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In this article I show you the physical quantity “density” and an example how you can calculate it with the help of volume and mass.

Table of Contents

## Basics of Density

The density (rho) indicates the ratio of mass to volume of a substance. The density of a substance depends on the temperature and the pressure. The density is given in or .

When a substance is heated or pressure reduced, it expands, increases in volume and decreases in density.

When a substance cools or increases pressure, it contracts, the volume decreases and the density increases. So you can keep this in mind:

**NOTICE:****increasing temperature:** increasing volume, decreasing density**decreasing temperature:** decreasing volume, increasing density**increasing pressure:** decreasing volume, increasing density**decreasing pressure:** increasing volume, decreasing density

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## Anomaly of Water

One exception is the water. Because water has its highest density at 4°C (39,2°F). This phenomenon is also called the anomaly of water. The density of water at 4°C is 1 g/cm³. That means 1000 cm³ water (1 liter) have a mass of 1000 g. The following relationship applies:

**1000** kg/m3 = **1000** g/l = **1** kg/dm3 = **1** kg/l = **1** g/cm3 = **1** g/ml

## Example Calculation: How to Calculate Density of Water?

In the following I show you the increase and decrease of the density using an example with water. There is a simple reason for this: In building services engineering, the density of water plays an important role. Gravity heating, for example, is based on the knowledge of the density of water.

The water tank (Figure 1) contains exactly 1,000 cm³ (1 liter) of water at a water temperature of 4 °C. The mass of the water is then 1,000 g. This results in a density of raw=1g/cm³.

When the water is now heated to 85 °C (Figure 2), the water expands, changing its volume, density and mass. According to the table book, the density of water at 85 °C is rho=0.9686 g/cm³.

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The mass of water at 85 °C is then 968,61 g as represented by the following formula. Here we have simply converted to m (mass).

The part of the water that expands flows into the overflow container. The overflow mass can be calculated by simple subtraction:

The overflow volume is :

At a water temperature of 85 °C, there is still **1,000 cm³ (1 liter)** of water in the water container, but the mass is **968.61 g**. The overflow container then contains **31.39 g** or **32.41 cm³ (32.41 milliliters)** of water.

## Fazit

Density is one of the most important quantities in physics and is often used in building technology. I hope with this article I was able to bring you a little closer to the physical quantity “density” and its behavior. If you have any questions I’m looking forward to see your comments

Greetings! Martin

*Further links and sources:*

Wikipedia – Density

Wikipedia – Negative Thermal Expansion