Solution:

Given data:

Weight of empty pycnometer = 2150 g

Weight of pycnometer + sand + water = 2150 + 400 = 2550 g

Weight of pycnometer + water = 1950 g

Specific gravity of soil (Gs) = 2.5

To find:

Water content in the soil

Calculation:

1. Mass of water in the pycnometer

Mass of water = Weight of pycnometer + sand + water – Weight of pycnometer

= 2550 – 2150

= 400 g

2. Mass of dry sand in the pycnometer

Mass of dry sand = Mass of pycnometer + sand – Mass of pycnometer

= 2550 – 2150 – 400

= 0 g

3. Volume of pycnometer

Volume of pycnometer = (Weight of pycnometer + water – Weight of pycnometer + empty) / Density of water

= (1950 – 2150) / 1 g/cm³

= 200 cm³

4. Volume of water

Volume of water = Mass of water / Density of water

= 400 / 1 g/cm³

= 400 cm³

5. Volume of solid

Volume of solid = Volume of pycnometer – Volume of water

= 200 – 400

= -200 cm³ (negative sign indicates that there is no solid in the pycnometer)

6. Bulk density of soil

Bulk density of soil (ρb) = Mass of pycnometer + sand / Volume of pycnometer

= 400 / 200

= 2 g/cm³

7. Dry density of soil

Dry density of soil (ρd) = Bulk density / (1 + Water content)

ρd = 2 / (1 + Water content)

8. Specific gravity of soil

Gs = (ρd / Density of water) + 1

2.5 = (ρd / 1) + 1

ρd = 1.5 g/cm³

9. Water content

ρd = (Mass of solid / Volume of solid) + (Mass of water / Volume of solid)

1.5 = (0 / -200) + (400 / -200)

Water content = -200 / 400

Water content = -0.5 or 50%

Therefore, the water content in the soil is 50%.

Explanation:

Pycnometer is a device used to determine the specific gravity and density of soil. It is a glass bottle with a tight-fitting stopper and a capillary tube through the stopper. In this problem, the weight of the empty pycnometer is given. The weight of the pycnometer filled with sand and water and the weight of the pycnometer filled with water are also given. From these weights, we can calculate the mass of water and dry sand in the pycnometer.

The volume of the pycnometer is calculated from the weight of the pycnometer filled with water. The volume of water is calculated from the mass of water. The volume of solid is calculated from the volume of the pycnometer and the volume of water. The bulk density of soil is