A brass cube of side 10cm is heated through 30°C. If the linear expansivity of brass is 2.0 × I0\(^{-5}\) K-1 , what is the increase in its volume?

obig6479

1 year ago

To find the increase in volume, we need to calculate the volume expansion of the brass cube.

The formula for volume expansion is:

ΔV = βV₀ΔT

where:

- ΔV is the change in volume
- β is the volumetric expansivity (approximately 3 times the linear expansivity)
- V₀ is the initial volume
- ΔT is the change in temperature

Given:

- Linear expansivity (α) = 2.0 × 10⁻⁵ K⁻¹
- Volumetric expansivity (β) ≈ 3α = 6.0 × 10⁻⁵ K⁻¹
- Initial side length (s) = 10 cm
- Initial volume (V₀) = s³ = 1000 cm³
- Temperature change (ΔT) = 30°C

Now, calculate the change in volume:

ΔV = βV₀ΔT
= (6.0 × 10⁻⁵ K⁻¹) × (1000 cm³) × (30 K)
= 0.18 cm³

The correct answer is B: 0.18 cm³.

Karrylove

4 years ago

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