Density and volume are inversely related: If the mass of a substance remains constant, an increase in volume leads to a decrease in density, and a decrease in volume leads to an increase in density.
Density and Volume Relationship Explained
Density is defined as mass per unit volume (ρ = m/V). This formula highlights the inverse relationship between density (ρ) and volume (V) when mass (m) is held constant.
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Increased Volume (Constant Mass): If you increase the volume of a substance without adding any more mass, the existing mass is spread out over a larger space. This results in a lower density. Imagine stretching out a ball of clay; you're increasing its volume but not its mass, so its density decreases.
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Decreased Volume (Constant Mass): Conversely, if you decrease the volume of a substance without removing any mass, the existing mass is compressed into a smaller space. This results in a higher density. Imagine compressing the same ball of clay; you're decreasing its volume but not its mass, so its density increases.
Examples
Here are some examples illustrating how changes in volume affect density:
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Gas Compression: Compressing a gas into a smaller container decreases its volume. Since the mass of the gas remains the same, its density increases. This principle is used in air compressors and aerosol cans.
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Expansion of a Balloon: If you inflate a balloon (increase its volume) with the same amount of air (constant mass), the air inside the balloon becomes less dense than the air outside.
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Heating a Metal: When you heat a metal, it expands (increases in volume). If the mass stays the same, the density will slightly decrease.
Table Summarizing the Relationship
| Change in Volume | Effect on Density (Constant Mass) |
|---|---|
| Increase | Decrease |
| Decrease | Increase |
In summary, when the mass remains constant, the density of a substance is inversely proportional to its volume. A larger volume means a lower density, and a smaller volume means a higher density.
