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Summer 2024 ?General Physics with Cal I (PHY-213-02)
PHY 213 ?Final Exam SP 2024
90 ?minutes remaining
53
Test Content
Page 12 ?of 64
Question 12
The density of a substance will increase when we decrease its volume.
True
False
The correct answer and explanation is:
The correct answer to this question is True.
Explanation:
Density is a physical property of matter that describes the mass per unit volume of a substance. It is mathematically expressed by the formula: Density(ρ)=MassVolume\text{Density} (\rho) = \frac{\text{Mass}}{\text{Volume}}
Where:
- Mass is the amount of matter in the substance, typically measured in kilograms (kg) or grams (g).
- Volume is the amount of space that the substance occupies, usually measured in liters (L) or cubic meters (m³).
Now, to address the question: when we decrease the volume of a substance (while keeping its mass constant), its density will increase. This is because the density is directly related to the inverse of the volume. When volume decreases and the mass remains unchanged, the ratio of mass to volume increases, thus making the density larger.
This principle is consistent with the idea that compression of matter leads to higher density. For example:
- If you compress a gas, its molecules are forced closer together, and since the mass of the gas remains constant, the density increases as the volume decreases.
- On the other hand, in the case of solids and liquids, even though they are not as compressible as gases, reducing the volume (through external pressure or temperature changes) will still lead to an increase in density.
For example, let’s consider a hypothetical substance with a mass of 10 kg. If the volume of the substance decreases from 5 m³ to 2 m³, the density will change as follows:
- Initial density: ρ=10 kg5 m3=2 kg/m3\rho = \frac{10\,\text{kg}}{5\,\text{m}^3} = 2 \, \text{kg/m}^3
- New density: ρ=10 kg2 m3=5 kg/m3\rho = \frac{10\,\text{kg}}{2\,\text{m}^3} = 5 \, \text{kg/m}^3
Thus, by reducing the volume, the density of the substance increases.
In conclusion, the density of a substance increases when its volume decreases, provided the mass remains unchanged, because the density is inversely proportional to volume.