A glass flask has a volume of 500 mL at a temperature of 20°C. The flask contains 492 mL of mercury at 20°C. The temperature of the mercury and flask is raised until the mercury reaches the 500 mL reference mark. The coefficients of volume expansion of mercury and glass are 18 × 10^-5 K^-1 and 2.0 × 10^-5K^-1, respectively. The temperature at which this occurs is closest to A) 122°C. B) 112°C. C) 102°C. D) 110°C. E) 132°C.

Question

Quizplus · Accepted Answer

First, we need to calculate how much the volume of the mercury will increase with a temperature rise of ΔT. We can use the coefficient of volume expansion of mercury:
ΔV = V₀βΔT
where V₀ is the initial volume of the mercury at 20°C, β is the coefficient of volume expansion of mercury, and ΔT is the temperature rise needed to increase the volume of the mercury from 492 mL to 500 mL.

Using the given values, we get:
ΔV = (492 mL)(18 × 10⁻⁵ K⁻¹)(ΔT)
ΔV = 0.08856 ΔT

Next, we need to calculate how much the volume of the flask will increase with the same temperature rise of ΔT. We can use the coefficient of volume expansion of glass:
ΔV = V₀αΔT
where V₀ is the initial volume of the flask at 20°C, α is the coefficient of volume expansion of glass, and ΔT is the same temperature rise as before.

Using the given values, we get:
ΔV = (500 mL - 492 mL)(2.0 × 10⁻⁵ K⁻¹)(ΔT)
ΔV = 0.008 ΔT

Now we can set up an equation for the total volume increase:
ΔV(total) = ΔV(mercury) + ΔV(flask)
0.08856 ΔT + 0.008 ΔT = 0.09656 ΔT

We want to solve for ΔT when ΔV(total) = 500 mL - 492 mL = 8 mL:
0.09656 ΔT = 8 mL
ΔT = 82.85°C

Finally, we add this temperature rise to the initial temperature of 20°C to get the temperature at which the mercury and flask will have the same volume:
T = 20°C + 82.85°C = 102.85°C

Rounding to the nearest degree, we get an answer of 103°C, which is closest to choice (A) 122°C.

A Glass Flask Has a Volume of 500 ML at a Temperature