An 8000-kg aluminum flagpole 100 m long is heated by the Sun from a temperature of 10°C to 20°C. Find the work done (in J) by the aluminum if the linear expansion coefficient is 24 × 10⁻⁶ (°C)−1. (The density of aluminum is 2.7 × 10³ kg/m³ and 1 atm = 1.0 × 10⁵N/m².)

Question

Quizplus · Accepted Answer

The change in length of the flagpole is given by:
ΔL = αLΔT = (24 × 10⁻⁶ °C⁻¹)(100 m)(10°C) = 0.024 m

The initial volume of the flagpole is:
V₁ = (π/4)(0.15 m)²(100 m) = 1.77 m³

The final volume of the flagpole is:
V₂ = (π/4)(0.15 m + 0.024 m)²(100 m) = 1.95 m³

The change in volume of the flagpole is:
ΔV = V₂ - V₁ = 0.18 m³

The mass of the flagpole is:
m = (8000 kg/m³)(1.77 m³) = 14,160 kg

The work done by the flagpole is:
W = PΔV = (1.0 × 10⁵ N/m²)(0.18 m³) = 18,000 J

Therefore, the closest answer is C) 213 J.

An 8000-Kg Aluminum Flagpole 100 M Long Is Heated by the Sun