A blacksmith heated a metal whose cubic expansivity is 6.3 x 10\(^{-6}\)K\(^{-1}\). The area expansivity is
2.0 x 10-6K-1
2.1 x 10-6K-1
4.2 x 10-6K-1
6.3 x 10-6K-1
Explanation
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y = 3x
b=2x
where x = linear expansivity
b = area expansivity
y = cubic expansivity
from b=2x
rewrite x =b/2
now substituting on y
y= 3x
y = 3b/2
6.3×10^-6 = 1.5b
dividing both sides by 1.5
b = (6.3×10^-6)/1.5
b = 4.2×10^-6
β = ⅔ × γ
Given:
γ = 6.3 × 10⁻⁶ K⁻¹
β = (2/3) × 6.3 × 10⁻⁶
β = 4.2 × 10⁻⁶ K⁻¹
Answer
The area expansivity is *4.2 × 10⁻⁶ K⁻¹*.
This is how the question was set
A blacksmith heated a metal whose cubic expansivity is 6.3 x 10^-6K^-1. The real expansivity is
The solution go like this
6.3 X 10^-6 = 3X
Since it is cubic expansivity
Then X = 6.3 X 10^-6/3
X = 2.1 X 10^-6
Option A
