Notes : Density and Relative Density , Definition, Dimensions and Units

By -

Study Density and Relative Density Class 11 Physics with complete NCERT notes. Learn density, relative density, SI unit, dimensional formula, density of liquids and gases, common fluid densities, formulas, FAQs, MCQs, true/false, fill in the blanks, and important questions for CBSE, NEET & JEE.- Physicskund

Density

Density is one of the most important physical quantities used to describe fluids. It is defined as the mass contained in unit volume of a substance. Density helps in comparing different substances and determines whether a substance will float or sink in a fluid.

Definition of Density

Density of a substance is defined as the ratio of its mass to its volume.

$$ \rho=\frac{m}{V} \qquad ...(1) $$

where,

  • \(\rho\) = Density of the substance
  • \(m\) = Mass of the substance
  • \(V\) = Volume occupied by the substance

Definition

Density is the mass per unit volume of a substance.

Physical Meaning of Density

Density indicates how much mass is contained in a unit volume of a substance.

  • A substance with higher density contains more mass in the same volume.
  • A substance with lower density contains less mass in the same volume.

Nature of Density

Density is a positive scalar quantity. It has magnitude only and no direction.

Dimensional Formula of Density

The dimensional formula of density is

$$ [ML^{-3}] $$

SI Unit of Density

The SI unit of density is kilogram per cubic metre (kg m-3).

$$ \mathrm{SI\ Unit}=kg\,m^{-3} $$

Important Points

  • Density is an important physical property of every substance.
  • Different substances have different densities.
  • The density of a substance depends upon its mass and volume.
  • Density is widely used in the study of fluids and fluid mechanics.

Density of Liquids and Gases

Density is an important property used to describe fluids. The density of liquids and gases behaves differently when pressure changes.

Density of Liquids

Liquids are nearly incompressible. Therefore, their density remains almost constant even when pressure changes.

Density of Gases

Gases are compressible. Therefore, their density changes considerably with changes in pressure.

Density of Water

The density of pure water is maximum at 4°C (277 K).

$$ \rho_{\text{water}}=1.0\times10^{3}\ \mathrm{kg\,m^{-3}} \qquad ...(2) $$

Relative Density (Specific Gravity)

Relative density is defined as the ratio of the density of a substance to the density of water at 4°C (277 K).

$$ \text{Relative Density} = \frac{\text{Density of the substance}} {\text{Density of water at }4^\circ\mathrm{C}} \qquad ...(3) $$

Properties of Relative Density

  • Relative density is a dimensionless quantity.
  • It has no SI unit.
  • It is a positive scalar quantity.

Example

The relative density of aluminium is 2.7.

Therefore, the density of aluminium is

$$ \rho_{\text{Al}} = 2.7\times10^{3}\ \mathrm{kg\,m^{-3}} \qquad ...(4) $$

Densities of Some Common Fluids at STP

Fluid Density ($$\mathrm{kg\,m^{-3}}$$)
Water $$1.00\times10^{3}$$
Sea Water $$1.03\times10^{3}$$
Mercury $$13.6\times10^{3}$$
Ethyl Alcohol $$0.806\times10^{3}$$
Whole Blood $$1.06\times10^{3}$$
Air $$1.29$$
Oxygen $$1.43$$
Hydrogen $$9.0\times10^{-2}$$
Interstellar Space $$\approx10^{-20}$$

Important Formulae

Density

$$ \rho=\frac{m}{V} $$

Relative Density

$$ \text{Relative Density} = \frac{\text{Density of the substance}} {\text{Density of water at }4^\circ\mathrm{C}} $$

Key Points

  • Density is the mass per unit volume of a substance.
  • Liquids are nearly incompressible; therefore, their density changes very little with pressure.
  • Gases are compressible; therefore, their density changes significantly with pressure.
  • The density of water at 4°C is $$1.0\times10^{3}\ \mathrm{kg\,m^{-3}}$$.
  • Relative density has no unit because it is the ratio of two densities.
  • The relative density of aluminium is 2.7.

Frequently Asked Questions (FAQs)

1. What is density?

Density is the mass per unit volume of a substance.

2. What is the SI unit of density?

The SI unit of density is kilogram per cubic metre (kg m-3).

3. Why is density a scalar quantity?

Density has magnitude only and no direction; therefore, it is a scalar quantity.

4. What is relative density?

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

5. Why does relative density have no unit?

Relative density is the ratio of two quantities having the same unit, so the units cancel out.

6. What is the density of water at 4°C?

$$ \rho_{\text{water}}=1.0\times10^{3}\ \mathrm{kg\,m^{-3}} $$

Multiple Choice Questions (MCQs)

1. Density is defined as

A. Volume per unit mass
B. Mass per unit volume
C. Force per unit area
D. Weight per unit volume

Answer: B. Mass per unit volume

2. The SI unit of density is

A. kg
B. N m-2
C. kg m-3
D. g cm-2

Answer: C. kg m-3

3. Density is a

A. Vector quantity
B. Scalar quantity
C. Tensor quantity
D. None of these

Answer: B. Scalar quantity

4. The density of water at 4°C is

A. $$100\ \mathrm{kg\,m^{-3}}$$
B. $$1.0\times10^{3}\ \mathrm{kg\,m^{-3}}$$
C. $$10^{4}\ \mathrm{kg\,m^{-3}}$$
D. $$13.6\times10^{3}\ \mathrm{kg\,m^{-3}}$$

Answer: B. $$1.0\times10^{3}\ \mathrm{kg\,m^{-3}}$$

5. Relative density is

A. A quantity with SI unit
B. A dimensionless quantity
C. Equal to density
D. A vector quantity

Answer: B. A dimensionless quantity

True or False

1.

Density is a scalar quantity. True

2.

Liquids are nearly incompressible. True

3.

Gases are incompressible. False

4.

Relative density has an SI unit. False

5.

The density of water at 4°C is $$1.0\times10^{3}\ \mathrm{kg\,m^{-3}}$$. True

Fill in the Blanks

1.

Density is __________ per unit volume.

Answer: Mass

2.

The SI unit of density is __________.

Answer: kg m-3

3.

Relative density is a __________ quantity.

Answer: Dimensionless

4.

Liquids are nearly __________.

Answer: Incompressible

5.

The density of water at 4°C is __________.

Answer: $$1.0\times10^{3}\ \mathrm{kg\,m^{-3}}$$

Very Short Answer Questions

1. Define density.

Density is the mass per unit volume of a substance.

2. Write the formula for density.

$$ \rho=\frac{m}{V} $$

3. Write the SI unit of density.

kg m-3

4. Is density a scalar or vector quantity?

Density is a scalar quantity.

5. Define relative density.

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

Short Answer Questions

1. Define density.

Density is the mass per unit volume of a substance.

$$ \rho=\frac{m}{V} $$

2. Why is density a scalar quantity?

Density has only magnitude and no direction; therefore, it is a scalar quantity.

3. Why do liquids have nearly constant density?

Liquids are nearly incompressible, so their density changes very little with pressure.

4. Define relative density.

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

$$ \text{Relative Density} = \frac{\text{Density of the substance}} {\text{Density of water at }4^\circ\mathrm{C}} $$

5. Why is relative density dimensionless?

It is the ratio of two densities having the same unit; therefore, the units cancel out.

Long Answer Questions

1. Define density and derive its expression.

Density is defined as the mass per unit volume of a substance. If a substance has mass m and volume V, then its density is

$$ \rho=\frac{m}{V} $$

2. Explain the difference between the density of liquids and gases.

Liquids are nearly incompressible, so their density remains almost constant with pressure. Gases are compressible; therefore, their density changes considerably with pressure.

3. Define relative density and explain why it has no unit.

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

$$ \text{Relative Density} = \frac{\text{Density of the substance}} {\text{Density of water at }4^\circ\mathrm{C}} $$

Since it is the ratio of two quantities having the same unit, it is dimensionless and has no SI unit.

4. State the SI unit and dimensional formula of density.

The SI unit of density is kg m-3.

The dimensional formula is

$$ [ML^{-3}] $$

Comments

Post a Comment

Popular posts from this blog

NCERT Solution Class 10 Science Chapter 11 Electricity -

By -
Image
NCERT Exercise Solution Class 10 Science Chapter 11 Electricity  Example 11.1 A current of 0.5 A is drawn by a filament of an electric bulb for 10 minutes. Find the amount of electric charge that flows through the circuit. Solution: Given  I = 0.5 A ,   t = 10 min = 600 s. We have Q = It = 0.5 A × 600 s = 300 C Page Number 172 – Question with solution 1 to 3 : 1. What does an electric circuit mean? Solution : It is a continuous and closed path through which electric current flows. It contains different components like • Cell or Battery Plug Key • Wires • Electric Components (like Ammeter,Voltmeter) • Bulb etc  2. Define the unit of current. Solution :  The unit of electric current is ampere (A). I  = $\frac{Q}{t}$ When Q = 1 C and t = 1 sec then I = $\frac{1C}{1S}$ I = 1A 1 A is defined as the flow of 1 C of charge through a wire in 1 s. 3. Calculate the number of electrons constituting one coulomb of charge. Solution :  We know  Q...
Read more

Ncert Solution CBSE Class 11 Chapter 10 THERMAL PROPERTIES OF MATTER

By -
Image
Ncert Solution CBSE Class 11 Chapter 10 THERMAL PROPERTIES OF MATTER - 10.1 The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales. Solution :  On Celsius scale  t(°C) = T(K) - 273.15 Triple point of neon = 24.57 - 273.15 = - 248.58°C Triple point of carbon dioxide = 216.55 - 273.15 = -56.6°C On Fahrenheit scale  $t(^{o}F) = \frac{9} {5} (t^{o}C)+32$ Triple point of neon = $\frac{9} {5} (-248.58)+32$  Triple point of neon= -447.444+32=-415.44°F Triple point of carbon dioxide = $\frac{9} {5} (-56.6)+32$  Triple point of carbon dioxide = - 101.88 +32 = -69.88°F 10.2 Two absolute scales A and B have triple points of water defined to be 200 A and 350B. What is the relation between $T_{A}$ and $T_{B}$? Solution :  Triple point of  water in  absolute scale A = 200A absolute scale B = 350 B Temperature on Kelvin scale = 273.16K 200A = 273.16K $1A = \frac{273.16}{...
Read more

NCERT Solutions for Class 11 Physics Chapter 11 Thermodynamics

By -
Image
NCERT Solutions for Class 11 Physics Chapter 11 Thermodynamics 11.1 A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is $4.0 × 10^{4} J/g$ ?  Solution:   Given  Mass of flowing water , m = 3.0 litre/ min = 3000 g/min The geyser heats the water , raising the temperature from 27 °C to 77 °C. Initial temperature, $T_{1}$ = 27°C Final temperature $T_{2}$ = 77°C Rise in temperature ,  $T = T_{2} -  T_{1}$ = 77-27= 50°C Heat of combustion =$ 4.0 × 10^{4} J/g$ Specific heat of water , $c= 4.2 J/g^{o}C$ Total heat used ,  $$Q = mcT$$ $$Q = 3000 \frac{g}{min} \times 4.2 \frac{J}{g^{o}C}\times 50^{o}C$$ $$Q = 6.3 × 10^{5}J/ min$$ $$Rate \ of \ consumption = \frac{6.3 \times 10^{5}}{(4 \times 10^{4})}$$ $$= 15.75 g/min$$ Therefore, rate of consumption is 15.75 g/min 11.2 What amount of heat must be supplied to $2.0 × 10^{–...
Read more