A glass thermometer using a thin column of ethyl alcohol at room temperature (293.0 K) is cooled.When the temperature reaches 273.0 K the column of alcohol is 15.50 cm high.How tall was it when the temperature was 293.0 K? The coefficient of volume expansion of mercury is 1120 $\times$ 10^-6 K^-1. A) 15.85 cm B) 15.86 cm C) Cannot answer without knowing the diameter of the column D) 15.62 cm

Question

Quizplus · Accepted Answer

We can use the formula for volume expansion to find the initial height of the column:
V2/V1 = 1 + β(T2 - T1)
where V2 is the final volume, V1 is the initial volume, β is the coefficient of volume expansion, T2 is the final temperature, and T1 is the initial temperature.

We are given that T1 = 293 K and T2 = 273 K. Let's assume that the initial and final volumes are proportional to the heights of the column, so V2/V1 = h2/h1.

Substituting and simplifying:
h2/h1 = 1 + β(T2 - T1)
h2/h1 = 1 + (1120 x 10^-6 K^-1)(273-293)
h2/h1 = 1 - 0.0224
h2/h1 = 0.9776

Finally, we can solve for the initial height h1:
h1 = h2 / (0.9776) = 15.50 / 0.9776 = 15.86 cm.

Therefore, the answer is B, 15.86 cm.

A Glass Thermometer Using a Thin Column of Ethyl Alcohol ×\times×

A Glass Thermometer Using a Thin Column of Ethyl Alcohol $\times$