Thermodynamics: MDCAT Notes and MCQs
Heat & thermal equilibrium
Heat is energy transferred from a higher-temperature region to a lower-temperature region. When no net transfer occurs, bodies are in thermal equilibrium (same temperature — zeroth law). Internal energy U of an ideal gas depends only on temperature.
Specific heat vs molar specific heat
- Specific heat c: heat to raise temperature of 1 kg by 1 K — Q = mcΔT, unit J kg−1 K−1 (water: 4200).
- Molar specific heat C: heat to raise temperature of 1 mole by 1 K — Q = nCΔT, unit J mol−1 K−1. C = Mc.
- For gases: Cv (constant volume) and Cp (constant pressure); Cp > Cv because at constant pressure extra heat is needed to do work in expansion.
Work in volume change
At constant pressure: W = PΔV (area under P–V graph). Work done by gas in expansion is positive.
First law of thermodynamics
Q = ΔU + W (Q = heat supplied to system, W = work done by system) — equivalently ΔU = Q − W, or ΔU = Q + Won. It is the law of conservation of energy.
| Process | Condition | First law |
|---|---|---|
| Isothermal | ΔT = 0 → ΔU = 0 | Q = W |
| Adiabatic | Q = 0 | W = −ΔU (expansion cools gas) |
| Isochoric | ΔV = 0 → W = 0 | Q = ΔU |
| Isobaric | ΔP = 0 | Q = ΔU + PΔV |
Derivation: Cp − Cv = R
For 1 mole heated through ΔT: at constant volume Qv = CvΔT = ΔU. At constant pressure Qp = CpΔT = ΔU + PΔV. For an ideal gas PΔV = RΔT. So CpΔT = CvΔT + RΔT → Cp − Cv = R (8.314 J mol−1 K−1).
γ = Cp/Cv: monoatomic 5/3 ≈ 1.67; diatomic 7/5 = 1.4.
PMDC learning outcomes for this unit
- Heat & first law: 7.1 Describe that thermal energy is transferred from a region of higher temperature to lower temperature.
- Heat & first law: 7.2 Differentiate between specific heat and molar specific heat.
- Heat & first law: 7.3 Calculate work done by a thermodynamic system during a volume change.
- Heat & first law: 7.4 Describe the first law of thermodynamics in terms of change in internal energy, heating of the system and work done on the system.
- Heat & first law: 7.5 Explain that the first law of thermodynamics expresses conservation of energy.
- Heat & first law: 7.6 Define specific heat and molar specific heats of a gas.
- Heat & first law: 7.7 Apply the first law of thermodynamics to derive Cp − Cv = R for an ideal gas