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Density of Water: Units, Values, Formulas & Applications

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Density of Water at Different Temperatures: Table & Conversion Guide

The density of water is a fundamental Physics concept that reflects how much mass is contained in a given volume of water. Understanding the standard value and unit conversions of water's density is crucial in solving problems related to fluids, buoyancy, and various practical experiments. The density of water is also an excellent reference point for comparing other substances and is frequently used in competitive exams and classroom learning.
Water's density is not only vital for theoretical Physics but also has practical roles in day-to-day applications, engineering, and environmental studies. Staying clear on its values and conversions ensures accuracy in all scientific contexts.


Definition of Density

Density is defined as the mass per unit volume of a substance. In Physics, this is a core property that helps explain the behavior of fluids, solids, and gases under different conditions.
Density determines whether an object will float or sink in a fluid. It is represented by the symbol "ρ" (rho).


Standard Value of Density of Water

The density of water at the standard condition is 1 g/cm³.
This means that one cubic centimeter (cm³) of water has a mass of one gram, under normal atmospheric pressure and at about 4°C.

For broader scientific and engineering usage, density is often converted into SI units, which is kilograms per cubic meter (kg/m³).
The conversion for water's density is:

  • 1 g/cm³ = 1000 kg/m³

So, the value of water's density commonly used in Physics is 1000 kg/m³.


Unit Value for Water
Gram per cubic centimeter (g/cm³) 1
Kilogram per cubic meter (kg/m³) 1000

Formula to Calculate Density

The basic formula to calculate density is:

  • Density (ρ) = Mass (m) / Volume (V)

Where,
ρ = density
m = mass
V = volume


Unit Conversion Example

Sometimes, you need to convert the density from one unit to another, especially in numerical problems. Here's a step-by-step example based on the reference data:

  1. Start with the value in g/cm³: 1 g/cm³
  2. Convert grams to kilograms (1 g = 0.001 kg) and centimeters to meters (1 cm = 0.01 m)
  3. Calculate:
    1 g/cm³ = 0.001 kg / (0.01 m)3 = 0.001 kg / 0.000001 m³ = 1000 kg/m³

Solved Example Problem

Question: What is the density of water in kg/m³ if its density is 1 g/cm³?

Solution:
1 g/cm³ = 1000 kg/m³.
Thus, the density of water in SI units is 1000 kg/m³.


Stepwise Approach for Density Problems

Step Action Example
1 Write the density formula Density = Mass / Volume
2 Plug in known quantities If water mass = 200 g
Volume = 200 cm³
3 Check units Are both in g and cm³?
4 Calculate 200 g / 200 cm³ = 1 g/cm³

Applications in Physics

Knowing the density of water is vital in understanding fluid statics, buoyancy, flotation of objects, hydrostatics, and other fluid mechanics concepts.
It also provides a direct reference for comparing densities of various substances and is essential in laboratory experiments.


Practice and Next Steps

  • Remember that 1 g/cm³ = 1000 kg/m³ for water under standard conditions.
  • Always convert all quantities to the same unit system before calculating density.
  • Practice simple problems to build accuracy in unit conversion and formula application.
  • Compare the density of water with substances like air or ice for deeper understanding.

Related Vedantu Resources

FAQs on Density of Water: Units, Values, Formulas & Applications

1. The value of density of water is ________.

The density of water at 4°C (standard temperature) is 1 g/cm³ or 1000 kg/m³. This is the commonly accepted value used in most Physics and exam problems, unless a different temperature is specified.

2. What is the SI unit of density?

The SI unit of density is kilogram per cubic metre (kg/m³).

  • In CGS system: gram per cubic centimetre (g/cm³)
  • For liquids, sometimes gram per millilitre (g/mL) is used

3. Is the density of water always 1 g/cm³?

No, the density of pure water is 1 g/cm³ only at 4°C.

  • At temperatures above or below 4°C, the density changes slightly.
  • For example, at 25°C, the density is about 0.997 g/cm³.
Always check the temperature specified in the problem.

4. How do you convert the density of water from g/cm³ to kg/m³?

To convert density from g/cm³ to kg/m³, multiply by 1000.

  • Example: 1 g/cm³ × 1000 = 1000 kg/m³
This is because 1 g = 0.001 kg and 1 cm³ = 0.000001 m³.
So, 1 g/cm³ = 1000 kg/m³.

5. What is the formula for density?

The formula for density (ρ) is:
Density (ρ) = Mass (m) / Volume (V)
Where:

  • ρ = density
  • m = mass
  • V = volume
This formula is used in all density calculations and Physics numerical questions.

6. Does the density of water depend on temperature?

Yes, the density of water changes with temperature.

  • The maximum density is at 4°C (1 g/cm³).
  • At higher or lower temperatures, density decreases slightly due to thermal expansion or contraction.
  • Always use the value corresponding to the specified temperature in exam problems.

7. What is the density of water at room temperature?

At room temperature (around 25°C), the density of water is approximately 0.997 g/cm³ or 997 kg/m³. This value is important for practical and laboratory calculations when temperature is not exactly 4°C.

8. What are the common units used for expressing the density of water?

The common units for density of water are:

  • kg/m³ (SI unit)
  • g/cm³ (CGS unit)
  • g/mL
  • lb/ft³ (Imperial unit)
  • lb/gal (US, sometimes in engineering)
Conversion between these units is frequently tested in exams.

9. Why is the density of water important in Physics and Engineering?

The density of water is a reference point in many Physics and Engineering problems because:

  • It is used to calculate buoyancy and Archimedes' principle.
  • It serves as a basis for specific gravity calculations of other substances.
  • It is essential for solving fluid mechanics and hydrostatics questions.
  • Standard lab experiments use water as the default reference.

10. Does salt or impurities change the density of water?

Yes, adding salt or impurities increases the density of water.

  • Pure (distilled) water has its highest density at 4°C.
  • Seawater is denser than pure water due to dissolved salts (density ≈ 1.025 g/cm³ at 20°C).
Always use correct values if the problem mentions seawater or impure water.

11. What is specific gravity in relation to water density?

Specific gravity is the ratio of the density of a substance to the density of water at 4°C.

  • For water at 4°C, specific gravity = 1
  • Specific gravity = (density of substance) / (density of water)
This is a dimensionless number commonly used in Physics and Chemistry.

12. How do you avoid mistakes in density unit conversions for exams?

Follow these steps to avoid unit conversion mistakes in density problems:

  1. Always write out the units for each value before calculation.
  2. Convert all quantities to the same unit system (preferably SI) before solving.
  3. Remember standard conversions: 1 g/cm³ = 1000 kg/m³, 1 mL = 1 cm³.
  4. Double-check calculations to ensure units cancel or result in correct density units.
Unit errors are a common source of mistakes in CBSE, NEET, and JEE exams.