Science - post-graduate level subjects
The science domain of GATE EY is pitched at postgraduate level: questions assume the undergraduate facts and test whether you can reason from first principles - thermodynamic consistency, equilibrium and distribution laws, kinetics versus thermodynamics, and the quantum rules behind spectra.
Core reasoning patterns
- Equilibrium means a minimum of the relevant free energy: ΔG = 0 at constant T and p, and equality of chemical potentials across phases.
- Every intensive-variable relation has a Maxwell partner; use it when the derivative you need is hard to measure but its twin is easy.
- Populations follow Boltzmann statistics: N₂/N₁ = (g₂/g₁)·exp(−ΔE/kT), with degeneracies never omitted.
- Kinetic control (Arrhenius, activation energy) and thermodynamic control (ΔG°) answer different questions; a fast reaction can still be unfavourable.
- Selection rules and intensities come from transition dipole moments, not from energy-level spacing alone.
Worked example
A two-level system with ΔE = 1.0×10⁻²¹ J at 300 K, g₁ = g₂ = 1. kT = (1.38×10⁻²³)(300) = 4.14×10⁻²¹ J, so ΔE/kT = 0.242 and N₂/N₁ = exp(−0.242) = 0.785. The upper level holds about 44 % of the population - far from the high-temperature limit where both levels would be equally filled. If g₂ = 3, multiply by 3: N₂/N₁ = 2.36 and the upper level now dominates.
Traps
- ΔG used where ΔG° is meant, or kJ fed into ln K = −ΔG°/RT alongside J.
- Celsius temperatures placed inside an exponent.
- Degeneracy dropped from a Boltzmann ratio.
- Wavenumber, wavelength and frequency interconverted without the factor of c.
- ΔH° assumed constant over a wide temperature range.
- Equilibrium constants and rate constants treated as interchangeable.