Properties of Bulk Matter and Thermodynamics
This large domain covers elasticity, fluid mechanics, thermal expansion and calorimetry, heat transfer, kinetic theory and the laws of thermodynamics including Carnot efficiency.
Core rules
- Stress = force/area, strain = fractional change, and Young's modulus Y = stress/strain in the linear region; energy density = ½ × stress × strain.
- Bernoulli: P + ½ρv² + ρgh = constant along a streamline; continuity gives Av = constant.
- Stokes' law F = 6πηrv; terminal velocity varies as r².
- Surface tension gives excess pressure 2T/r inside a drop and 4T/r inside a bubble; capillarity h = 2T cosθ/(rρg).
- Expansion: ΔL = LαΔT, ΔA = A(2α)ΔT, ΔV = V(3α)ΔT.
- First law ΔQ = ΔU + ΔW; isothermal work W = nRT ln(V₂/V₁); adiabatic process obeys PV^γ = constant.
- Carnot efficiency η = 1 − T₂/T₁, with temperatures in kelvin.
Worked example
A Carnot engine works between 500 K and 300 K. Its efficiency is η = 1 − 300/500 = 0.40, so 40% of the absorbed heat becomes work. Absorbing 1000 J per cycle, it delivers 400 J and rejects 600 J to the sink. No real engine between these two reservoirs can exceed 40%.
Traps
Putting Celsius temperatures into the Carnot formula; mixing gauge and absolute pressure; assuming Y is unchanged beyond the elastic limit; forgetting that ΔU = 0 for an ideal gas in both isothermal and free expansion.