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4.6 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.

• 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 100^oC 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 80^oC.

  • 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 80^oC 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.

INDEX of notes on Particle model theory state changes and latent heat

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Keywords, phrases and learning objectives for particle models, thermal energy and cooling curve

Be able to draw, describe and explain the graph of a cooling curve as the temperature of material is steadily lowered.

Know that this is decreasing the internal energy of system, eventually causing the state changes of condensing,  freezing, as latent heat released and removed from the system.

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INDEX of notes on Particle model theory state changes and latent heat