How Is Density Affected by Temperature? A Guide to Thermal Expansion

For most substances, density decreases as temperature rises. Heating causes a material to expand, so the same mass occupies more volume. Since density is mass divided by volume, its value falls. Cooling usually reverses the change.

This pattern is called thermal expansion. It is clear in gases, which can expand substantially when heated. Solids and liquids also expand, but their density changes are generally smaller over the same temperature range.

Why heating usually lowers density

Density is the mass of a substance per unit volume:

[ \rho = \frac{m}{V} ]

When a substance warms, its atoms or molecules move more. In most materials, their average spacing increases, expanding the substance. If no material enters or leaves, its mass stays the same while its volume grows, so its density decreases.

Cooling usually brings particles closer together. The volume shrinks and density rises.

The size of the effect depends on the substance and the conditions. Gases tend to show larger changes because they can expand readily. Solids and liquids resist expansion more strongly, so their density often changes less.

One example: calculating a liquid’s density change

For a solid or liquid over a modest temperature range, volume expansion can be estimated with:

[ V = V_0(1 + \beta \Delta T) ]

Here, (V_0) is the starting volume, (\beta) is the volumetric expansion coefficient, and (\Delta T) is the temperature change. The coefficient describes how much volume changes per degree of warming. For an isotropic solid, the volumetric coefficient is approximately three times the linear expansion coefficient HyperPhysics.

Suppose a liquid has a starting volume of 1,000 cm³ and a mass of 1,000 g. It is heated by 50 °C. For illustration, use a volumetric expansion coefficient of 0.0002 per °C:

[ V = 1{,}000(1 + 0.0002 \times 50) = 1{,}010 \text{ cm}^3 ]

The new density is:

[ \rho = \frac{1{,}000}{1{,}010} \approx 0.990 \text{ g/cm}^3 ]

The starting density was 1.000 g/cm³, so the estimate gives a decrease of about 1%. The coefficient is an assumed example value, not a universal value for liquids. Actual expansion depends on the substance and temperature range.

What changes for gases

For a gas at constant pressure, the ideal gas law implies that density is inversely proportional to absolute temperature. Temperature must be measured in kelvins for this relationship. If the kelvin temperature doubles while pressure and gas composition stay constant, density becomes about half its original value.

The pressure condition matters. A gas in an open or flexible container can expand as it warms, so its density falls if pressure stays roughly constant. In a sealed, rigid container, volume cannot increase. Heating raises the pressure instead, while the gas density remains essentially unchanged because the same mass occupies the same volume Britannica.

This distinction explains why “heating a gas lowers its density” is not true in every setup. The gas needs room to expand for its density to fall.

The exception: water near freezing

Water does not follow the usual pattern across its entire liquid range. Its density is greatest at about 4 °C The Engineering ToolBox. From 0 °C to about 4 °C, water becomes denser as it warms. Above about 4 °C, it generally becomes less dense as it warms.

This behavior helps explain winter conditions in lakes and ponds. Water near 4 °C is denser than colder water, so it tends to sink. Water near freezing stays closer to the surface, where it can freeze. Ice floats, leaving liquid water below it.

Key Takeaways

• Heating usually expands a substance while its mass stays the same, so density decreases. Cooling usually raises density.
• For solids and liquids, estimate volume change with (V = V_0(1 + \beta \Delta T)), then divide the unchanged mass by the new volume.
• At constant pressure, gas density is inversely proportional to absolute temperature. In a sealed, rigid container, heating raises pressure while density stays essentially constant.
• Water is densest at about 4 °C. Below that temperature, it becomes denser as it warms.