Question

A cube of solid aluminum has a volume of 1. 00 m³ at 20°C. What temperature change is required to produce a 110 cm³ increase in the volume of the cube?

A) 273.15°C
B) 100.00°C
C) 45.45°C
D) 25.00°C

Answer 1

To find the required temperature change to produce a 110 cm³ increase in volume for a cube of aluminum, we use the volumetric expansion formula, resulting in a change of approximately 1.6°C. None of the provided options are correct.

Step-by-step explanation:

To determine the temperature change required to produce a 110 cm³ increase in the volume of a cube of solid aluminum, we need to consider the thermal expansion of aluminum. Aluminum has a linear expansion coefficient, α, which also relates to the volumetric expansion coefficient, β, such that β ≈ 3α. Given that the volume expansion ∆V for a change in temperature ∆T can be approximated as ∆V ≈ 3αV∆T, we can rearrange this to calculate ∆T:

∆T = ∆V / (3αV)

Using the volume of aluminum, V = 1.00 m³, the increase in volume, ∆V = 110 cm³ = 110 x 10^-6 m³, and the linear expansion coefficient for aluminum, α = 23 x 10^-6 1/°C, we can calculate the change in temperature.

∆T = (110 x 10^-6 m³) / (3 x 23 x 10^-6 1/°C x 1.00 m³) = 1.590°C

When rounding to two significant figures, the final answer is a temperature change of 1.6°C, which is not one of the options provided in the question. Therefore, none of the multiple-choice options (A, B, C, D) are correct.