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3.3 Pressure In Gas

The basic assumptions of kinetic molecular theory

1. Gases are made of tiny,individual particles. The volume of the particles themselves is insignificant  compared with the volume occupied by the gas; therefore gases are mostly empty space.

 

2. Gas particles move rapidly and randomly in straight-line motion. Particles collide with one another  and with the walls of the container in elastic collisions (no overall loss or gain of energy)

 

3.  Individual particles are far apart and have very little attraction for each other . Particles are consider to move independently of each other.

4. The average kinetic energies of particles of different gasses are equal at given temperature.

5. The average kinetic energies of gas particles increase as the temperature increases.

 

Existence of Gas pressure based on the kinetic theory

1. Based on the kinetic molecular theory, gas molecules move freely and randomly.

2. The gas molecules collide with one another and also collide with the walls of their container.

3. The collision of gas molecules with one another is an elastic collision (no overall loss or gain of energy).

4. The collision of gas molecules with the wall of the container produces change of momentum or impulsive force

5. So the gas molecules exert a pressure on the inside of the container because pressure is force per unit area ( P = F )

                                                      A

The conclusion  about gas pressure

Gas pressure is the force  per unit area exerted by the gas molecules as they collide with the walls of their container.

What happen if the volume  inside  a container  decreases?

 

(1)    The number of the gas molecules remain unchanged

(2)     The number of the gas molecules per unit volume ncrease The number Bilangan molekul,ketumpatan molekul,saiz molekul adalah tetap.

(3)    The volume of the gas molecules  remain unchanged

(4)     The size of the gas molecules  remain unchanged

(5)    The density of the gas molecules  remain unchange                                                                                                                                                                     

(6)    The duration of the collision between the gas   

          molecules  with the walls of the container

          decrease

(7)     The frequency of collisions between the gas

          molecules with the walls of the container

          increase

(8)     The density of the gas increases

 (9)     The pressure of the gas increases

 

What happen if the number of gas molecules in a container increase?

 

(1)     The collision rate between the gas molecules with the walls of container increase

(2)     The pressure of the gas increases

 

What happen if the container is heated?

 

(1)    The average velocity of the gas molecules increase

(2)     The kinetic energy of the gas molecules increase

(3)     The collision rate between the gas molecules with the walls of container increase

(4)     The force of collisions between the gas molecules  with the walls of container increase

(5)     The pressure of the gas increases 

Measuring Gas Pressure

(i)            Manometer

A manometer consists of a U-shaped glass tube filled with liquid- normally liquid.

Water is used in a manometer to measure low gas pressure.

One arm of the manometer is exposed to the atmosphere whereas another arm is connected to gas supply.

There are three possible methods to read the pressure of a gas by using the manometer when the tap is opened.

(i)

            clip_image002

                Pgas  =  Patmosfera +  h

 

                (ii)          

                     clip_image004   

 

      Pgas  =  Patmosfera   h

(iii)

          clip_image006

 

     Pgas  =  Patmosfera 

 

Example 1

The figure shows a manometer containing mercury is connected to a gas supply.

 

clip_image008

Calculate the pressure of the gas supply in the units

(i) cm Hg

(ii) Pa

[ Density of mercury = 1.36 x 104 kg m-3 and   Atmospheric pressure = 76 cm Hg ]

Solution

 

 

 

 

 

 

(ii)           Bourdon Gauge

clip_image010

               

When the gas supply is connected to a Bourdon gauge, the pressure in the curved metallic tube will try to straighten it.

Hence the pointer will rotate.

The magnitude of the gas pressure can be read off the scale of the gauge.

The another use of U-Tube

The U-tube can also be used to determine the density of a liquid.

 

clip_image012

 

                                Pressure P1    =    Pressure P2

                                                h1r1g     =     h2r2g    

                                         h1r1     =     h2r2  

 Example 2

 

The figure shows a U-tube use to determine the density of  a liquid K. When liquid K is poured into one arm, the water level in the other  arm rises.

 

clip_image014

 

                If the density of water is 1 000 kg m-3, determine the density of liquid K.

 

                Solution

 

 

 

Atmospheric pressure

Existance of Atmosheric

According to kinetic molecular theory , gases consistof molecules which are apart and in random motion at high speeds.

The gas molecules possess mass and experience the pull of gravity. The result is that gases have weight.

The weight of the gas molecules will produce force and as a result will exert pressure on you because pressure is force per area ( P = F )

                                                   A

The pressure is called as at the atmospheric pressure.

 

Characteristics  of Atmospheric Pressure

 

Atmospheric  pressure acts equally in all directions.

The atmospheric pressure on any object is not dependent on the surface area of the object.

Atmospheric pressure is influenced by the height of an object above the sea level ( altitude).

Hence as the altitude increases , the atmospheric pressure decreases because the higher it is from the surface of the Earth , the lower is the density  of air.

We do not experience the atmospheric pressure at sea level  because the pressure of body equal to the atmospheric pressure.

The atmospheric pressure at sea level is approximately  1 atm = 1x 105 Pa =  76 cm Hg

 = 10 m of water.

 

Example 3

The atmospheric pressure is 76 cm Hg. Calculate the atmospheric pressure in the units Pa.

[Density of mercury =  1.36 x104  kg m-3 ].

 

Solution  

Example 4

 

The atmospheric pressure at the sea level 760 mm Hg , while the atmospheric preesure on the top of a mountain is 600 mm Hg. If the density of mercury is 1.36 x 104 kg m-3 and the average density of the air is 1.25 kg m-3 , estimate the height of the mountain.

Solution

 

 

Activities to show the existence of atmospheric pressure.

Activity 1

clip_image016

Fill the glass to the top with water and wet rim slightly.

Lie the cardboard  on the top of the glass.

Hold the card firmly in place and turn the glass over.

Take away your hand.

The cardboard does not fall and the water remains in the glass.

The explanation for this phenomenon is that  the resultant force caused by the atmospheric pressure acts on the surface of the cardboard is greater than the weight of the water in the glass.

 

Activity 2

clip_image018

 

A metal can containing water is heated until the water in it vaporizes.

Allow the steam  to exit from the mouth of the can.

The can is then capped and cooled down with tap water.

As the result , the can is crushed and crumpled.

The explanation for this phenomenon is that  the pressure inside the metal can decrease  and the external atmospheric pressure ,which is higher compresses the metal can.

 

Measuring atmospheric pressure

(i)The Simple  Fortin barometer

The simple barometer Fortin is along glasstube that has been filled with mercury and the inverted into a dish of mercury.

The mercury column rises or falls according to the pressure of air on the mercury in the dish.

The space above the mercury column isa vacuum so it exerts no pressure on the top of the mercury column.

clip_image020

If the vertical height of the mercury is h cm ,

thefore  the  atmospheric pressure  reading is

“ h cm mercury  ”.

 

How does the height ,h vary?

 

The height, h will remains uchanged when

(i)            the diameter of the glass tube increases

(ii)           the glass tube is tilted

(iii)    the glass tube is lowered  further into the dish

(iv)    the glass tube is lifted up from the dish

(iv)           the quantity of mercury in the dish is increased

 

The height, h will  increases when the barometer is slowly submerged in water.

 

The height, h will decreases when

(i)      the vacuum space in the glass tube is filled with gas

(ii)           the barometer is carried out to a montain

Example 4

The figure shows a mercury barometer is placed in a school laboratory where the atmospheric pressure is 75 cm Hg.

 

clip_image022

(a)           What is the value of  h

(b)     What is the length of the vacuum space when the glass tube is

         (i)   uplifted at height of  5 cm

         (ii)   lowered  further into the dish at a depth of  4 cm

(c)    If the density of mercury is 1.36 x 104 kgm-3 and the density of water is 1 x 103 kgm3, 

       determine

         (i)   the atmospheric pressure in the units Pa

        (ii)   the value of h if the mercury is replaced by water.

(iii)   the value of h if  the barometer is submerged in water at depth of 40.8 cm.

 

Solution

 

 

 

Example  5

 

The figure shows a barometer. The vacuum space is filled with a gas X.

clip_image024

What is the pressure of the gas X?

[ Take atmospheric pressure = 76 cm Hg ]

 

Solution

Aneroid Barometer

clip_image026

 

When the atmospheric pressure decreases , the container will expand.

When the atmospheric pressure increases, the container will constrict.

The slight movement of the box is magnified by a lever system which is connected to a pointer.

The Aneroid barometer can be used as an altimeter by mountaineers or in an aeroplane to determine its altitude.

Applications of Atmospheric Pressure

(i) Drinking straw

clip_image028

When we suck through a straw ,the air pressure in the straw is lowered. Then the pressure of the atmosphere acting on the surface  of the drink in the glass pushes the water up the straw and into our mouth.

(ii) Rubber sucker

.clip_image030

 

When the sucker is pressed into place, most of  the air behind it is squeezed out. The sucker is held in position by the pressure of atmosphere on the outside surface of the rubber. If the seal between the sucker and the surface is airtight , the sucker will stick permanently.

(iii) Syringe

clip_image032

 

Pulling up the piston reduces the atmospheric pressure inside the cyclider. The atmospheric pressure on the liquid surface then pushes the luquid up into the syringe.

If we then hold the plunger in place and lift the syringe out of liquid , none will fall out. This is again due to atmospheric pressure .

(iv)Vacuum cleaner

clip_image034

 

A vacuum cleaner produces only  a partial vacuum. The fan inside the cyclinder blows air out  of the vents. Which less air inside , the air pressure there drops. The atmospheric pressure outside then pushes air up the cleaner hose ,carrying dust and dirt with it.

(v) Lift pump

              clip_image036

 

When the plunger is lifted ,valve A closes and valve B opens. The atmospheric pressure ,acting on the surface of the water ,causes water to flow past valve B into the cylinders .

When the plunger is pushed down ,valve B closes and valve A opens.Water flows above the plunger.

When the plunger is next lifted,valve A closes and valve B opens . The atmospheric pressure ,acting on the surface of the water ,forces water past valve B into the cyclinder. Simultaneously ,the water above the plunger is lifted and flows out  through the mouth.

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