An aluminum plate has a length of 0.12 m and a width of 0.10 m at 25 °C. The plate is uniformly heated to 225 °C. If the linear expansion coefficient for aluminum is 2.3 × 10^-⁵/C°, what is the change in the area of the plate as a result of the increase in temperature? A)1.2 × 10^-⁴m² B)6.1 × 10^-⁴m² C)3.2 × 10^-⁵m² D)4.9 × 10^-⁶m² E)7.8 × 10^-⁶m²

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Quizplus · Accepted Answer

The change in length is given by:$$\Delta L = \alpha L \Delta T$$where:$$\alpha$$ is the linear expansion coefficient$$L$$ is the original length$$\Delta T$$ is the change in temperatureThe change in area is given by:$$\Delta A = 2L\Delta L + 2W\Delta W$$where:$$W$$ is the original widthSubstituting the given values, we get:$$\Delta A = 2(0.12 	ext{ m})(2.3 	imes 10^{-5}/	ext{C})(200 	ext{ C}) + 2(0.10 	ext{ m})(2.3 	imes 10^{-5}/	ext{C})(200 	ext{ C})$$$$\Delta A = 1.2 	imes 10^{-4} 	ext{ m}^2$$Therefore, the correct answer is A.

An Aluminum Plate Has a Length of 0