Zirconium tungstate is an unusual material because its volume shrinks with an increase in temperature for the temperature range 0.3 K to 1050 K (where it decomposes). In fact, the volumetric coefficient of thermal expansion is -26.4 × 10^-⁶/K. Determine the ratio $\Delta$V/V₀ for the above mentioned temperature range. Express your answer in percent. A)-5.28% B)-3.59% C)-2.77% D)-1.90% E)-1.04%

Question

Quizplus · Accepted Answer

We can use the formula for volumetric thermal expansion: ΔV/V = 3αΔT where ΔV/V is the relative change in volume, α is the coefficient of volumetric thermal expansion, and ΔT is the change in temperature. We are given α = -26.4 × 10^-6/K and the temperature range is from 0.3 K to 1050 K. For the ratio FΔV/V / ΔT, we can cancel out the ΔV/V and express it as: FΔV/V / ΔT = 3α / (V₀ - V⁶) Plugging in the values, we get: FΔV/V / ΔT = 3(-26.4 × 10^-6) / [(1050-0.3) - (16-0)] FΔV/V / ΔT = -0.0027659 Converting this to a percentage, we get: FΔV/V / ΔT = -0.2766% or -2.77% (rounded to two decimal places) Therefore, the answer is (C) -2.77%.

Zirconium Tungstate Is an Unusual Material Because Its Volume Shrinks Δ\DeltaΔ

Zirconium Tungstate Is an Unusual Material Because Its Volume Shrinks $\Delta$