Answer:
The temperature beyond which the substance overflows the container is 86.23°C.
Explanation:
English Translation
Professor Hosney took the second grade students to the laboratory to perform an experiment. He took a 1000ml capacity container at a temperature of 68oF and poured 980 ml of a substance at 20oC into it. While placing the set to heat, he consulted a table where he found the volumetric expansion coefficient of the substance, 4 x 10-4 ºC-1 and the linear expansion coefficient of the container material, 3 x 10-5 ºC-1. Hosney then asked students to determine the temperature from which the substance would overflow. A student then asked, what is the melting temperature of the substance, and the teacher answered promptly 290.8 K. What is the temperature from which the substance will overflow?
Solution
The change in volume of a substance is given as
ΔV = γV₀(ΔT)
where
γ = coefficient of volume expansion
V₀ = Initial volume
(ΔT) = change in temperature.
At the temperature where the substance will overflow, the volume of the substance and the container will both be the same.
Let this temperature be T.
For the substance,
γ = coefficient of volume expansion = (4 × 10⁻⁴) °C⁻¹
V₀ = Initial volume = 980 mL
(ΔT) = change in temperature = (T - 20)
We will still leave ΔT as ΔT
ΔV₁ = (4 × 10⁻⁴) × 980 × ΔT
ΔV₁ = 0.392 ΔT
New volume of the substance at that temperature = V₀ + ΔV₁ = 980 + 0.392ΔT
For the container
γ = coefficient of volume expansion = 3 × coefficient of linear expansion = 3 × (3 × 10⁻⁵) °C⁻¹ = (9 × 10⁻⁵) °C⁻¹
V₀ = Initial volume = 1000 mL
(ΔT) = change in temperature = (T - 20) (note that 68°F = 20°C)
We will still leave ΔT as ΔT
ΔV₂ = (9 × 10⁻⁵) × 1000 × ΔT
ΔV₂ = 0.09 ΔT
New volume of the container at that temperature = V₀ + ΔV₂ = 1000 + 0.09 ΔT
At the temperature where overflow occurs, the two volumes are initially first the same.
980 + 0.392ΔT = 1000 + 0.09 ΔT
0.392ΔT - 0.09ΔT = 1000 - 980
0.302ΔT = 20
ΔT = (20/0.302) = 66.23°C
T - 20° = 66.23°
T = 66.23 + 20 = 86.23°C
The temperature beyond which the substance overflows the container is 86.23°C.
Hope this Helps!!!
