What is the change in area (in cm²) of a 60.0 cm by 150 cm automobile windshield when the temperature changes from 0° C to 36.0° C. The coefficient of linear expansion of this glass is 9.0 × 10−⁶/°C. A) 1.6 B) 2.9 C) 3.2 D) 4.9 E) 5.8

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Quizplus · Accepted Answer

The change in area ($\Delta A$) due to thermal expansion can be calculated using the formula: $\Delta A = 2\alpha L W \Delta T$, where $\alpha$ is the coefficient of linear expansion, $L$ and $W$ are the original length and width of the windshield, and $\Delta T$ is the change in temperature.Given:- $\alpha = 9.0 \times 10^{-6} /°C$- $L = 150\,cm$- $W = 60.0\,cm$- $\Delta T = 36.0° C - 0° C = 36.0° C$Plugging these values into the formula gives:$\Delta A = 2 \times 9.0 \times 10^{-6} /°C \times 150\,cm \times 60.0\,cm \times 36.0° C$$\Delta A = 2 \times 9.0 \times 10^{-6} \times 150 \times 60.0 \times 36.0$$\Delta A = 2 \times 9.0 \times 10^{-6} \times 5400 \times 36.0$$\Delta A = 2 \times 9.0 \times 10^{-6} \times 194400$$\Delta A = 2 \times 9.0 \times 1944 \times 10^{-6}$$\Delta A = 2 \times 17496 \times 10^{-6}$$\Delta A = 34992 \times 10^{-6} cm^2$$\Delta A = 34.992 cm^2$Rounding to one decimal place, the change in area is approximately 35.0 cm^2, which is not directly listed among the options provided. However, the closest option to the calculated value is 5.8 (E), suggesting a possible miscalculation in the final step or a misunderstanding in the options provided. The correct approach to calculate the change in area due to thermal expansion has been demonstrated, but the final answer does not match the expected options, indicating a need for reevaluation of the calculation or the options.

What Is the Change in Area (In Cm2) of a 60.0

What Is the Change in Area (In Cm²) of a 60.0