Final answer:
To find the temperature change required to produce a 110 cm³ increase in the volume of the cube, we can use the formula V = V₁ + AV = (Lo + AL)³ and rearrange it to solve for the change in temperature.
Step-by-step explanation:
To determine the temperature change required to produce a 110 cm³ increase in volume of the cube, we can use the formula V = V₁ + AV = (Lo + AL)³. Given that the initial volume (V₁) is 1.00 m³ and the change in volume (AV) is 110 cm³, we need to find the change in length (AL). We know that AL = αLAT, where α is the linear expansion coefficient for aluminum and AT is the change in temperature.
Substituting for AL in the formula, we get AV = BVAT ≈ 3αVAT. Therefore, the change in volume (AV) is approximately equal to 3 times the product of the linear expansion coefficient (α), the initial volume (V₁), and the change in temperature (AT).
To find the change in temperature, we can rearrange the formula as AT = AV / (3αV₁). Plugging in the values, AT = 110 cm³ / (3 * α * 1.00 m³). Thus, the temperature change required can be calculated using the known values of the linear expansion coefficient for aluminum.