If Diameter of a Steel Ball is 40 cm at 0 °C — Find Its New Volume at 100 °C
If diameter of a steel ball is 40 cm at 0 °C — find its new volume at 100 °C is a typical physics problem dealing with volumetric expansion of solids due to temperature rise.
Concept: Volumetric Thermal Expansion
When a solid body is heated, its volume increases. The change in volume depends on its initial volume, temperature change, and coefficient of volumetric expansion. The formula generally used: ΔV = 3 α V₀ ΔT, where α is linear expansion coefficient.
Calculation Steps
Given: initial diameter = 40 cm → radius = 20 cm. So initial volume V₀ = (4/3) π r³ = (4/3) π (20 cm)³.
Assume coefficient of linear expansion of steel, α ≈ 12 × 10⁻⁶ /°C. Then volumetric expansion coefficient is approx 3α ≈ 36 × 10⁻⁶ /°C. With ΔT = 100 °C − 0 °C = 100 °C, change in volume ΔV ≈ 3α V₀ ΔT.
So new volume V = V₀ + ΔV = V₀ [1 + 3α ΔT].
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If Diameter of a Steel Ball is 40 cm at 0 °C — Find Its New Volume at 100 °C
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