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GCSE Physics notes: Particle models of state changes and latent heat

Particle model theory applied to energy transfer in state changes

What is internal energy and latent heat?

Particle motion in gases and gas pressure

Doc Brown's Physics Revision Notes

Suitable for GCSE/IGCSE Physics/Science courses or their equivalent

Sub-index for this page

1. Introduction to using kinetic particle theory to explain the states of matter

2. What is the internal energy of a substance

3. Energy transfer in state changes and conservation of mass

4a. Introduction to latent heat and state changes

4b. A heating Curve - steadily increasing the internal energy of a system

4c. A cooling Curve - steadily decreasing the internal energy of a system

4d. Some everyday examples of latent heat - internal energy transfers

4e. Defining specific latent heat

4f. Examples of worked-out heat calculations involving specific latent heat

5a. The particle model of a gas - motion and gas pressure

5b. Considering the internal and external pressures of a container of gas - the effects of changing quantity, volume or temperature

5c. Increasing the energy store of gas - work done and temperature effects

6. Factors that affect the rate of evaporation and condensation

7. What is the lowest temperature possible? Kelvin absolute temperature scale



 1. INTRODUCTION to using kinetic particle theory to explain the properties of the three different states of matter

 The particle model has been developed to explain the properties of the three states of matter, namely gas, liquid and solid.

 The particle model also provides a way of describing the changes of state between a gas, liquid and the solid state of a material.

To change the state of a material requires either the input of heat or the removal of heat from the material and this is called the latent heat. and consider the concept of internal energy.

The 'model' particle pictures below give you an idea of how the states of matter (gas, liquid and solid) are viewed when applying the theoretical ideas to explain how the three states of matter behave, especially when subjected to a change in temperature.

(c) doc b (c) doc b (c) doc b

You should be able to recognise simple diagrams to model the difference between solids, liquids and gases - the three states of matter.

Gases: There are almost no forces of attraction between gas particles, they have the most kinetic energy of the three states, the particles are completely free to move around at random and they move at high speeds in all directions - so they have a higher kinetic energy store than liquids. The free moving particles have kinetic energy of movement and there is much empty space between the particles.

Liquids: There are weak forces of attraction between liquid particles (if there wasn't, you couldn't have a liquid!), the particles are relatively close together but free to move around at random but with lower speeds than in the gas. The free moving particles still have kinetic energy of movement from one place to another - not quite as high a kinetic energy store as gases.

Solids: In solids there are stronger forces of attraction between the particles which prevents the particles moving around and passing each other. The particles are held in fixed positions in a regular arrangement. Their even lower kinetic energy is due to the particles (atoms or molecules) vibrating around their mean or average positions in the crystal structure. So solids have virtually no movement kinetic energy store from one place to another, as in the case of gases or liquids.

See also The density of materials and the particle model of matter

and More detailed descriptions of states of matter


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2. What is the internal energy of a substance    (KE shorthand for kinetic energy)

  • The particles of solids, liquids and gases all have kinetic energy (KE).

  • In solids the particles vibrate with kinetic energy but can't move around to another position, but in gases and liquids the particles freely move from place to place with kinetic energy.

  • Particles also have energy in their potential energy stores due to their positions - the motion from their kinetic energy keeps them separated as it opposes the forces attracting the particles together.

    • The particles in gases have the most potential energy because they are the farthest apart.

    • In potential energy order: gases >> liquids > solids

    • Remember there is a little space on average between liquid particles, but virtually non between the particles of a solid.

  • Therefore the internal energy of a system is stored by the particles (atoms, ions, molecules) because of their kinetic energy and spacing-position.

    • Total internal energy of particle system = kinetic energy store plus potential energy store

      • The thermal energy store of the particles = kinetic energy stores of the particles

  • When you heat a system energy is transferred to the particles eg they move faster in gases and liquids (increase in KE of movement from one place to another) or the particles vibrate more strongly in a solid (increase in vibrational KE), so the internal energy is increased when you heat a material.

    • Here, due to increase n temperature, the increase in the thermal energy store is effectively the increase in kinetic energy store of the particles.

  • This absorption of heat, ie increase in internal energy can cause an increase in temperature OR a change of state e.g. melting or boiling if the particles are given sufficient thermal energy.

  • Removing heat decreases the internal energy, so the material cools to a lower temperature OR undergoes a change of state e.g. condensing or freezing.

  • The size of the change depends on the energy input, the mass of substance involved and the specific heat capacity (which depends on the nature of the material).

  • See Specific heat capacity: how to determine it, use of data, calculations and thermal energy stores


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3. Energy transfer in state changes and conservation of mass

(c) doc b

FREEZING

MELTING

(c) doc b

SUBLIMING

(c) doc b   (c) doc b

BOILING or EVAPORATING

SUMMARY of the CHANGES of STATE between a gas, liquid and solid

All mass conserved in these PHYSICAL CHANGES

(c) doc b

CONDENSING

These are NOT chemical changes !

  • As well as the transfer of heat energy by conduction, convection and radiation, state changes like evaporation and condensation also involves heat energy transfers and the particle model can be used to explain them.

    • ON HEATING - adding thermal kinetic energy, increasing internal energy

    • When you heat a solid, the vibrational kinetic energy of the particles is increased until they have enough KE to weaken the interparticle bonds to allow melting and the particles are free to move around in the liquid state.

    • With further heating above the melting point, the particles gain more kinetic energy and the inter-particle bonds are further weakened so that the particles at the surface with the highest KE can escape the surface (evaporate) or vapourise to the gaseous state in the bulk liquid (bubbles!) at the boiling point.

    • The graph below shows how the distribution of kinetic energy and speed of particles changes with changes in temperature - with increase in temperature, the average speed and kinetic energy of the particles increases.

    • Note that the random movement and collisions of the particles creates a wide range of speeds/kinetic energies.

    • gcse chemistry change in distribution of speeds kinetic energies with change in tempearture

    • When the temperature is increased, more particles have a greater kinetic energy and greater speed, but only the highest speed/kinetic energy particles can escape from the surface (only the very right-hand section of the graph curves)

    • Below is a particle model of evaporation.

    • particle model explaining evaporation from liquid surface to gas vapour higher speed kinetic energy molecules escape

  • ON COOLING - removing thermal kinetic energy - decreasing internal energy

  • If you cool the substance, the reverse happens e.g. cool a gas so the interparticle bonds bring the particles together to condense and form a liquid.

  • Further cooling reduces the KE of the liquid particles so that when the temperature is reduced to the freezing point, the interparticle forces are sufficient to 'club' the particles together to form a solid.

  • All these physical state changes are reversible by adding or removing thermal energy, no new substances are formed (NOT a chemical change) and all mass is conserved. What you start with is what you finish with and all the original properties are retained.

  • The only difference between the states of a substance is how the particles are arranged (as described in section 1. above).

  • Note that in a closed system, mass is conserved in a system undergoing a change in state.

    • If you melt 100 g of ice, you get 100 g of water!

    • However, even with mass conservation, you can get a volume change, except for water, for the same mass, liquids occupy a slightly larger volume and gases occupy a massively greater volume than the liquid or solid form.

    • Ice is unusual that the solid ice crystals are less dense than water - which is why ice floats!

 


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4. State changes and latent heat

4a. Introduction to latent heat and changes of state g <=> l <=> s

  • The energy needed to change the physical sate of substance at constant temperature is called the latent heat.

  • There are two latent heat values:

    • (i) The numerical energy store transfer at the temperature corresponding to melting or freezing.

      • The latent heat of fusion for melting (solid ==> liquid), thermal energy added to the system.

        • The internal energy is increased to a point where the interparticle forces are weakened enough for the solid lattice of particles breaks down to form a liquid.

      • The latent heat of freezing (liquid to solid), thermal energy removed from the system.

        • The internal energy is decreased to a point where the interparticle forces are strong enough for liquid particles to come together and form a solid.

      • These two latent heats are numerically the same for state changes involving solid <=> liquid

    • (ii) The numerical energy store transfer at the temperature corresponding to boiling or condensing.

      • The latent heat of vaporization (liquid ==> gas), thermal energy added to the system.

        • The internal energy is increased to a point where the interparticle forces are weakened enough for liquid particles to escape to form a gas.

      • The latent heat of condensation (gas/vapour ==> liquid), thermal energy added to the system.

        • The internal energy is decreased to a point where the interparticle forces are strong enough for gas particles to come together and form a liquid.

      • Again, these two latent heats are numerically the same for the state changes involving liquid <=> gas/vapour.

  • A historical curiosity - latent heat ('hidden' heat), which was unexplained until the particle theory of matter was developed and inter-particle bonding understood.

  • Changes of state can be represented as a temperature - time graphs.

    • Heating curve - increasing temperature due to the addition of thermal energy, increasing the internal energy of the system.

    • Cooling curve - decreasing temperature due to the removal of thermal energy, decreasing the internal energy of the system.

    • BUT, the graphs are not simple 'curves', there are horizontal sections that need explaining using the concept of latent heat.


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4b. A heating Curve - steadily increasing the internal energy of a system

  • When a solid is heated from the solid state to the gaseous state and the temperature of the system measured continuously, there are two horizontal sections on the graph where the temperature does not rise, despite the constant input of thermal energy (continuous heating). Typical results are shown in the heating curve graph below.

  • (c) doc b)This is called a HEATING CURVE

    • You need to be able to accurately label and sketch a heating curve graph AND explain it!

  • As you heat the substance you are increasing the internal energy. BUT the temperature stays constant during the state changes of melting at temperature Tm and boiling at temperature Tb (see diagram above).

  • This is because all the extra ('hidden') energy absorbed in heating at these two temperatures (called the latent heat of state change), goes into weakening the inter–particle forces (intermolecular bonds) .

    • This induces the state change without temperature rise, to cause melting and then boiling to take place.

  • The thermal energy gain at this point equals the heat energy absorbed needed to reduce the interparticle forces in melting or boiling - the latent heat.

  • During the state change the temperature stays constant until all the latent heat is absorbed and the state change completed, so no temperature rise can occur.

  • In between the 'horizontal' state change sections of the graph, you can see the energy input increases the kinetic energy of the particles and raising the temperature of the substance as you expect as the internal energy increases.

  • For these state changes you have the addition of the latent heat of melting at temperature Tm and the addition of the latent heat of boiling at temperature Tb.

  • The diagram involving the brown half-arrows illustrates what is happening to the energy stores in a heating curve.

  • A simple experiment to illustrate a 'heating curve'

    • You start with a beaker of crushed ice into which you place a thermometer (-10 to 100oC thermometer).

    • Place on a tripod and gauze and record the temperature at the start.

    • To speed things up, heat the beaker of ice steadily with a bunsen flame.

    • Continue to record the temperature every minute until all the ice has melted and eventually the water will boil.

    • Finish taking temperature readings after 5 minutes of boiling.

    • Plot a graph of temperature versus time.

    • It should look like the graph above, apart from the initial rise of temperature of solid ice.

    • You should get two horizontal sections on the graph where the latent heat of fusion (melting at 0oC) or the latent heat of boiling (vapourising at 100oC) are being absorbed to weaken the intermolecular forces between the water molecules, without rise in temperature.

      • There is one rising section on your graph as the liquid water from the melted ice rises in temperature until the water boils - see the graph below.


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4c. A cooling Curve - steadily decreasing the internal energy of a system

  • As you cool a substance you are decreasing the internal energy. BUT the temperature stays constant during the state changes of condensing at temperature Tc and freezing at temperature Tf (see diagram below).

  • Similarly when a gas is cooled from the gaseous state to the solid state and the temperature of the system measured continuously, there are two horizontal sections on the graph where the temperature does not fall, despite the constant removal of heat energy (continuous cooling). Typical results are shown in the cooling curve graph below.

  • (c) doc b)This is called a COOLING CURVE

    • You need to be able to accurately label and sketch a cooling curve graph AND explain it!

  • As you cool the substance you are decreasing the internal energy. BUT the temperature stays constant during the state changes of condensing at temperature Tc, and freezing/solidifying at temperature Tf.

  • This is because all the extra ('hidden') heat energy removed on cooling at these temperatures (the latent heat of state change), reduces the KE and potential energy of the particles.

    • This allows the strengthening of the inter–particle forces without temperature fall to allow condensation and then freezing to take place.

  • The heat loss is compensated by the increased intermolecular force attraction which releases heat energy.

  • During the state change the temperature stays constant until all the latent heat is removed and the state change completed, so no temperature fall can occur.

  • In between the 'horizontal' state change sections of the graph, you can see the energy 'removal' reduces the kinetic energy of the particles, lowering the temperature of the substance.

  • For these state changes you have the removal of the latent heat of condensation at temperature Tc and the removal of the latent heat of freezing at temperature Tf.

  • The diagram involving the blue half-arrows illustrates what is happening to the energy stores in a cooling curve.

  • A simple experiment to illustrate a 'cooling curve'

    • Its not so easy to do a cooling curve by reversing the experiment described above for a 'heating curve'.

    • However, you can do a 'partial' cooling curve experiment using a low melting solid like stearic acid.

    • You start with boiling tube with a few cm depth of stearic acid in it plus a 0 to 100oC thermometer.

    • Place the boiling tube in hot water until all the 'waxy' stearic acid melts.

    • Keep on heating it until the temperature reads at least 80oC.

    • Remove the boiling tube and record the temperature of the melted acid.

    • Allow the tube of melted acid to cool on its own and record the temperature every minute until all of the acid has gone solid AND keep on recording for at least another 5 minutes.

    • Plot a graph of temperature versus time and it should look like the right-hand sections of the graph above.

    • In the middle of the graph should be a horizontal section corresponding to the transfer of the latent heat of fusion to the surroundings at the freezing point - to enable the kinetic energy of the molecules to fall sufficiently for the intermolecular forces to increase and cause solidification (crystallisation of the stearic acid molecules).

    • Your graph should look something like the right-hand section of the graph above and the graph below.

    • The temperature of the horizontal section is the freezing/melting point, and is 80oC for stearic acid.

    • Note for (a) and (b) ...

      • in terms of latent heats - changes in internal energy of the system at constant temperature

        • know the latent heat of melting numerically equals the latent heat of freezing (solid <=> liquid),

        • the latent heat of boiling numerically equals the latent heat of condensation (liquid <=> gas)

        • AND you must be able to relate state changes to ...

          • (i) the particle model, and ...

          • (ii) relate the particle model to the latent heat of state changes.


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4d. Some everyday examples of latent heat - internal energy transfers

  • Whenever materials at different temperatures are placed in contact with each other, there will be an internal energy transfer of thermal energy from the hotter material to the colder material.

  • (1) Using ice to cool a drink

    • When you add ice to a drink to cool it, an internal energy change takes place involving the latent heat of melting.

    • The ice is at a lower temperature than the liquid drink.

    • The higher energy liquid particles transfer kinetic energy to the ice, increasing its internal energy.

    • Sufficient thermal energy - the latent heat of melting, is absorbed by the ice to melt it.

    • The energy is needed to weaken the intermolecular forces between the water molecules in the ice sufficiently to cause melting - when the particles have sufficient energy to break free from the inter-particle attractive forces.

    • The ice warms up and your drink cools down - an internal thermal energy transfer!

  • (2) Refrigerator - freezer

    • In a refrigerator system, an electric pump is used to compress a gas to liquefy it - this pump-compressor is forcing condensation to take place and releases the latent heat of condensation.

    • The liquid is then allowed to evaporate, absorbing its latent heat of vapourisation.

    • This thermal internal energy is taken from the contents of the fridge-freezer.

    • The internal energy of the freezer contents is reduced, lowering the temperature of the food.

    • You can feel the warm air at the back of your fridge, this is from the release of the latent heat of condensation.


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4e. Defining specific latent heat

  • The specific latent heat of a substance is the quantity of energy need to change 1 kg of the material from one state to another without change in temperature.

    • (a) In heating a material to effect a state change e.g. melting or boiling, the specific latent heat must be added.

    • (b) In cooling a material to effect a state change e.g. condensing or freezing, the specific latent heat must be removed (released) from the system.

  • Specific latent heat values differ from substance to substance because of different values of inter-particle forces (intermolecular bonding) and also the state change itself for a specific substance (solid <=> liquid OR liquid<=> gas).

  • Generally speaking latent heats of boiling/condensing are numerical much greater than latent heats of melting/freezing.

  • The latent heat for the state changes solid <=> liquid is called the specific latent heat of fusion (for melting or freezing).

  • The latent heat for the state changes liquid <=> gas is called the specific latent heat of vaporisation (for condensing, evaporation or boiling)

  • Specific heat capacity is dealt with on a separate page


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4f. Examples of worked-out specific latent heat calculations

  • To work out the energy needed or released to change the state of mass m of a substance the following formula applies

    • thermal energy transfer = mass x specific latent heat

    • E (J) = m (kg) x L (J/kg)

    • E = mL

      • (sometimes quoted as Q = mL, where Q = amount of thermal energy transferred)

    • You may also need the specific heat capacity equation

      • energy transferred = mass x specific heat capacity x temperature change

      • E (J)  =  m (kg)  x  SHC (J/kgoC)  x  ∆T (oC)

      • SHC often denoted by c, ∆T often denoted as ∆θ

      • so the equation is simply E = mc∆T  or  E = mc∆θ

      • Its a bit of a nuisance that the same notation isn't used uniformly, but get used to it!

    • You may also need the electricity power equations P (W) = I (A) x V (V)  or  P (W) = E (J) / t (s)

  • Some examples of latent heat calculations

    • Q1 The latent heat of fusion of water is 334 000 J/kg (334 kJ/kg).

      • How much energy is needed to melt 5.5 kg of ice?

      • E = mL

      • E = 5.5 x 334 000 = 1 837 000 J  = 1837 kJ = 1840 kJ or  1.84 x 106 J (3 sf)

      • -

    •  Q2 The specific latent heat of vaporisation of water is 2 265 000 J/kg (2265 kJ/kg).

      • How much energy is needed to boil 250 g of water at 100oC?

      • 250g = 250/1000 = 0.25 kg

      • E = mL = 0.25 x 2 265 000 = 566 250 J = 566 kJ or 5.66 x 105 J (3 sf)

      • -

    • Q3 For aluminium, the latent heat of fusion is 397 000 J/kg and the latent heat of vaporisation is 11 400 000 J/kg.

      • How much energy is needed to completely vapourise 1.5 kg of aluminium

      • For melting: E = mL = 1.5 x 397 000 = 595 500 J, 595.5 kJ

      • For vaporisation:: E = mL = 1.5 x 11 400 000 = 17 100 000 J, 17 100 kJ

      • Total energy needed = 595.5 + 17 100 = 17 700 kJ or 1.77 x 107 J (3 sf)

      • -

    • Q4 What mass of ice can be melted by 1 million J of heat energy?

      • Latent heat of fusion of water is 334 000 J/kg

      • E = mL, rearranging gives m = E / L

      • m = 1 000 000 / 334 000 = 3.0 kg

      • -

    • Q5 In an experiment 5 g of solid gold required 322 J of heat energy to melt it at 1063oC.

      • Calculate the latent heat of fusion of gold.

      • 5 g = 5 / 1000 = 0.005 kg

      • E = mL, rearranging gives L = E / m

      • L = 322 / 0.005 = 64 400 J/kg

      • -

    • Examples Q6 and Q7 are a bit more tricky to work out, so see if you follow the arguments!

    • Q6 (a) How much energy is needed to convert 500 g of ice at 0oC to steam at 100oC?

      You need three other pieces of information to complete the calculation and three intermediate calculations to get to the final answer.

      The SHC of water is 4180 J/kgoC, the latent heat of fusion of water (ice) is 334 000 J/kg and the latent heat of vaporisation of water is 2 265 000 J/kg and 550 g = 0.50 k.

      (i) The energy to melt the ice:

      • E = mL

      • E = 0.5 x 334 000

      • E = 167 000 J

      (ii) The energy to raise the temperature of the water from 0oC to 100oC:

      • E = mc∆T

      • E = 0.5 x 4180 x 100 = 209 000 J

      (iii) The energy to boil the water at 100oC:

      • E = mL

      • E = 0.5 x 2 265 000 = 1 132 500 J

      (iv) Finally, add all of (i) to (iii) together.

      • Total energy needed = 167 000  +  209 000  +  1 132 500 = 1 508 000 J = 1.51 x 106 J  (3 sf)

      • -

    • (b) If you monitored the temperature rise with time as the ice was being heated up, sketch the temperature - time graph you might expect and explain its features.

      •   

      • Initially the ice is melting at 0oC and the ice/water mixture stays at a constant temperature as the latent heat of fusion is absorbed.

        • This is an increase in internal energy that weakens the inter-particle forces sufficiently to cause melting.

      • Then the liquid water steadily rises in temperature until the boiling point is reached at 100oC.

        • The kinetic energy of the molecules is steadily increasing, increasing the temperature of them.

      • The temperature of the water then remains constant at 100oC as the water boils away it is absorbing the latent heat of vapourisation.

        • This is a further increase in internal energy that further weakens the inter-particle forces sufficiently to cause boiling.

    • Q7 A block of ice at -10oC was melted and further heated up to 20oC.

      • The SHC of ice is 2100 J/kgoC, the SHC of water is 4180 J/kgoC and the latent heat of fusion of water (ice) is 334 000 J/kg.

      • (a) If 200 000 J of thermal energy were supplied to the ice, what was the original mass of ice?

        • This involves multiple stages of calculation and some clear logical thought!

        • Let m be the mass of ice.

        • (i) Energy needed to warm the ice from -10oC to 0oC.

          • E = mc∆T

          • E = m x 2100 x 10 = 21 000 m J

        • (ii) Energy needed to melt the ice

          • E = mL

          • E = m x 334 000 = 334 000 m J

        • (iii) Energy needed to warm the water from 0oC to 20oC.

          • E = mc∆T

          • E = m 4180 x 20 = 83 600 m J

        • (iv) The total energy needed

          • Etot = 21 000  +  334 000  +  83 600 = 438 600 m J

        • (v) Now the total energy needed = total energy supplied

          • So: 438 600 m = 200 000

          • m = 200 000 / 438 600 = 0.456 kg of ice

          • -

      • (b) If you monitored the temperature rise with time, sketch the temperature - time graph you might expect and explain its features.

        • Initially the solid ice steadily heats up from -10oC until its melting point is reached at 0oC.

          • The kinetic energy of vibration of the solid particles is increasing.

        • The temperature stays constant as the ice melts in absorbing the latent heat of fusion.

          • This is an increase in internal energy that weakens the inter-particle forces sufficiently to cause melting.

        • When all the ice is melted the water steadily increases in temperature to 20oC as the molecules gain kinetic energy of movement from place to place.

    • Q8 A 500 Watt heating element is used to heat up 1.50 kg of a solid until it just reaches its melting point, but before it actually starts melting.

      • If it takes 10.0 minutes more of heating to melt all the solid, what is the latent heat of fusion of the solid?

      • P (W) = E / t (J/s)

      • energy supplied = E = P x t = 500 x 10 x 60 = 300 000 J

      • latent heat fusion = 300 000 / 1.5 = 200 000 J/kg

      • -

    • Q9

 


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5a. The particle model of a gas - motion and gas pressure

  • (c) doc bAll particles have mass and their movement gives them kinetic energy and momentum.

  • The particles in a gas are in constant random motion - random direction, variety of velocities and kinetic energies.

  • Although the collisions occur at random in any direction, there is a resultant force acting at right angles to any surface.

  • There will always be a gas pressure, unless a container is under vacuum, no particles - no collisions - no pressure!

  • When the fast moving gas particles collide with a surface, their millions of impacts create a force that we measure as gas pressure - the total force of impacts per unit area.

  • The particles collide with the container surface completely at random and impact at every angle, BUT, the effect is to create a net force at right angles to the surface - gas pressure!

  • The more forceful the collisions on a surface or the greater the number of collisions per unit area of surface, the greater the pressure, assuming the gas volume keeps constant.

    • If the temperature is kept constant and the volume increased, the impacts are more spread out and less frequent per unit area, so the gas pressure decreases.

    • Conversely, if a gas is compressed into a smaller volume at constant temperature, the number of impacts per unit area increases, so the pressure increases.

    • If the sides of a gas container are 'flexible' (e.g. balloon), the volume will only be constant when the internal and external pressures are equal.

    • Boyle's Law, P versus V graphFrom measurements of volumes and pressure of gases at constant pressure, a numerical inverse law can be formulated - see graph on right.

    • pressure x volume = a constant (at constant temperature)

    • pV = constant

    • p = pressure in pascals (Pa = N/m2), V = volume (m3)

    • You can connect two pressure and two volumes by the simple equation

    • p1 x V1 = p2 x V2

    • where 1 represent the original conditions, and 2 the final situation if an enforced change of p1 or V1 is made.

    • Examples of simple gas calculations

      • (i) 5 m3 volume of a gas at a pressure 101 300 Pa was compressed to a volume of 2.8 m3.

        • Calculate the final pressure.

        • p1 x V1 = p2 x V2

        • rearranging gives p2 = (p1 x V1) / V2

        • p2 = (101 300 x 5) / 2.8 = 180893 Pa

      • (ii) 10m3 of gas at a pressure of 100 000 Pa was compressed to a pressure of 300 000 Pa.

        • Calculate the final volume of the gas.

        • p1 x V1 = p2 x V2

        • rearranging gives V2 = (p1 x V1) / p2

        • V2 = (100 000 x 10) / 300 000 = 3.33 m3

For more gas calculation see P-V-T pressure-volume-temperature gas laws and calculations


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5b. Considering the internal and external pressures of a container of gas

Pressure in fluids

Fluids are materials that can flow because the attractive forces between the particles are weak in liquids and almost non-existent in gases.

Since the particles are free to move, they collide with any surface they make contact with.

This produces a net resultant force at 90o to the surface.

The basic formula for pressure is:

Pressure = Force normal to the surface ÷ area of contact surface

P (Pa) = F (N)  ÷ A (m2)

 

For more on liquid fluid and atmospheric pressure see:

Pressure in liquid fluids and hydraulic systems

Pressure & upthrust in liquids, why do objects float/sink?, variation of atmospheric pressure with height

 

However, here, I'm only concerned with explaining more about gas pressure, using the model illustrated below to describe, explain and quantify the behaviour of a gas.

The effects of changing the amount or temperature of a gas in a container

The particles in a gas are in constant motion - flying around in all directions with frequent collisions (e.g. in air the collision rate is 109/s !!!).

As already described, increasing the temperature of a gas, increases the kinetic energy store of the gas particles.

This is the kinetic energy of movement from one place to another, its not vibrational kinetic energy.

In fact, the average kinetic energy of the gas particles is directly related to the temperature.

The higher the gas temperature, the greater the average kinetic energy of the particles,

and the cooler the gas the lower the average kinetic energy of the particles.

As you increase temperature, the average speed of the particles increases and the average kinetic energy - remember the kinetic energy formula:

KE = ½mv2  (m = mass of particle, v = velocity of particle)

 

We can now discuss particular 'pressure' situations and the starting point is the fact that ...

... gas pressure is caused by the collision of particles with any surface ...

... because when particles collide with a surface, the exert a force on that surface.

Pressure is related to the number or force of particle impacts per unit area of the surface.

The more impacts or more forceful impacts on the surface, the greater the pressure created.

Increasing temperature of a gas actually increases both.

  • (i) Consider a steel cylinder of gas - a rigid containing wall

    • When a gas is contained a rigid vessel you can pump lots of gas in to a pressure much higher than the surrounding atmospheric pressure.

    • Steel cylinders are used in industry to store gaseous chemicals and in the home we used cylinders of hydrocarbon gases for heating and cooking.

    • The effect of increasing the amount of gas in the cylinder

    • The more gas you force in, the greater the internal pressure because of the increase in the number of particle impacts per unit area - a greater concentration of particles means more impacts on the same surface area.

      • For a given cylinder, the gas volume is constant and the pressure is proportional to the amount of gas pumped in at constant temperature.

      • Pressure and volume are inversely proportional to each other.

      • P x V = constant,   P = pressure in Pa (pascals), V = volume in m3.

      • At constant temperature, increasing the volume decreases pressure because the collisions are more spread out over the same area - less particle collisions per unit area.

      • At constant temperature, decreasing the volume increases pressure because the collisions are more concentrated over the same area - more particle collisions per unit area.

      • See also P-V-T pressure-volume-temperature gas laws and calculations

    • If the internal and external pressures are not balanced, that's no problem with a strong steel walled cylinder!

      • After all, we store gases at high pressure in steel cylinders e.g. butane gas for heating.

    • The effect of increasing the temperature of the gas in a cylinder

    • If the cylinder is heated it will expand a little, but this will not compensate for the increase in gas pressure as the gas tries to expand.

    • If the cylinder and its contents increase in temperature, then the thermal energy store is increased as the gas particles gain kinetic energy.

    • This increase in the particle kinetic energy store increases the rate of particle collision AND the force of the particle impacts on the container surface - thus raising the pressure with increase in temperature.

    • This is quite a dangerous situation that fire-fighters face when tackling a fire at a factory where gas cylinders are used - the high temperatures and high pressures created in the gas cylinders will cause them to explode violently.

  • (ii) Consider a balloon of gas - a flexible containing wall

    • If the sides of a gas container are 'flexible' (e.g. like a balloon), the volume will only be constant when the internal and external pressures are equal.

      • If the external pressure is greater than the internal pressure the balloon will decrease in volume (size).

      • If the internal pressure is greater than the external pressure the balloon will increase in volume (inflate).

    • To blow up the balloon you blow in with a force greater than atmospheric pressure to create the volume of trapped gas.

    • The size of the balloon is then determined by how much air you have blown in and the ambient atmospheric pressure.

    • The pressure of a gas in a balloon produces a net outward force at right angles to the container surface due to the internal gas particle impacts.

    • BUT, as you observe with a blown-up balloon, it doesn't seem to be expanding or contracting.

    • The reason being that the external air particle impacts on the outside surface of the balloon create an opposing and equal balancing pressure.

    • By blowing in air you increase the internal pressure and force the balloon to expand, pushing the rubber skin outwards, until the internal and external pressures are equal when expansion will stop.

      • When you blow in you are increasing the number of particle impacts per unit area of the internal surface to create the greater outward acting force.

      • Remember, increasing the volume of a gas at constant temperature decreases the pressure (pV = constant).

      • The pressure you create initially when blowing up the balloon, must decrease as it expands - less particle impacts per unit area.

      • If you let air out of the balloon, or it leaks out, there are less particle impacts per unit area of surface and the pressure is reduced, so the greater external pressure causes the balloon to contract until the volume is reduced creating a pressure equal to the external atmospheric pressure.

    • If a balloon inflated with air is heated, the gas particles inside will increase in kinetic energy producing more collisions and more forceful collisions - increase in net force acting on the surface.

      • Therefore the pressure increases and the balloon expands.

      • BUT, the expansion spreads out the collisions (which decreases pressure - less force per unit area), so the balloon only expands until the internal pressure equals the external pressure of the cooler air.

      • When the balloon cools down it will decrease in size, less forceful particle collisions, balloon shrinks until, again, the internal and external pressures are equal.

    • When helium weather balloons are released, they rapidly rise up through the atmosphere and greatly expand because atmospheric pressure significantly decreases with increase in height above the earth's surface.

      • As the external pressure decreases (less particle impacts per unit area) the internal pressure is greater (more impacts) and so the greater number of internal impacts per unit area force the volume of the gas in the balloon to increase.

      • The helium balloon will continue to expand as long as the external pressure is less than the internal pressure.

      • It will stop expanding when the internal balloon pressure drops to the same as the external pressure.

      • However, since it is filled with less dense helium, it will continue to rise and rise!

  • (iii) The same arguments apply to blowing up a bicycle tyre or motor car tyre or anything else!

    • Any increases in the external pressure from a pump system will allow expansion of the tyre if it exceeds the internal pressure inside the tyre - otherwise no further inflation!

      • More on compression and work done in the next section.

    • When you seal the end of a gas syringe (like you see in chemistry), with your hand  and press the plunger in.

      • You can compress the air to create a greater gas pressure than the external atmospheric pressure. BUT, although the pressures are not initially balanced, as in the case of blowing up balloon, its your extra muscle force that helps create the balancing force.

      • internal pressure in syringe = atmospheric pressure + pressure from muscle force

    • -

 


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5c. Increasing the energy store of gas - work done and temperature effects

  • Increasing the energy store of gas by compressing it

    • When you pump air into a bicycle tyre as energetically as you can, you can detect a rise in temperature, particularly near the pump connection point. So, why the increase in temperature of the gas?

    • When you compress a gas by applying a mechanical force you do work of compression on the gas.

    • This work in compressing the gas increases the internal energy and increases the temperature - increasing the thermal energy store - the kinetic energy store is increased.

    • You have to do work on the gas because as you compress the air in the pump, the pressure rises as the force of the particle impacts acts against you, so you have to do work against this increased force/unit area (pressure) to get the air into the tyre.

    • By doing work on a gas in this way the increase in the internal energy store of the gas ends up as increased kinetic energy of the particles, which causes the temperature rise of the air, tyre and pump.

    • This effect is used in refrigerators where a refrigerant gas is compressed to release energy in a closed system - this thermal energy is obtained from the refrigerant liquid evaporating by absorbing the latent heat of vaporisation from the interior of the fridge-freezer.

      • Check out the sections on latent heat, but know that ....

    • If you compress a gas, decreasing its volume, you increase its internal energy, increasing the average kinetic energy of the particles and the gas gets warmer with an increase its temperature.

    • If you expand a gas, increasing its volume, you decrease its internal energy, decreasing the average kinetic energy of the particles, the gas cools as the temperature is reduced.

  • Increasing the energy store of gas by heating it

    • Increasing the temperature of a gas increases its kinetic energy store.

    • Increasing the temperature increases the average speed of particles and their kinetic energy.

    • In fact, the temperature of a gas is proportional to the average kinetic energy of the particles.

    • This means on heating a gas in a sealed container there are more particle impacts and more forceful impacts on the surface per unit area.

    • Therefore heating a gas at constant volume increases the gas pressure.

    • Conversely if you cool and sealed cylinder of gas, the pressure decreases.

  • More on gases and more on gas calculations

 


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6. Factors that affect the rate of evaporation and condensation

  • Condensation occurs when a gas/vapour is cooled sufficiently to a low enough temperature to allow the attractive forces to be strong enough to attract the particles together as a liquid. This can only happen if the kinetic energy of the particles is low enough (the lower the temperature the smaller the kinetic energy).

    • Water vapour in the air condenses out on cold surfaces in the winter eg window condensation, invisible steam from a boiling kettle condenses out into clouds of tiny droplets of water, which technically isn't steam! and rain drops form in the higher cooler regions of the atmosphere.

    • Factors affecting the rate of condensation

      • The cooler the gas, the faster it condenses - more lower KE particles can be attracted together.

      • The lower the temperature of the surface the gas is in contact with.

      • The lower the airflow over the surface, this keeps the concentration of the condensing gas as high as possible.

    • When a vapour/gas is condensed the latent heat of vaporisation must be removed to cool the particles down sufficiently for condensation to take place.

      • Because of this, being scalded by steam is worse than be scalded by boiling hot water.

      • Both involve transfer of thermal energy due to the heat capacity of liquid water.

      • BUT, water vapour must be first condensed, so initially you are scalded by the release of the latent heat of vaporisation = the 'latent heat of condensation'.

  • Evaporation is when the highest kinetic energy particles of a liquid escape from the surface ie can overcome the attractive forces of the bulk of particles. The greater the KE of a liquid surface particle, the greater the chance to escape and become a gas particle. Evaporation can take place at any temperature between a substance's melting point and boiling point. As the highest KE particles escape, leaving the slower lower KE particles, the bulk of the liquid will cool, so a cooling effect accompanies the evaporation of a liquid. The cooling effect of sweating is due to evaporation of water from your skin.

  • Factors affecting the rate of evaporation

    • gcse chemistry change in distribution of speeds kinetic energies with change in tempearture

    • The higher the liquid temperature, the faster the rate of evaporation - more particles with enough kinetic energy to escape from the surface (graph above).

    • particle model explaining evaporation from liquid surface to gas vapour higher speed kinetic energy molecules escape Reminder of particle model of evaporation

    • The greater the surface area, the faster the evaporation - more area, more chance of evaporation.

    • The greater the airflow over the surface of the faster the evaporation rate - the air can become saturated with the vapour of the liquid, so it is more readily replaced if the already evaporated liquid is swept away by air flowing over the surface.

      • Efficient drying of washing is a good example of these three factors - you need a warm sunny day (higher temperature), the washing well spread out on the line (surface area) and a nice breeze (sweeping the evaporated water away)!

    • When water evaporates the latent heat of vaporisation is absorbed by the water molecules giving a cooling effect.

      • This is why sweating cools your body, especially if you in a cooling breeze on a hot summer's day.


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7. What is the lowest temperature possible? Kelvin absolute temperature scale

We know the temperatures of the cores of stars can be millions of degrees, so there doesn't seem to be any upper limit to temperature!

BUT, is there limit at the lower end of the temperature scale?  The answer is YES!

Charles's Law, V versus T graphCharles's Law, P versus T graph

The first experimental evidence for a lower temperature limit came from graphs of volume versus temperature and pressure versus temperature for a fixed mass of gas.

The plots for these were linear until the gas liquefied or the liquid solidified.

BUT, if you extrapolated the gaseous data back, you find every line ended up at a theoretical pressure of zero and temperature of -273oC.

Explanation ....

As you cool a material, the particles have less and less kinetic energy of movement around (gases or liquids) or vibration in fixed positions (solid).

The kinetic energy of particles is a function of temperature.

You can also say, that what we measure as temperature, is a measure of the average kinetic energy particles have.

BUT, eventually virtually all movement ceases at a temperature of -273oC, particles have ~zero kinetic energy.

Therefore that's it as regards particle KE, and the temperature as we know it, cannot fall any further - there is no more internal energy to remove!

So, the lowest possible temperature that is -273oC. (-273 on the Celsius scale, unit oC).

Theoretically, at this temperature, the particles have no kinetic energy of movement or vibration, the coldest they can be - nothing left in the kinetic energy store of the particles.

In fact by then, every substance will have solidified, but at -273oC there is zero vibration of the particles.

In 1848 a Scottish-Irish scientist called William Thompson (later became Lord Kelvin) proposed a new temperature scale starting at zero (called absolute zero), which became known as the 'Kelvin' scale of temperature - unit K.

Therefore the difference between the Celsius and Kelvin scales is 273.

To convert from one to the other, the following simple formulae apply.

K = 273 + oC     or     oC = K - 273    (absolute zero 0 K is the same temperature as - 273oC)

Examples of temperature Celsius (oC) and Kelvin (K) scale conversions:

Freezing point of water = 0oC, therefore 0 + 273 = 273 K.

Boiling point of water = 100oC, therefore 100 + 273 = 373 K.

Melting point of pure iron = 1811 K, therefore 1811 - 273 = 1538 oC

Note: Do NOT write degrees Kelvin, do NOT write oK !!!,

and don't write just C for Celsius, you need the degree symbol o too!!


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