Notes : Mercury Barometer | Construction, Working, Principle, Derivation, Formula

By -

Mercury Barometer Notes | Construction, Working, Principle, Derivation, Formula, MCQs & FAQs (NCERT Class 11 Physics) Chapter 9 Mechanical Properties of Fluids - Physics kund 

Mercury Barometer (NCERT Based Notes)

A Mercury Barometer is an instrument used to measure atmospheric pressure. It was invented by the Italian scientist Evangelista Torricelli in 1643. The mercury barometer is one of the most accurate instruments for measuring atmospheric pressure and is based on the principle of hydrostatic pressure.

In a mercury barometer, the atmospheric pressure acting on the mercury surface in the trough supports a column of mercury inside a glass tube. The height of this mercury column indicates the value of atmospheric pressure.

Definition of Mercury Barometer

Mercury Barometer: A mercury barometer is an instrument used to measure atmospheric pressure by balancing it against the pressure exerted by a column of mercury.

Construction of Mercury Barometer

A mercury barometer consists of the following parts:

  • A long, uniform glass tube closed at one end.
  • The tube is completely filled with pure mercury so that no air bubbles remain inside it.
  • The open end of the tube is temporarily closed with a thumb or stopper.
  • The tube is then inverted carefully into a trough containing mercury.
  • After the open end is immersed in mercury, the thumb or stopper is removed.
  • Some mercury flows from the tube into the trough.
  • The mercury finally comes to rest at a height \(h\) above the mercury level in the trough.
  • The space above the mercury column contains almost no air except negligible mercury vapours. This space is called the Torricellian Vacuum.
  • A graduated scale is attached alongside the glass tube to measure the height of the mercury column.

Principle of Mercury Barometer

A mercury barometer works on the principle that the atmospheric pressure acting on the mercury surface in the trough is balanced by the hydrostatic pressure due to the mercury column inside the tube.

Mathematically,

\[ P_a=\rho hg \]

where,

  • \(P_a\) = Atmospheric pressure
  • \(\rho\) = Density of mercury
  • \(h\) = Height of mercury column
  • \(g\) = Acceleration due to gravity

Working of Mercury Barometer

When the mercury-filled glass tube is inverted into the mercury trough, some mercury flows downward because of its weight.

As mercury falls, an empty space is formed above the mercury column. This space is known as the Torricellian Vacuum.

The atmospheric pressure acts on the free surface of mercury in the trough and pushes mercury upward into the tube.

The mercury column finally becomes stationary when the upward force due to atmospheric pressure becomes exactly equal to the downward weight of the mercury column.

Thus, the atmospheric pressure is measured by the height of the mercury column.

If atmospheric pressure increases, the mercury column rises. If atmospheric pressure decreases, the mercury column falls.

Derivation of the Mercury Barometer Equation

Let,

  • \(A\) = Cross-sectional area of the glass tube
  • \(h\) = Height of the mercury column
  • \(\rho\) = Density of mercury
  • \(g\) = Acceleration due to gravity
  • \(P_a\) = Atmospheric pressure

Step 1: Calculate the Weight of the Mercury Column

The volume of the mercury column is

\[ V = Ah \]

Therefore, the mass of the mercury column is

\[ m = \rho V = \rho Ah \]

Hence, the weight of the mercury column is

\[ W = mg = \rho Ahg \]

Step 2: Calculate the Upward Force Due to Atmospheric Pressure

Atmospheric pressure acts on the mercury surface in the trough.

The upward force is

\[ F = P_aA \]

Step 3: Condition of Equilibrium

When the mercury column becomes stationary, the upward force due to atmospheric pressure is equal to the downward weight of the mercury column.

\[ P_aA = \rho Ahg \]

Dividing both sides by \(A\), we get

\[ \boxed{P_a = \rho hg} \]

This is the fundamental equation of a mercury barometer.

Standard Atmospheric Pressure

At sea level, the average atmospheric pressure is called standard atmospheric pressure.

The standard values are:

  • Height of mercury column, \(h = 76\,\text{cm} = 0.76\,\text{m}\)
  • Density of mercury, \(\rho = 13.6 \times 10^3\,\text{kg m}^{-3}\)
  • Acceleration due to gravity, \(g = 9.8\,\text{m s}^{-2}\)

Using the equation

\[ P_a = \rho hg \]

\[ P_a = (13.6 \times 10^3)(0.76)(9.8) \]

\[ \boxed{P_a = 1.013 \times 10^5\,\text{Pa}} \]

Therefore,

\[ \boxed{1\,\text{atm} = 1.013 \times 10^5\,\text{Pa}} \]

Why is Mercury Used in a Barometer?

  • Mercury has a very high density, so only a 76 cm column is required. If water were used, the column would have to be about 10.3 m high.
  • Mercury has a very low vapour pressure, so the space above the mercury column remains almost a perfect vacuum.
  • Mercury does not wet the glass tube, giving a clear and accurate mercury level.
  • Its shiny surface makes the mercury level easy to observe.
  • Mercury remains in the liquid state over a wide range of temperatures, making it suitable for accurate measurements.

Advantages of a Mercury Barometer

  • Measures atmospheric pressure with high accuracy.
  • Simple construction and easy principle of operation.
  • Provides reliable and stable readings.
  • Does not require frequent calibration.
  • Widely used as a standard instrument for pressure measurement.

Limitations of a Mercury Barometer

  • Mercury is poisonous and must be handled carefully.
  • The glass tube is fragile and can break easily.
  • It is bulky and difficult to transport.
  • It cannot be used conveniently in moving vehicles because the mercury oscillates.
  • Readings may be affected if the instrument is not kept vertical.

Important Points to Remember

  • A mercury barometer is used to measure atmospheric pressure.
  • It was invented by Evangelista Torricelli in 1643.
  • The empty space above the mercury column is called the Torricellian Vacuum.
  • The atmospheric pressure is given by

\[ \boxed{P_a=\rho hg} \]

  • At sea level, the height of the mercury column is 76 cm.
  • Standard atmospheric pressure is

\[ \boxed{1\,\text{atm}=1.013\times10^5\,\text{Pa}} \]

  • The height of the mercury column increases when atmospheric pressure increases and decreases when atmospheric pressure decreases.
  • The pressure at the top of the mercury column is nearly zero because it is a Torricellian vacuum.

Frequently Asked Questions (FAQ)

Q1. What is a mercury barometer?

Answer: A mercury barometer is an instrument used to measure atmospheric pressure.

Q2. Who invented the mercury barometer?

Answer: Evangelista Torricelli invented the mercury barometer in 1643.

Q3. What is the Torricellian Vacuum?

Answer: The nearly empty space above the mercury column containing negligible mercury vapours is called the Torricellian Vacuum.

Q4. On what principle does a mercury barometer work?

Answer: It works on the principle that atmospheric pressure is balanced by the hydrostatic pressure of the mercury column.

Q5. Why is mercury used instead of water?

Answer: Mercury has a high density, low vapour pressure, and does not wet glass, making it ideal for barometers.

Q6. What is the standard atmospheric pressure?

Answer: Standard atmospheric pressure is \(1.013 \times 10^5\,\text{Pa}\) or 1 atmosphere (1 atm).

Q7. What is the height of the mercury column at sea level?

Answer: The height of the mercury column at sea level is 76 cm (0.76 m).

Q8. Write the formula for atmospheric pressure.

Answer:

\[ \boxed{P_a=\rho hg} \]

Multiple Choice Questions (MCQs)

1. A mercury barometer is used to measure:

A) Temperature
B) Atmospheric Pressure
C) Density
D) Humidity

Answer: B) Atmospheric Pressure

2. Who invented the mercury barometer?

A) Newton
B) Pascal
C) Torricelli
D) Galileo

Answer: C) Torricelli

3. The empty space above the mercury column is called:

A) Air Chamber
B) Vacuum Chamber
C) Torricellian Vacuum
D) Atmospheric Space

Answer: C) Torricellian Vacuum

4. The atmospheric pressure is given by:

A) \(P=\rho hg\)
B) \(P=mg\)
C) \(P=F/m\)
D) \(P=\rho V\)

Answer: A) \(P=\rho hg\)

5. The standard height of the mercury column at sea level is:

A) 50 cm
B) 76 cm
C) 100 cm
D) 120 cm

Answer: B) 76 cm

6. The SI unit of pressure is:

A) Joule
B) Pascal
C) Newton
D) Watt

Answer: B) Pascal

Fill in the Blanks

  1. A mercury barometer measures atmospheric pressure.
  2. The mercury barometer was invented by Evangelista Torricelli.
  3. The empty space above the mercury column is called the Torricellian Vacuum.
  4. The height of the mercury column at sea level is 76 cm.
  5. The atmospheric pressure is given by \(P=\rho hg\).
  6. The SI unit of pressure is Pascal (Pa).
  7. Mercury is preferred because of its high density.
  8. Standard atmospheric pressure is \(1.013\times10^5\) Pa.

True or False

1. A mercury barometer measures atmospheric pressure. True

2. Mercury wets the glass tube. False

3. The space above the mercury column is called the Torricellian Vacuum. True

4. Atmospheric pressure depends upon the height of the mercury column. True

5. The pressure at the top of the mercury column is nearly zero. True

6. Mercury has a lower density than water. False

7. A mercury barometer can easily be used in moving vehicles. False

8. One atmosphere is equal to \(1.013\times10^5\) Pa. True

Very Short Answer Questions

Q1. What is a mercury barometer?

Answer: An instrument used to measure atmospheric pressure.

Q2. Who invented the mercury barometer?

Answer: Evangelista Torricelli.

Q3. What is the SI unit of pressure?

Answer: Pascal (Pa).

Q4. What is the Torricellian Vacuum?

Answer: The nearly empty space above the mercury column.

Q5. Write the formula for atmospheric pressure.

Answer: \(P=\rho hg\).

Short Answer Questions

Q1. Explain the construction of a mercury barometer.

Answer: A long glass tube closed at one end is completely filled with mercury and inverted into a mercury trough. Some mercury flows down into the trough, leaving a mercury column inside the tube. The space above the mercury column is called the Torricellian Vacuum.

Q2. Explain the working of a mercury barometer.

Answer: Atmospheric pressure acts on the mercury in the trough and supports the mercury column inside the tube. The column becomes stationary when atmospheric pressure balances the weight of the mercury column.

Q3. Why is mercury used in a barometer?

Answer: Mercury has high density, low vapour pressure, does not wet glass, and provides accurate readings.

Long Answer Questions

Q1. Describe the construction, working and principle of a mercury barometer.

Answer: Explain the construction of the instrument, the formation of the Torricellian Vacuum, the action of atmospheric pressure on the mercury in the trough, and how equilibrium is achieved. Finally, derive the equation:

\[ \boxed{P_a=\rho hg} \]

Q2. Derive the expression for atmospheric pressure using a mercury barometer.

Answer: Let the cross-sectional area of the tube be \(A\), height of mercury column be \(h\), density of mercury be \(\rho\), and acceleration due to gravity be \(g\). The upward force due to atmospheric pressure is \(P_aA\), while the downward weight of the mercury column is \(\rho Ahg\). At equilibrium,

\[ P_aA=\rho Ahg \]

Dividing both sides by \(A\),

\[ \boxed{P_a=\rho hg} \]

Key Formulae

Atmospheric Pressure:

\[ \boxed{P_a=\rho hg} \]

Standard Atmospheric Pressure:

\[ \boxed{1\,\text{atm}=1.013\times10^5\,\text{Pa}} \]

Height of Mercury Column at Sea Level:

\[ \boxed{h=76\,\text{cm}=0.76\,\text{m}} \] bhi

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