Simple Kinetic Molecular Model of Matter

IGCSE Cambridge Syllabus Area 2.1

.1       States of Matter – Solids, Liquids and Gases

State the distinguishing properties of solids,
liquids and gases (in terms of simple kinetic molecular model of matter)

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Matter can be in 3 possible states: solids, liquids or gaseous states.

In solids: the constituent particles are closely packed in regular / lattice arrangement and vibrating in fixed position - the higher the temperature, the more vigorous the vibration and vice versa. Solids have fixed volumes and fixed shapes

In liquids: the constituent particles are no longer in  regular arrangement - they are constantly translating past each other. Liquids have fixed volume and take the same of their containers.

In gases: the constituent particles are far apart and they move randomly in straight lines in all direction, colliding with each other and with the walls of their containers in the process. The higher the temperature, the higher the kinetic energy of the particles.


.2 Molecular Model (of Matter)

1.    Matter is made up of tiny particles which can be: mono-atomic (as in noble gases like helium, He), molecular (as in water, H₂O; oxygen, O₂; nitrogen, N_2;  etc) or (as in common salt, sodium chloride, NaCl). The atoms that make up the particles of each substance are unique in terms of: the type of atoms and the ratio they bear to each other - eg. the particles of water are made up of hydrogen and oxygen atoms in the ration of 2:1 whatever the states (solid, liquid or gaseous) that water is in.

2.    The particles of matter are too tiny to be seen with our naked eyes - however, they can only be seen with the aid of instruments such as electron microscope. Nevertheless, their random nature of motion can be indirectly seen with normal microscope: When large smoke particles are in suspension in air in a glass cell or smoke chamber or larger pollen grains are in suspension in liquid water and seen through normal microscope, these larger particles can be seen as moving around haphazardly - in what is known as Brownian motion - due to random bombardments by the tiny but fast-moving energetic particles of the air or liquid water, whichever is applicable. 

3.    Depending on its temperature, a substance can exist either in solid, liquid and/or gaseous states. In solid state, its temperature is lower than that in liquid state; and in gaseous state, its temperature is even higher.

4.    The melting or freezing point of a substance refers to the temperature (under normal atmospheric pressure) below which the substance exists as a solid; and at which, the substance changes state from solid to liquid or vice versa. This temperature is a unique physical property of the substance. For pure water, it is 0^o C or 273^o K and is also referred to as the ice point.

5.    The boiling or condensation point of a substance refers to the temperature below which the substance exists as a liquid or solid; and at which the substances changes state from liquid to gaseous state or vice versa. Again, this temperature is unique to each substance. For pure water, this temperature is 100^o C or 373^o K and is also known as the steam point.

6.    The distinguishing properties of a substance in solid, liquid or gaseous states may be described in terms of the following characteristics of its constituent particles:

i)      distance between them – closely-packed, further apart or furthest apart;

ii)    their arrangement - in fixed position, in loose-attachment or without any attachment;

iii)   their movement – to and fro vibrations about fixed position; moving and changing position while loosely attached to one another; or dashing randomly and independently from one another;

iv)  forces of attraction and repulsion between them – strongest to hold the particles in fixed positions, present to hold them loosely together or negligible.

7.    Hence, in terms of kinetic molecular model of matter, a substance in solid, liquid or gaseous state may be described as follows (syllabus area 2.1 (b)):

a.       In Solid State:

Its constituent particles are closely-packed, vibrating to and fro in fixed positions experiencing the strongest forces of attraction and repulsion between them much like having springs holding them together in fixed shape and volume.

Temperature and Expansion: When the temperature of the solid rises (without exceeding its melting point), the vibrations become more vigorous resulting in the distance between neighbouring particles getting bigger and hence the expansion of the solid.

b.      In Liquid State:

The constituent particles are further apart and in loose attachments, vibrating vigourously and changing positions and slipping past each other easily – resulting liquid having fixed volume with shape that varies with the shape of its container.

Convection and Expansion: When the temperature of the liquid rises (without exceeding its boiling point), the vibrations and movement of the particles become even more vigorous resulting in the distance between neighbouring particles getting bigger - hence, the hotter part of the liquid becomes less dense and the particles rise as in convection; and, hotter liquid expands.

Evaporation (syllabus area 2.1 (c)):

Energetic liquid particles at the surface of the liquid, though still below its boiling point, may have enough kinetic energy to escape from the main body of the liquid in what is known as evaporation.

Evaporation results in cooling because the evaporated particles leave with higher energy level leaving behind particles with lower thermal energy.

Factors influencing rate of evaporation: The higher the room temperature, the bigger the surface area for evaporation, the higher the movement of air (draught) and the lower the humidity of the surrounding, the higher the rate of evaporation.

Evaporation, unlike boiling that only occurs at boiling point, can occur at any temperature below boiling point as long as the surface particles have enough energy to break away from the main body of the liquid.

c.       In Gaseous State:

The constituent particles are furthest apart (least dense of all), no longer experiencing any significant force of attraction and repulsion between them and dashing around at high speed (about 500 m/s for air molecules at 0^o C), randomly and independently of one another in all directions. The higher the temperature of gas particles, the faster and more vigourous the random motion of the particles and the higher the force and rate of bombardment on the inner walls of its container and hence, the higher the gas pressure exerted. 

Brownian Motion (in gas):

When randomly-moving gas particles collide with other more massive particles such as smoke particles, they have enough energy to exert a net force on the more massive particles in what is seen as Brownian motion – the random bombardments of massive particles by high-energy tiny particles.

Pressure Changes in Gas (syllabus area 2.1 (d)):

When gas particles collide with the internal walls of its container, the particles exert a force and therefore a pressure on the inner walls of its container.

At constant temperature, the pressure exerted by a gas is directly proportional to its density. The higher its density ρ, the higher the pressure exerted P due to the higher rate of collisions of the particles on the inner walls of its container:

Thus, P α ρ    ⇔ P α mass (m)/volume (V) ≡ P α m/V

Hence,

·        when mass m increases (such as by pumping in more air into a tyre) with temperature and volume remaining constant, pressure P increases because density ρ of the gas has increased.

Thus, P₁/m₁ = P₂/m₂  = constant

·        when volume V decreases (such as by squeezing a balloon) with temperature and mass remaining constant, pressure P also increases because lower volume means greater density ρ.

Thus, P₁V₁ = P₂V₂ = constant (Boyle’s Law)

At constant volume, the pressure exerted by a gas is directly proportional to its temperature. The higher the temperature, the higher the pressure exerted because at higher temperature, the gas particles hit the inner walls of its container at higher frequency and with greater force.

Thus, P α T ⇔ P₁/T₁ = P₂/T₂ = constant (Pressure Law)

Thermal Physics

IGCSE Cambridge Syllabus (2020-2021) Area 2 on 'Thermal Physics'

Scope:

2.1 Simple Kinetic Molecular Model of Matter

.1 States of Matter

.2 Molecular Model (of Matter)

.3 Evaporation

.4 Pressure Changes (in Gases)

2.2 Thermal Properties and Temperature

.1 Thermal Expansion (and Contraction) of Solids, Liquids and Gases

.2 Measurement of Temperature

.3 Thermal Capacity - Heat Capacity (and Specific Heat Capacity)

.4 Melting and Boiling

2.3 Thermal Processes

.1 Conduction

.2 Convection

.3 Radiation

.4 Consequences of Heat Transfer

Chapter Review Questions: "Intro to Physics" - Form 4 Chapter 1

A)  Base Quantity and Derived Quantity

1.    What is a base quantity? Name 5 base quantities.

2.    Define derived quantity. And, state 5 derived quantities.

3.    State two main advantages of standardisation of all units of measurement for physical quantities.

4.    Give the name and symbol of the SI unit of measurement for each of the following physical quantities:

a.       Length

b.      Mass

c.       Time

d.      Temperature

e.       Current

f.        Force

g.       Energy

h.       Power

5.    Some derived quantities have been given special names by SI (International System of Units). State these derived quantities (that you know of) and their special names.

B)  Standard Form / Scientific Notation / Prefixes

6.    Express each the following physical quantities in its SI unit and in scientific notation to 3 significant figures:

a.    Acceleration due to gravity, g = 9.783 ms^-2

b.    Speed of light in vacuum, c = 298,000 kms^-1

c.    Length of an onion cell, L = 0.000 028 m

d.    Charge of an electron = -1.6 x 10^-7 pC (pico coulombs)

7.    For each of the following symbol of prefixes, state its name and its numerical value in index form (i.e. in power or exponential form):

a.    da

b.    h

c.    k

d.    M

e.    G

f.      T

g.    d

h.    c

i.      m

j.      µ

k.    n

l.      p

8.    Identify the largest and the smallest measurements from the following values:

A.     3.14 x 10³ km

B.     3.14 x 10⁸ nm

C.     3.14 x 10¹⁰ µm

D.     3.14 x 10^-2 cm

9.    Convert:

a.       Density of sea water from 1.05 x 10³ kg m^-3 to g cm^-3

b.      Velocity of cyclist from 5.6 m s^-1 to km h^-1

c.       Radio frequency from 102.3 MHz to Hz

d.      470 pF to F in standard form to 3 significant figures

e.       0.0006 Gm to Mm

f.        26 µm to mm

C)  Scalar Quantity and Vector Quantity

10.    State the main difference between a scalar quantity and a vector quantity.

11.    An object moves 40 km on a bearing of 090o from O to A in 20 minutes; it then immediately moves north 30 km also in 20 minutes to B. Find:

a.       The total distance travelled by the object from O to B

b.      The final displacement of the object in moving from O to B in terms of both magnitude and bearing from O.

c.       For the whole journey from O to B:

                                                               i.      The object’s average speed

                                                             ii.      The object’s average velocity

12.    Is pressure a scalar or vector quantity? Name 5 scalar quantities.

13.    Name 5 vector quantities and state their respective SI units of measurement.

D)    Measurements in Science

14.     All measurements in science are Man’s attempts to make an acceptable estimate of the true and actual value of a physical quantity – True or False?

15.    The difference between the true and actual value of a physical quantity and the value obtained in a measurement is known as ________________.

16.    There are two main types of errors. State them, describe their differences and how each type of error may be minimised or avoided – give examples where appropriate.

17.    Attempts the following past year SPM questions:

a.         2007 P1 Q3 pg. 92 - Which balance is more sensitive?

b.         2011 P1 Q2 at pg. 280 on sensitivity in measurement

c.         2005 P1 Q2 Pg 3 on consistency and precision in measurement 

d.         2008 P1 Q2 Pg. 140 – consistency and precision

e.         2011 P1 Q1 at pg. 280 – on use of vernier calipers

f.           2005 Paper 1 Q1 at Pg 3 – on use of micrometer srew gauge

g.         2010 Paper 2 Q1 at Pg. 246 – on use of stopwatch to measure 20 oscillations of pendulum

h.    2005 P2 Q1 Pg. 16 – on use of ammeter, anti-parallax mirror, etc.

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Thermal Energy of Matter – Temperature, Mass and Heat Capacities

a)      Temperature and Heat:

o   Temperature refers to the degree of hotness of a substance. It is measured by thermometers (liquid-in-bulb thermometers, air thermometer, thermo-couple thermometer, etc.). When two bodies in contact have different temperatures, there will be net flow of heat (or thermal energy) from the body of higher temperature to that of lower temperature.

o   Heat therefore refers to thermal energy of the substance. Thermal energy Q that a substance has depends not only on its temperature T but also on its heat capacity C; or, its specific heat capacity c and mass m (please see (c) below).

o   The SI unit for temperature is K (Kelvin) and that for heat or thermal energy is J (joules). Temperature is often measured in ^oC (where, ^oC = K - 273.15 and 1^oC = 1 K) and, at times, in ^oF (Farenheit)

b)      At absolute zero (0 Kelvin (K) temperature or -273.15^o C), all matter theoretically has zero thermal energy (although it may have entry point energy). In the universe that we know so far, nothing has registered temperature of absolute zero or below. The lowest recorded temperature is about 2.73 K. However, in labs., scientists have achieved temperature near to but not below absolute zero.

c)      All matter with temperature above absolute zero has thermal energy which depends on

§  Its temperature T (K, Kelvin) and heat capacities C (Q K^-1);

§  Its temp. T   (K, Kelvin), mass m (kg) and specific heat capacity c (Q kg^-1 K^-1).

Thus, the thermal energy Q of a solid substance may be calculated as follows:

·      Q = TC

·      Q = Tm c

where, C (heat capacity) = heat energy required to raise the substance by 1 K

 c (specific heat capacity) = heat energy needed to raise 1 kg of the matter by 1 K or 1 ^oC  (note: 1 K = 1 ^oC) .

·      From the above formulae, it is not difficult for you to figure out the definitions of heat capacity C and specific heat capacity c that we will be dealing with in greater depth in a later posting.

d)      Thermal equilibrium refers to the situation when two bodies, say A and B, in contact with one another are at equal temperature (though may not be at equal thermal energies) and the rate of flow of thermal energy (heat) from A to B is the same as from B to A – the net rate of heat transfer between them is zero

e)      Kinetic molecular (or particle) model of matter describes how temperature (and thus thermal energy) of a substance affects:

o   at the microscopic level

§  motion of its constituent particles: whether vibrating about fixed position; moving freely while still being attracted to one another; or moving freely and independently of one another;

§  distance between the particles: getting further apart (expansion) or getting closer (contraction)

§  force of attraction between particles: Strongest in solid state; present in liquid state; negligible in gaseous state

§  force and rate of collisions at which its constituent particles at gaseous state hit any surface in contact including the internal surface of its container resulting in pressure being exerted;

And;

o   at the macroscopic level:

§  3 states of the matter – solid, liquid or gaseous states.

§  volume of the matter – due to expansion or contraction i.e. due to change in the average distance of particles at different temperatures; and

§  pressure and volume of gas due to different temperatures.

Heat / Thermal Physics

A)  IGCSE Syllabus: Thermal Physics

B)  SPM: Form 4 Chapter 4 - Heat

Thermal Physics / Heat

Areas Covered (in upcoming posts):

1.    Introduction: Thermal Energy of Matter - Temperature,Mass and Heat Capacities

2.    Kinetic Molecular (Particle) Model of Matter

3.    Evaporation and Boiling

4.    Gas and Gas Laws – Pressure, Volume and Temperature

A)      Pressure and Volume (Boyle’s Law)

a.       Pressure and Volume Relationship

b.      Applications

B)       Pressure and Temperature (Pressure Law)

a.       Pressure and Temperature Relationship

b.      Applications (balloon bursts when subject to heat, etc.)

C)      Volume and Temperature (Charles’ Law)

a.       Pressure and Volume Relationship

b.      Applications (hot air balloon, etc.)

(Do the above gas laws explain why pressure increases when we pump more air into, say, a ball or a tyre? the n in the ideal gas law pv = nRT can explain the missing factor) 

5.    Thermal Expansion: Solid, Liquid and Gas

6.    Thermal Quantities – Temperature, Heat Capacities & Latent Heat:

A)      Temperature

B)       Heat Capacity and Specific Heat Capacity

a.       Heat Capacity

b.      Specific Heat Capacity

c.       Applications of Specific Heat Capacity

C)      Latent Heat and Specific Latent Heat

a.       Latent Heat

b.      Heating Curve

c.       Cooling Curve

d.      Specific Latent Heat

                                                                 i      Specific Latent Heat of Fusion

                                                                 i      Specific Latent Heat of Vaporisation

e.       Applications of Specific Latent Heat

Forces and Pressure

1.   Pressure Generally

Pressure = Force / Perpendicular Area

P = F / A

·               P α F: Pressure is directly proportional to the force (in newtons, N)

·               P α 1/A: Pressure is inversely proportional to the perpendicular area (in square metres, m²)

SI unit of pressure is pascal (Pa)

1 Pa = 1 N m^-2

(The pressure of 1 Pa is equivalent to the pressure exerted by 1 squashed apple spread evenly over an area of 1 m² – it’s a very small pressure!)

Pressure exerted by solid = Weight of Solid / Perpendicular Area

P = Weight / Base Area = mg / A

2.   Pressure in Fluid

Pressure in fluid (air and liquid) acts in all direction.

Pressure in fluid, P = ρgh

P = ρgh (= Pressure due to fluid)
Where,      ρ = density of the fluid (in kg m^-3)

g = gravitational strength, g (in N kg^-1 or m s^-2)

h = height of column of fluid above the object (in m)
 

Basis:       P = Weight of Liquid / Area = W_L / A_L

where,        W_L = m_{L x} g (= Mass of Liquid x g) 

m_L = ρ x V_L (= Density of Liquid x Volume of Liquid) 

and,           V_L = A_L x h_L (= Cross-sectional Area x Height of Liquid_L 

Therefore, P = W_L / A_L = m_{L x} g / A_L = (ρ x V_L x g) / A_L

= (ρ x A_L x h_L x g) / A_L

 = ρg h_L

When an object is submerged into a liquid, it experiences a pressure totalling the pressure exerted by the liquid, P_L (= ρgh) and the pressure exerted by the air above the liquid P_Atm (atmospheric pressure):

P_total = P_L + P_Atm

3.   Gas Pressure and Atmospheric Pressure

In thermal physics, kinetic molecular model of matter tells us that all gas at temperature above absolute zero exerts pressure on its container due to the collisions of the gas particles with the inner surface of the container. The pressure P exerted depends on the rate and the force of collisions of its particles which in turn depends on two factors, namely:

Density ρ of the gas

P α ρ, (however, ρ = mass/volume i.e. ρ = m/V)

therefore,       P α 1/V (where mass is a constant)

P = k/V

P₁V₁ = P₂V₂ = constant (Boyle’s Law)

Temperature T of the gas

P α T

therefore,       P/T = constant

P₁/T₁ = P₂/T₂ = constant (Pressure Law)

4. Measurement of Pressure

4.1    Measuring Atmospheric Pressure

4.1.1      Liquid Barometer (e.g. Fortin Barometer with liquid mercury): Just as in the device called liquid thermometer, we use column of liquid due to thermal expansion to measure temperature: in the device called liquid barometer, we use column of liquid supported by air pressure to measure atmospheric pressure.

                                  

                                             Fortin Barometer

4.1.2      Aneroid Barometer:

4.1.2.1       to measure atmospheric pressure by using the contraction or expansion of air in a sealed chamber to move the pointer along a calibrated scale

4.1.2.2       to foretell weather – a sudden drop of atmospheric pressure foretells that rain clouds are fast forming above the barometer

4.1.2.3       to use as altimeter to measure altitude because at higher altitude, air pressure will be lower and this can be calibrated to measure altitude

Aneroid Barometer

4.2. Measuring Gas Pressure

4.2.1      Liquid Manometer: This device uses differential pressure to push liquid (mercury, oil, etc.) of known density up or down one arm of a U-tube relative to the other arm. If pressure of the arm connected to the gas is higher than atmospheric pressure, then the liquid in open arm which is exposed to atmospheric pressure will be pushed upwards.

Then, the pressure of the gas in the closed arm

              = Atm. Pressure + Pressure Measured by Column of Liquid in the Open Arm.

Manometer

4.1.2      Bourdon Gauge: This device uses the gas pressure to press against a copper coil which will cause the movement of a calibrated pointer to measure the gas pressure.

                  

5. Pascal’s Principle – Uniform Transmission of Pressure in Enclosed Liquid

Pascal’s Principle states that:

“Pressure exerted on an enclosed liquid is transmitted equally throughout the liquid”

Meaning of Pascal’s Principle:

§  Energy can be transferred from one place to another by the use of liquid pressure

§  A large force can be created by a small force

Applications of Pascal’s Principle in Hydraulic System

§  Hydraulic Jacks:

            

§  Hydraulic Brakes

        

§  Hydraulic Pumps

           

6.  Archimedes’ Principle – Buoyant Force Due to Weight of Fluid Displaced

Archimedes’ Principle states that:

“An object, whether wholly or partially, immersed, in a fluid is acted on by a buoyant force, which is equal to the weight of the fluid displaced”

       

Meaning of Archimedes’ Principle:

§   Buoyant Force = Reduction in weight of object immersed in fluid

                                   = Weight of fluid displaced

 

§   Buoyant Force Due to Fluid, F_buoyant = ρgV (contrast: P_fluid = ρgh)

Applications of Archimedes Principle:

Law of Flotation: A floating object displaces its own weight of fluid in which it floats.

Weight of floating object = Weight of fluid displaced (W_object = W_fluid)

Mass of floating object = Mass of fluid displaced (since, gM_object = gM_fluid)

Ship: It floats because the volume of water displaced has weight equals to the weight of the ship.

Hydrometer: This device floats to different depths in liquids of densities. It is calibrated to measure relative density of liquids such as milk and accumulators.

                         

Submarine:

          

                

Hot-Air Balloon

         

Cartesian Diver

7.  Bernoulli’s Principle – Differential Pressure Due to Differential Flow of Fluid – Fast Flow Creates Low Pressure

Bernoulli’s Principle states that:

“In a steady flow of fluid, the pressure of the fluid decreases when the velocity of the fluid increases – and the converse is also true”

        

        

Meaning of Bernoulli’s Principle:

§  Region of faster fluid flow = Region of lower pressure

§  Region of slower fluid flow = Region of higher pressure which will exert a force on region of faster fluid flow or low fluid pressure

Natural Phenomena that Demonstrate Bernoulli’s Principle:

§  Canvas roof of fast-moving vehicle bulges upwards but is flat when vehicle is at rest.

§  Spinning ball curves while non-spinning ball moves straight.         

Venturi Tube that Demonstrates Bernoulli’s Principle:

A venturi tube is a pipe that has a temporary narrowing somewhere in the middle to reduce the pressure and increase the velocity...

         

§  Upright Venturi Tube with liquid flowing through – liquid flows faster through the narrow part therefore creating lower pressure which support shorter column of liquid in the narrow tube above it.

           

§  Upright Venturi Tube with air flowing through – air flows faster through the narrow part therefore creating lower pressure which offers lesser support to the ping-pong ball above the narrow tube.

§  Inverted Venturi Tube with air flowing through – air flows faster through the narrow part therefore creating lower pressure which allows higher column of liquid to rise up the tube below it.

Applications of Bernoulli’s Principle:

§   Aerofoil:     

      

§   Hydrofoil

     

§   Bunsen Burner

    

§   Insecticide Sprayer

     

§   Carburettor

     

§   Ski Jumper Curving His Body

       

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