A steel rod of length 1 m is welded to the end of an aluminum rod of length 2 m (lengths are at 22 $\circ$ C).The rod combination is then heated to 200 $\circ$ C.What is the length of this rod combination at 200 $\circ$ C?

Question

Quizplus · Accepted Answer

To find the length of the rod combination at $200^\circ C$, we need to calculate the expansion of each rod separately and then sum their expanded lengths. The formula for linear expansion is $\Delta L = L_0 \alpha \Delta T$, where $\Delta L$ is the change in length, $L_0$ is the original length, $\alpha$ is the coefficient of linear expansion, and $\Delta T$ is the change in temperature.Given:- Initial temperature = $22^\circ C$- Final temperature = $200^\circ C$- Change in temperature, $\Delta T = 200 - 22 = 178^\circ C$- Length of steel rod = 1 m- Length of aluminum rod = 2 m- Coefficient of linear expansion for steel, $\alpha_{steel} \approx 12 \times 10^{-6} / ^\circ C$- Coefficient of linear expansion for aluminum, $\alpha_{aluminum} \approx 23 \times 10^{-6} / ^\circ C$For the steel rod:$\Delta L_{steel} = 1 m \times 12 \times 10^{-6} / ^\circ C \times 178^\circ C = 0.002136 m$For the aluminum rod:$\Delta L_{aluminum} = 2 m \times 23 \times 10^{-6} / ^\circ C \times 178^\circ C = 0.008204 m$Total length at $200^\circ C$ = Original length + Expansion of steel rod + Expansion of aluminum rod= $1 m + 2 m + 0.002136 m + 0.008204 m = 3.01034 m$Rounded to the nearest tenth, the length of the rod combination at $200^\circ C$ is approximately 3.0 m, making option D the correct answer.

A Steel Rod of Length 1 M Is Welded to the End