A $3.00 \mathrm{~cm} \times 5.00 \mathrm{~cm}$ rectangular piece of copper is at a temperature of $10.0^{\circ} \mathrm{C}$. The coefficient of linearexpansion of copper is $ 17.0 \times 10^{-6} /{ }^{\circ} \mathrm{C} $. If the temperature of the copper rectangle increases by $ 2.00^{\circ} \mathrm{C} $, thenwhat is its change in area?
A) $1.02 \times 10^{-3} \mathrm{~cm}^{2}$
B) $0.550 \times 10^{-3} \mathrm{~cm}^{2}$
C) $2.44 \times 10^{-3} \mathrm{~cm}^{2}$
D) $1.95 \times 10^{-3} \mathrm{~cm}^{2}$
E) $0.830 \times 10^{-3} \mathrm{~cm}^{2}$

Question

Quizplus · Accepted Answer

The change in area can be calculated using the formula for area expansion, which is $\Delta A = 2\alpha A_0 \Delta T$, where $\alpha$ is the coefficient of linear expansion, $A_0$ is the initial area, and $\Delta T$ is the change in temperature. Given $\alpha = 17.0 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, $A_0 = 3.00 \mathrm{~cm} \times 5.00 \mathrm{~cm} = 15.00 \mathrm{~cm}^2$, and $\Delta T = 2.00^{\circ} \mathrm{C}$, we find $\Delta A = 2 \times 17.0 \times 10^{-6} \times 15.00 \times 2.00 = 1.02 \times 10^{-3} \mathrm{~cm}^{2}$.

A 3.00 cm×5.00 cm3.00 \mathrm{~cm} \times 5.00 \mathrm{~cm}3.00 cm×5.00 cm Rectangular Piece of Copper Is at a Temperature Of

A $3.00 \mathrm{~cm} \times 5.00 \mathrm{~cm}$ Rectangular Piece of Copper Is at a Temperature Of