A blacksmith heated a metal whose cubic exp..

Question 1 Report

A blacksmith heated a metal whose cubic expansivity is 3.9 x 10 $^{- 6}$ K $^{- 1}$ . Calculate the area expansivity.

3.9 x 10

^{- 6}

^{- 1}

2.6 x 10

^{- 6}

^{- 1}

1.3 x 10

^{- 6}

^{- 1}

1.6 x 10

^{- 6}

^{- 1}

Answer Details

To find the area expansivity of a metal when given its cubic expansivity, you should understand the relationship between linear, area, and cubic expansivity.

Cubic expansivity ($ \beta $) is defined as the fractional change in volume per change in temperature, and is given by the formula:

\[ \Delta V = \beta V \Delta T \]

Area expansivity ($ \alpha_{A} $) corresponds to the fractional change in area per change in temperature and can be derived from the linear expansivity ($ \alpha $). The relationship between these expansivities is as follows:

\[ \text{Area Expansivity ($ \alpha_{A} $)} = 2 \times \text{Linear Expansivity ($ \alpha $)} \]

The cubic expansivity ($ \beta $) is related to the linear expansivity by:

\[ \text{Cubic Expansivity ($ \beta $)} = 3 \times \text{Linear Expansivity ($ \alpha $)} \]

Thus, based on these relationships, we can express the area expansivity in terms of the cubic expansivity:

$\text{Area Expansivity (\( \alpha_{A} $)} = \frac{2}{3} \times \text{Cubic Expansivity ($ \beta $)}

Given that the cubic expansivity $ \beta $ is $ 3.9 \times 10^{-6} \, \text{K}^{-1} $:

The area expansivity can be calculated as follows:

\[ \text{Area Expansivity ($ \alpha_{A} $)} = \frac{2}{3} \times 3.9 \times 10^{-6} \, \text{K}^{-1} = 2.6 \times 10^{-6} \, \text{K}^{-1} \]

Therefore, the **correct answer** is **2.6 x 10^{-6} K^{-1}**.

Read lesson note on Thermal Expansion (JAMB)

Thermal Expansion

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A blacksmith heated a metal whose cubic expansivity is 3.9 x 10−6 − 6 K−1 − 1 . Calculate the area expansivity.