Question

An electrician is wiring new electrical outlets in a house and has stored a 49.5-m length of copper wire outside where the temperature is −12.6°c. when the wire is brought inside and warmed to 23.5°c, by what amount in centimeters will the wire's length increase due to the temperature change?

Answer 1

The length of the copper wire will increase by approximately 2.94 cm when warmed from -12.6°C to 23.5°C, calculated using the coefficient of linear expansion for copper and the formula for thermal expansion.

Step-by-step explanation:

The student's question asks for the amount by which a copper wire's length increases when its temperature changes. This is a physics problem that involves the concept of linear thermal expansion. The formula to calculate the change in length (ΔL) due to thermal expansion is ΔL = αL₀ΔT, where α is the coefficient of linear expansion for copper (approximately 16.5 × 10⁻¶ /°C), L₀ is the original length of the wire, and ΔT is the temperature difference.

To find the change in length in centimeters, we'll use the given information: L₀ = 49.5 m (4950 cm) and ΔT = 23.5°C - (-12.6°C) = 36.1°C. Plugging these values into the formula yields:

ΔL = (16.5 × 10⁻¶ /°C)(4950 cm)(36.1°C)

Calculating this gives a length increase of approximately 2.94 cm.

The concept of thermal expansion of materials like copper is very relevant for practical applications, including electrical wiring in households, as it ensures proper function and safety by accounting for changes in materials due to temperature variations.