Thermodynamics
Zeroth, first and second laws; heat engines; entropy; refrigerators.
Zeroth and first law of thermodynamics
Thermal equilibrium, internal energy, heat, work.
The first law of thermodynamics is conservation of energy for a system that exchanges heat (Q) and work (W) with its surroundings:
ΔU = Q − W (physics convention — W is work done by the system)
OR
ΔU = Q + W (chemistry convention — W is work done on the system)
Both are correct; they're the same equation with opposite sign on W. JEE physics uses the first form. Pick one and stick with it for the whole problem.
Sign rules (physics):
- Heat absorbed by the system: Q > 0
- Heat released by the system: Q < 0
- Work done BY the system (gas expands): W > 0
- Work done ON the system (gas compressed): W < 0
- Internal energy increases: ΔU > 0
The four classic processes:
| Process | Constant | W = ∫P dV | ΔU | Q |
|---|---|---|---|---|
| Isothermal | T | nRT ln(V₂/V₁) | 0 | W |
| Adiabatic | Q = 0 | (P₁V₁ − P₂V₂)/(γ−1) | −W | 0 |
| Isobaric | P | P(V₂ − V₁) | nC_v ΔT | nC_p ΔT |
| Isochoric | V | 0 | nC_v ΔT | ΔU |
For an ideal gas, ΔU = nC_v ΔT always, regardless of process — internal energy depends only on temperature.
Thermodynamic processes
Isothermal, adiabatic, isobaric, isochoric, work-area on PV diagram.
Second law and entropy
Heat engines, Carnot cycle, refrigerators, entropy.
A Carnot engine is the theoretically most efficient heat engine operating between two reservoirs at T_hot and T_cold (in kelvin).
Carnot efficiency: η = 1 − T_cold / T_hot
Why no engine can do better. A Carnot cycle is reversible (no entropy increase). Any real engine has irreversibilities (friction, heat loss) that increase entropy and reduce efficiency below the Carnot limit.
Worked example. A power plant operates between 500 K and 300 K. Maximum theoretical efficiency = 1 − 300/500 = 0.4 = 40%. Real coal plants reach ~35–38% — close to but below the Carnot limit.
The Carnot cycle has 4 steps:
- Isothermal expansion at T_hot (absorbs Q_h)
- Adiabatic expansion (T drops to T_cold)
- Isothermal compression at T_cold (rejects Q_c)
- Adiabatic compression (T rises back to T_hot)
Refrigerators run the same cycle in reverse. The coefficient of performance for a Carnot fridge is COP = T_cold / (T_hot − T_cold). Note: COP can be greater than 1, unlike efficiency.