Energy Converter

Different fields developed different units before the SI system unified measurements. Physics uses Joules and eV; chemistry uses kJ/mol and kcal/mol; engineering uses BTU and kWh; nutrition uses kcal; spectroscopy uses wavenumber (cm⁻¹); atomic theory uses Hartrees. Each is convenient for its domain — just as miles make sense for driving distances while nanometers make sense for atomic spacing.

The Hartree (Eh) = 4.3597447 × 10⁻¹⁸ J = 27.211 eV = 627.5 kcal/mol is the atomic unit of energy. It equals twice the ground-state energy of hydrogen (the ionization energy is 0.5 Eh = 13.6 eV). Quantum chemistry calculations use atomic units (Hartree-Fock, DFT) where Eh = 1, making energy outputs in Hartrees. Chemical accuracy in computational chemistry is typically defined as 1 kcal/mol ≈ 0.0016 Eh.

Using kBT = 1 eV: T = 1 eV/kB = 1.602 × 10⁻¹⁹ / 1.381 × 10⁻²³ = 11,604 K. So 1 eV ≈ 11,600 K. Useful rule: at room temperature (300 K), kT ≈ 1/40 eV = 25 meV. Plasma temperatures are often stated in eV: solar corona at 1-2 million K ≈ 100-200 eV; fusion plasma at 100 million K ≈ 8,600 eV ≈ 8.6 keV.

Chemists often use kJ/mol (1 kJ/mol = 10.364 meV per molecule) or kcal/mol (1 kcal/mol = 43.4 meV per molecule). Chemical bond energies: H-H 432 kJ/mol, C-C 346 kJ/mol, C=C 602 kJ/mol, C≡C 835 kJ/mol. Hydrogen bond: ~20 kJ/mol. Room-temperature thermal energy: RT = 2.479 kJ/mol = 0.593 kcal/mol. 'Chemical accuracy' = 1 kcal/mol ≈ 4.2 kJ/mol.

Wavenumber (cm⁻¹, read as 'reciprocal centimeters') is the number of wavelengths per centimeter: ν̃ = 1/λ (in cm). It is proportional to frequency and energy: E = hcν̃. Infrared spectroscopy uses 400-4000 cm⁻¹; Raman spectroscopy uses 0-3500 cm⁻¹ shifts. The conversion: 1 cm⁻¹ = 1.986 × 10⁻²³ J = 0.1240 meV. Infrared light at 1000 cm⁻¹ = 10 μm wavelength = 0.124 eV photon energy.

An average adult requires about 2000-2500 kcal/day of food energy = 8.4-10.5 MJ/day. This is equivalent to about 2.3-2.9 kWh — less than leaving a single 100W light bulb on for a day. Physically active individuals can consume 3000-5000 kcal/day during intense exercise periods like marathon training or cycling.

The erg is the CGS unit of energy: 1 erg = 10⁻⁷ J = 100 nJ. It is named from the Greek 'ergon' (work). It was the standard in older physics textbooks and is still used in some astrophysics, X-ray astronomy, and surface energy measurements (erg/cm²). One erg is approximately the kinetic energy of a mosquito flying at 1 m/s.

Energy densities (approximate): hydrogen 142 MJ/kg; natural gas 55 MJ/kg; gasoline 46 MJ/kg; coal 24-35 MJ/kg; lithium-ion battery 0.5-0.7 MJ/kg; uranium-235 fission 82 × 10⁹ MJ/kg; D-T fusion 340 × 10⁹ MJ/kg. Nuclear fuels are roughly 10 million times more energy-dense than chemical fuels per unit mass.

E = hc/λ. For light: a 500 nm green photon has energy E = (6.626 × 10⁻³⁴ × 3 × 10⁸) / (5 × 10⁻⁷) = 3.98 × 10⁻¹⁹ J = 2.48 eV. Quick rule: E(eV) = 1.24/λ(μm). For 1 μm infrared: 1.24 eV. For 0.1 nm X-ray: 12,400 eV = 12.4 keV. For 1 fm gamma: 1.24 × 10⁹ eV = 1.24 GeV.