Reef Chemistry Question of the Day #29 Hydrometer

[Randy Holmes-Farley]

Reef Chemistry Question of the Day #29

You are measuring the salinity of your reef aquarium with a floating glass hydrometer. The room temperature is 72 degrees F, and the hydrometer has been in that room overnight. You take out some water at 81 degrees F, put it into a bucket, and take a quick look at the hydrometer in it. Just then the dog runs by, reeking of skunk, which it must have encountered in the back yard. By the time you get done dealing with the dog and get back to the aquarium, the water has cooled to 72 degrees F.

When you look at the hydrometer, what do you see?

A. It is floating higher in the water than it was earlier.
B. It is floating in exactly the same position as earlier.
C. It is floating lower in the water than it was earlier.
D. Not enough information is given to know.

Good luck!



















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[leptang]

C. i think

 

[Randy Holmes-Farley]

Anyone else?

 

[birdsnest]

D. I think it would be depend on what temp the hydrometer was calibrated to.

 

[Randy Holmes-Farley]

And the answer is....

A. It is floating higher in the water than it was earlier.

There are many ways to think this one through. Here's one way.

As the water cools from 81 to 72 degrees F, it gets denser. Actually, at any temperature above 4 degrees C, liquid water gets denser as it cools. That applies both to fresh and salt water.

The glass hydrometer will have a very small change in its density with temperature. That is a property of glass.

So, the water is getting denser and the hydrometer is staying about the same.

The easiest way to then proceed is to consider Archimedes' Principle:

http://en.wikipedia.org/wiki/Archimedes'_principle

From it, one can conclude that a floating body (like an iceberg or a hydrometer) displaces exactly the same weight of water as the object itself weighs. So if an iceberg weighs 1 million tons, it sinks into the water until the volume of the iceberg under water is exactly the volume of water that weighs 1 million tons.

Same with the hydrometer. It sinks until it exactly displaces a volume of water that exactly equals its weight.

At 81 degrees F, it displaces some volume and sinks to a certain depth.

As the water cools, it becomes denser. So since the hydrometer sinks to a depth that exactly displaces a certain WEIGHT of water, at the lower temperature (higher water density), the hydrometer displaces a smaller amount of volume to get to the same weight displaced.

Hence, the hydrometer is floating higher in the water (displacing a smaller volume of water).

Happy Reefing!