Particle model theory applied to energy transfer in state changes, internal energy, latent heat and particle motion in gases

Doc Brown's Physics Revision Notes

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

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.

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  • 1. Using the kinetic particle theory model to explain the three different states of matter.

    • 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. 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.

    • 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.

    • More detailed descriptions of states of matter


2. Internal energy    (KE shorthand for kinetic energy)

  • The particles of solids, liquids and gases have different amounts of 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 have energy in their potential energy stores due to their positions.

  • The energy stored in a system is stored by the particles (atoms, ions, molecules) and the internal energy is the total energy that the particles have in their kinetic and potential energy stores.

  • 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.

  • 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).


3. Energy transfer in state changes and conservation of mass

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FREEZING

MELTING

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SUBLIMING

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BOILING or EVAPORATING

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

All mass conserved in these PHYSICAL CHANGES

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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.

    • 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 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.

    • 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 heat 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).


4. State changes and LATENT HEAT

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

  • Changes of state require either ...

    • (a) the addition of energy, increasing the internal energy of the system, or ...

    • (b) the removal of energy, decreasing the internal energy of the system

  • (a) Heating Curve

    • 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 heat energy (continuous heating). Typical results are shown in the heating curve graph below.

    • (c) doc b)It is called the HEATING CURVE

    • 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.

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

    • The heat 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.

  • (b) Cooling Curve

    • 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)It is called the COOLING CURVE

    • 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 particle KE and 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.

    • 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.

    • -

  • (c) 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.

      • (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).

    • 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 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

      • energy (E in J) = mass (m in kg) x specific latent heat (L in J/kg)

        • E = mL

      • Some examples of calculations

        • (i) 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, 1.837 x 106 J)

        • (ii) 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, 5.66 x 105  J)

        • (iii) 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

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

          • Total energy needed = 5955 + 1 710 000 = 17 695 500 J (17 696 kJ,  ~1.77 x 107 J)

        • (iv) 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 g

        • (v) 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


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

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

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

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

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

  • 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 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.

    • From measurements of volumes and pressure of gases at constant pressure, a numerical inverse law can be formulated.

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

    • pV = constant

    • p = pressure in pascals (Pa), 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

  • The pressure of a gas in a container (e.g. a balloon) produces a net outward force at right angles to the container surface.

  • BUT, as you observe with a blown-up balloon, it doesn't seem to be expanding. The reason being that the air particle impact on the outside surface of the balloon itself creates an opposing and balancing pressure.

    • 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 same argument applies to blowing up a bicycle or motor car tyre.

    • Any changes in the external pressure (p) will allow expansion if p reduced or contraction if p increased.

    • 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.

  • 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.

    • You have to do work on the gas because as you compress the air in the pump, the pressure rises, and you have to do work against this increase in pressure to get the air into the tyre.

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

  • More on gases and more on gas calculations


6. The 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.

  • 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

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

    • 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, the washing well spread out on the line and a nice breeze!


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