Topic 6 of 8 · Form 5
Thermal physics and ideal gases
Thermal equilibrium; thermodynamic (kelvin) scale; internal energy as the sum of random kinetic and potential energies of molecules; first law of thermodynamics ΔU = q + W.
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Temperature and internal energy
Thermal equilibrium; thermodynamic (kelvin) scale; internal energy as the sum of random kinetic and potential energies of molecules; first law of thermodynamics ΔU = q + W.
Specific heat capacity and latent heat
Q = mcΔθ; Q = mL; experimental determination by electrical methods.
Ideal gases
pV = nRT = NkT; kinetic theory: pV = ⅓Nm⟨c²⟩; mean kinetic energy of a molecule = (3/2)kT; root-mean-square speed.
Worked example: Find the rms speed of nitrogen molecules (molar mass 0.028 kg mol⁻¹) at 300 K.
c_rms = √(3RT/M) = √(3 × 8.31 × 300 ÷ 0.028) = 517 m s⁻¹
Worked example: A gas at 27 °C and 100 kPa is heated at constant volume to 127 °C. Find its new pressure.
p₂ = 100 × 400 ÷ 300 = 133 kPa
Check yourself
- State the first law of thermodynamics.
- What happens to the mean kinetic energy of gas molecules when kelvin temperature doubles?
- Find the number of moles of gas in 0.024 m³ at 100 kPa and 300 K.
Show answers
- The increase in internal energy equals heat supplied to the system plus work done on the system.
- It doubles.
- 0.96 mol
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