delta V = 65 \cdot 0.000385 \cdot \left(105 - 95\right)$
$\Delta V = 0.25025 l$

So your volume will change by about one quarter of a liter. If your body expands in all directions equally, this is about the volume of water on your skin when you step out of the shower. You might imagine that this changes your height by about a millimeter. This distance is difficult to measure with a ruler and much smaller than the daily variation in your height.

On the question of changes to the ruler: The ruler will have a different coefficient of expansion. The best rulers are made with combinations of materials which do not expand or contract very much with temperature. So the answer may depend on the materials which make up your ruler.