Physics Fundamentals: Key Concepts, Formulas, and Energy Scales
Energy & Power
• Energy: ability to do work; conserved; transforms among heat, chemical, mechanical, electrical, nuclear, etc.
• Power: rate of energy use; determines how fast work is done or energy is converted.
Units & Conversions
• calorie (cal): energy to raise 1 g water by 1 °C ~ Calorie (food Cal) = 1 kcal = 1 000 cal ~ joule (J): SI unit; 1 J = 1 kg·m²/s²
• kilowatt-hour (kWh): industrial/domestic unit; 1 kWh = 3.6 MJ ≈ 1 000 Cal
• household uses ~12 000 kWh/yr
Typical Energy Uses
• 16 W bulb @10 h/day ≈ 58 kWh/yr ~ fridge ≈ 440 kWh/yr; dishwasher ≈ 492 kWh/yr ~ 1 can soda (150 Cal) ≈ 0.150 kWh ≈ 630 kJ
Power Examples
• 1 W = 1 J/s (small flashlight) ~ 100 W (light bulb, human heat) ~ 1 hp ≈ 746 W (horse’s continuous output) ~ 1 kW = 1 hp ~ 1 MW = 10⁶ W (small town) ~ 1 GW = 10⁹ W (large plant) ~ US avg power use ≈ 0.4 TW; world ≈ 2 TW
Energy Density & Sources
• energy per gram (kWh/kg) vs TNT: TNT: 0.65 Cal/g (2.7 kJ/g) = 1 ~ gasoline: 10 Cal/g (42 kJ/g) = 15× ~ uranium-235: 2×10⁷ Cal/g (8.2×10¹⁰ J/g) = 3×10⁷×
• renewables & fossils annual US TWh: coal ≈ 4–6, nuclear ≈ 6, hydro ≈ 5, gas ≈ 4, solar panels ≈ 0.001/2.8 acres, wind ≈ 0.004/acre
• costs ($/kWh): coal 0.036, nuclear 0.024, hydro 0.092, gas 0.049, onshore wind 0.04–0.15, solar PV 0.15–0.59
Atomic & Particle Basics
• atom = nucleus (protons + neutrons) + electrons ~ proton (+), neutron (0), electron (–) ~ quarks combine → baryons (3-quark: proton = uud, neutron = udd) or mesons (2-quark) ~ standard model: fermions (quarks/leptons), bosons (photons, gluons, W/Z, Higgs)
Heat & Temperature:
temperature ∝ average kinetic energy of molecules ~ scales: K (absolute), °C (water), °F (human/brine) ~ T (°C) = T (K) – 273.15o T (°F) = 9/5·T (°C) + 32 ~ room T ≈ 298 K = 20 °C = 68 °F
Heat Transfer :
conduction: direct contact; metals conduct best ~ convection: bulk fluid movement ~ radiation: electromagnetic waves
Phase & Gas Laws :
phases: solid → liquid → gas → plasma as energy ↑ ~ ideal gas: PV = nRT (R = 8.314 J/mol·K) ~ P∝T/V, V∝T/P, P∝1/V at constant T, etc.
Thermal Expansion ~ solids expand when heated (ΔL = αLΔT); contraction when cooled → structural stress
Waves & Speeds :
speed of sound ≈ 340 m/s (depends on medium stiffness) ~ speed of light ≈ 3×10⁸ m/s → see before hear Thermodynamics
• Zeroth law: thermal equilibrium implies equal T ~ First law: ΔE = Q – W (energy conservation) ~ Second law: entropy of universe ↑; no heat engine 100% efficient
Third law: entropy → 0 as T → 0 K
Gravity & Orbit:
Newton’s law: F = G·m₁m₂/r² (G = 6.67×10⁻¹¹ m³/kg·s²) ~ weight = mg; g ≈ 9.81 m/s² on Earth; on Moon ≈ 1.63 m/s² (1/6) ~ orbital speed: v = √(GM/r) ~ escape velocity: vₑ = √(2GM/r) ~ LEO <1200 mi (ISS ~250 mi, v ~17 000 mph → 90 min/orbit) ~ GPS ~12 000 mi, 12 h/orbit; geosynchronous ~24 h, ~22 300 mi
Newton’s Laws:
inertia: object at rest/motion stays so unless acted on ~ Fₙₑₜ = ma (vector) ~ action = –reaction
Circular Motion:
centripetal accel a_c = v²/r directed toward center ~ required centripetal force F_c = m v²/r
Momentum & Torque:
linear momentum p = mv; conserved in closed system ~ angular momentum L = I ω (I = moment of inertia); conserved if τ_net = 0 ~ torque τ = r × F = F d (perpendicular lever arm)Engines & Devices ~ heat engines (gasoline, diesel, steam) convert heat → work; efficiency η ≤ 1 – T_cold/T_hot ~ refrigerators/heat pumps use work to transfer heat; COP depends on T difference ~ airbags: rapid gas expansion (controlled explosion) cushions impact in <1 ms