Question 18 of 18intermediate🔧 ApplyNumerical3 marks

A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit?

Correct Answer

The specific gravity of spirit is 0.8.

Exercise: EXERCISES | Q: 9.9 | (Chapter: 21)
For More Understanding

Explanation

This is a straightforward application of the principle that when two liquids are in equilibrium separated by mercury, the pressures exerted by both liquid columns at the mercury interface must be equal. Since the mercury columns are in level, the pressure due to the water column equals the pressure due to the spirit column. Using the relationship between density, height, and pressure, we can find the specific gravity of spirit.

Solution Steps

  1. Step 1: Since the mercury columns in both arms are in level, the pressure exerted by the water column equals the pressure exerted by the spirit column at the mercury interface.

  2. Step 2: Pressure due to water column = Pressure due to spirit column

    ρw⋅g⋅hw=ρs⋅g⋅hs\rho_w \cdot g \cdot h_w = \rho_s \cdot g \cdot h_s

    where ρw\rho_w = density of water, ρs\rho_s = density of spirit, hwh_w = 10.0 cm, hsh_s = 12.5 cm.

  3. Step 3: Since gg cancels out:

    ρw⋅hw=ρs⋅hs\rho_w \cdot h_w = \rho_s \cdot h_s

    ρs=ρw⋅hwhs=ρw⋅10.012.5=ρw⋅0.8\rho_s = \rho_w \cdot \frac{h_w}{h_s} = \rho_w \cdot \frac{10.0}{12.5} = \rho_w \cdot 0.8

  4. Step 4: Specific gravity of spirit = ρsρw=0.8\frac{\rho_s}{\rho_w} = 0.8

    The specific gravity of spirit is 0.8.

Previous