Physical Science: Heat, Thermodynamics, and States of Matter; Classical Mechanics; Relativity
This domain combines mechanics, thermodynamics and states of matter, and special and general relativity.
Classical mechanics
Newton's laws: inertia; F = ma; equal and opposite forces. Momentum p = mv is conserved in collisions (elastic collisions also conserve kinetic energy). Impulse FΔt equals Δp. Work W = Fd cosθ; KE = ½mv²; PE = mgh; mechanical energy is conserved absent friction. Circular motion needs centripetal force mv²/r. Kinematics: v = v0 + at, x = v0t + ½at², v² = v0² + 2ax.
Heat and thermodynamics
Heat is energy in transit; temperature measures average kinetic energy. Q = mcΔT for heating, Q = mL for phase change. First law: ΔU = Q − W. Second law: entropy of an isolated system increases and heat flows spontaneously from hot to cold. A heat engine's Carnot limit is η = 1 − Tc/Th, with kelvin temperatures.
States of matter
Ideal gas law: PV = nRT. Kinetic molecular theory links pressure and temperature to molecular motion. Phase diagrams show melting, boiling, triple, and critical points; above the critical temperature a gas cannot be liquefied by pressure. Solids may be crystalline or amorphous; liquids show surface tension and vapor pressure.
Relativity
Special relativity rests on two postulates: physics is the same in all inertial frames, and the speed of light in vacuum is constant for every observer. Consequences include time dilation, length contraction, and E = mc²; no massive object reaches c. General relativity treats gravity as spacetime curvature and predicts gravitational lensing.
Worked example
A heat engine runs between 600 K and 300 K. Carnot efficiency = 1 − 300/600 = 0.50, so at most 50% of absorbed heat becomes work. Absorbing 1000 J per cycle, maximum work is 500 J and 500 J is rejected to the cold reservoir. Reasoning: the calculation requires kelvin, and the second law forbids full conversion.
Traps
Confusing heat with temperature; forgetting to convert °C to K in gas-law and Carnot problems; claiming entropy decreases in an isolated system; applying Galilean velocity addition to light; thinking efficiency can reach 1 unless Tc is 0 K.