A metal rod 800mm long is heated from 10oC to 95oC. If it expands by 1.36mm, the linear expansivity of the metal is
Question 1 Report
A metal rod 800mm long is heated from 10oC to 95oC. If it expands by 1.36mm, the linear expansivity of the metal is
Answer Details
The linear expansivity (α) of a material is defined as the change in length per unit length per degree Celsius (or Kelvin) change in temperature.
In this problem, we are given the initial length of the metal rod (800 mm), the change in temperature (∆T = 95°C - 10°C = 85°C), and the change in length (∆L = 1.36 mm).
We can use the formula:
∆L = αL∆T
where L is the initial length of the rod.
Solving for α, we get:
α = ∆L / (L∆T)
Substituting the given values, we have:
α = (1.36 mm) / (800 mm x 85°C)
Simplifying the denominator:
α = (1.36 mm) / 68000 mm°C
α = 0.00002°C^-1
Therefore, the linear expansivity of the metal is 2.0 x 10^-5 K^-1.
Answer: (D) 2.0 x 10^-5 K^-1.
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