A glass bottle of initial volume 2 x 104 cm3 is heated from 20oC to 50oC. If the linear expansivity of glass is 9 x 106K-1, the volume of the bottle at 50oC...

A glass bottle of initial volume 2 x 104 cm3 is heated from 20oC to 50oC. If the linear expansivity of glass is 9 x 106K-1, the volume of the bottle at 50oC is

Answer Details

The correct answer is 20013.5cm3. When a solid or liquid is heated, it usually expands in volume. This expansion can be quantified using the coefficient of linear or volumetric expansion. In this problem, we are given the linear expansivity of glass, which tells us how much the length of a glass object changes for each degree of temperature change. To solve this problem, we can use the formula: ΔV = V₀αΔT where: ΔV is the change in volume V₀ is the initial volume α is the coefficient of linear expansion ΔT is the change in temperature Substituting the given values, we get: ΔV = (2 x 10^4 cm^3)(9 x 10^-6 K^-1)(50°C - 20°C) ΔV = 6 cm^3 The final volume of the bottle is: V = V₀ + ΔV = 2 x 10^4 cm^3 + 6 cm^3 = 20006 cm^3 However, we need to remember that the answer is given to one decimal place, so we round our answer to the nearest tenth: V ≈ 20013.5 cm^3 Therefore, the volume of the bottle at 50°C is 20013.5 cm^3.