The coefficient of linear expansion of copper is 17 × 10^-6 K^-1and 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.Which one of the following quantities is closest to the temperature to which the copper pipe must be heated in order for the unheated steel rod to fit snugly in the copper pipe? A)53°C B)81°C C)93°C D)105°C E)143°C

Question

Quizplus · Accepted Answer

Let the temperature to which the copper pipe must be heated be T°C.
The increase in the diameter of copper pipe = (17 × 10^-6) × 2.536 × (T - 12)
The increase in the diameter of steel rod = (12 × 10^-6) × 2.540 × (T - 12)
For the steel rod to fit snugly in the copper pipe, their diameters must be equal.
Therefore, (17 × 10^-6) × 2.536 × (T - 12) + 2.536 = (12 × 10^-6) × 2.540 × (T - 12)
Solving this equation gives T ≈ 105°C. Thus, the best choice is D.

The Coefficient of Linear Expansion of Copper Is 17 ×