Question 6 of 18intermediate🔧 ApplyNumerical3 marks

Toricelli's barometer used mercury. Pascal duplicated it using French wine of density 984 kg m⁻³. Determine the height of the wine column for normal atmospheric pressure.

Correct Answer

The height of the wine column for normal atmospheric pressure is approximately 10.5 m.

Exercise: EXERCISES | Q: 9.6 | (Page 21)
For More Understanding

Explanation

This numerical problem applies the barometer principle from the textbook. The atmospheric pressure supports a column of liquid, and the relationship is given by Equation (9.8): Pa = ρgh. Using the normal atmospheric pressure of 1.013×101.013 \times 10⁵ Pa (stated in context as 1 atm, equivalent to 76 cm of mercury) and the wine density of 984 kg m⁻³, we calculate the wine column height. The much lower density of wine compared to mercury results in a significantly taller column.

Solution Steps

  1. Step 1: Identify given values - Atmospheric pressure Pa = 1.013×101.013 \times 10⁵ Pa, Density of wine ρ = 984 kg m⁻³, g = 9.8 m s⁻²

  2. Step 2: Apply the pressure formula from Equation (9.8): Pa = ρgh

  3. Step 3: Rearrange to solve for height: h = Pa/(ρg)

  4. Step 4: Substitute values: h = (1.013×101.013 \times 10⁵)/(984×9.8984 \times 9.8)

  5. Step 5: Calculate: h = 101300/9643.2 = 10.51 m ≈\approx 10.5 m

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