The coefficient of linear expansion of copper is 17 × 10^-6 K^-1 and that of steel is 12 × 10^-6 K^-1.At 12°C a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm.If they are heated together to a higher temperature,which one of the following quantities is closest to the common temperature at which the steel rod will fit snugly in the copper pipe? A)310°C B)330°C C)340°C D)350°C E)380°C

Question

Quizplus · Accepted Answer

The common temperature at which the steel rod will fit snugly in the copper pipe can be found by setting their final diameters equal to each other and solving for the temperature. Since copper has a higher coefficient of linear expansion than steel, it will expand more for a given temperature increase. Starting from the initial diameters and using the linear expansion formula $\Delta L = L_0 \alpha \Delta T$, 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, we can equate the final diameters of both the steel rod and the copper pipe after heating. Solving this equation for $\Delta T$ and adding it to the initial temperature of 12°C gives a temperature close to 330°C, making option B the closest answer.

The Coefficient of Linear Expansion of Copper Is 17 ×