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Thermal energy transfer and specific heat capacity

Internal energy is the particle-level bank account: kinetic energy in the jiggling, potential energy in the arrangement. Heating and working are the two ways to pay in, and two formulas price a temperature rise and a change of state.

Year 13AQA 3.6.2.1

Builds on Work, energy and power.

IN THIS TOPIC

  • Define internal energy and describe how heating and working change it.
  • Explain why temperature holds constant during a change of state.
  • Calculate energy transfers with Q = mcΔθ and Q = ml.

WHAT YOU PROBABLY THINK

Heat and temperature are the same thing.

Internal energy

Every object is a crowd of particles in random motion, and its internal energy is the sum of their randomly distributed kinetic and potential energies: kinetic in the jiggling, potential in the arrangement and separation.

Internal energy: the sum of the randomly distributed kinetic and potential energies of all the particleskinetic: how fastthey jigglepotential: how theyare arrangedinternal energy = the random total of both, over every particle
FIG. 1Internal energy keeps two accounts: kinetic energy in how fast the particles move, potential energy in how they are arranged.

The word randomly is doing spec-level work: a thrown ball's ordered motion is kinetic energy but not internal energy. There are exactly two ways to change internal energy, and this qualitative bookkeeping is the first law of thermodynamics: heating the system, or doing work on it (compressing a gas warms it with no flame in sight). Temperature, meanwhile, tracks only the kinetic account. That is the correction to the lie: heat is energy in transfer, measured in joules; temperature measures the average jiggle, in kelvin, and a sparkler and a bath can hold opposite rankings on the two scales.

Changes of state

The heating curve: temperature climbs while kinetic energy rises, and holds flat while a change of state rearranges the bondsenergy suppliedtemperaturemeltingboilingKE risingPE rising, T steadyflat sections: energy separates particlesinstead of speeding them up
FIG. 2The heating curve: temperature rises while kinetic energy grows, then holds flat through melting and boiling while the energy raises potential energy instead.

Supply energy steadily and the temperature climbs, until a change of state begins, and then it stops climbing entirely. During melting or boiling the incoming energy goes into potential energy, prising particles apart against their attractions, while the kinetic energy, and therefore the temperature, stays constant. The plateau ends only when the rearrangement is complete. Explaining a flat section in exactly these terms, PE rising, KE constant, is a bankable exam paragraph.

Pricing a temperature rise

The specific heat capacity c of a material is the energy needed to raise 1 kg of it by 1 K:

Q = mcΔθON YOUR DATA SHEET
Specific heat capacity: the same energy into equal masses of different materials produces very different temperature riseswateraluminiumsmall rise:c is largelarge rise:c is smallsame energy in, same mass: the rise depends on c alone
FIG. 3Equal masses, equal energy in: water barely warms while aluminium leaps, because c prices each material's temperature rise differently.

Water's enormous c (about 4200 J kg−1 K−1) is why the sea moderates coastal climates and why a kettle takes as long as it does. One practical method the spec points to: continuous-flow heating, where liquid streams past an electrical heater and c comes from the power, the flow rate and the temperature difference, with a second run at a different flow rate cancelling the heat losses.

Pricing a change of state

The specific latent heat l is the energy to change the state of 1 kg with no temperature change:

Q = mlON YOUR DATA SHEET

Latent heat of fusion for melting, of vaporisation for boiling, and the second is far larger, since boiling must separate the particles almost completely. A multi-stage problem, warm the ice, melt it, warm the water, is nothing more than Q = mcΔθ and Q = ml summed stage by stage, and keeping the stages separate is the whole of the technique.

THE EXAM BIT

  • Define internal energy with all three flags: the sum of the randomly distributed kinetic and potential energies of the particles.
  • Flat heating-curve sections: energy raises potential energy during the change of state; kinetic energy and temperature are unchanged. Both halves earn marks.
  • Δθ is a temperature difference, identical in °C and K: no conversion needed, and converting anyway wastes exam minutes.
  • Multi-stage heating: one Q per stage, summed. The planted error is applying mcΔθ across a plateau where ml belongs.
  • Continuous-flow method in one line: two flow rates, same temperature rise, subtract to eliminate heat loss. Name that purpose and the mark follows.

CHECK YOURSELF

A 2.2 kW kettle holds 0.80 kg of water at 15 °C. How long does it take to reach 100 °C? (c of water = 4200 J kg−1 K−1; assume no losses.)

Show a hint

Price the temperature rise first, then divide by the power.

Show the answer

Energy needed: Q = mcΔθ = 0.80 × 4200 × 85 = 2.86 × 105 J.

Time: t = Q/P = 2.86 × 105 / 2200 = 130 s, a little over two minutes.

A real kettle takes slightly longer: some energy heats the kettle body and the room, which is exactly the loss the continuous-flow method is designed to cancel.

Internal energy: random KE plus PE, summed over particles.

State changes spend energy on PE, so T stands still.

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