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Step 1:I'll solve this problem by explaining the concept of density as an intensive property step by step.
Step 2:: Define Density
- $$V$$ represents volume
Density is defined as the mass of a substance per unit volume, mathematically expressed as: Where:
Step 3:: Understand Intensive vs.
Extensive Properties - Extensive properties depend on the amount of substance (mass, volume) - Intensive properties do NOT depend on the amount of substance (temperature, density, specific heat)
Step 4:: Demonstrate Density's Independence from Sample Size
\rho_{bar} = \frac{1000 \mathrm{g}}{116 \mathrm{cm}^{3}} = 8.62 \mathrm{g/cm}^{3}
Consider two samples of pure gold: - Small gold nugget: 10 g with volume 1.16 cm³ - Large gold bar: 1000 g with volume 116 cm³ Density calculation for small nugget: Density calculation for large bar:
Step 5:: Key Insight
Notice that despite different masses and volumes, the density remains constant. This demonstrates density's intensive nature.
Final Answer
Density is an intensive property because its value remains constant regardless of the sample size, depending only on the substance's composition and not the amount of material present.
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