Properties of Bulk Matter and Thermodynamics
What this domain tests
Elasticity, fluid statics and dynamics, surface tension and viscosity, thermal expansion and calorimetry, heat transfer, and the first and second laws with Carnot efficiency.
Core rules
- Stress = F/A; strain is dimensionless; Young's modulus Y = (F/A)/(ΔL/L), valid within the elastic limit.
- Pressure at depth P = P₀ + ρgh; Archimedes upthrust equals the weight of fluid displaced; Bernoulli's equation assumes steady, non-viscous, incompressible flow along a streamline.
- Excess pressure: soap bubble 4T/r, liquid drop 2T/r; capillary rise h = 2T cosθ/(rρg).
- First law ΔQ = ΔU + ΔW: isothermal ΔU = 0, adiabatic ΔQ = 0, isochoric ΔW = 0.
- Carnot efficiency η = 1 − T₂/T₁ with temperatures in kelvin; real engines do worse.
Worked example
A steel wire 2.0 m long and 1.0 mm² in cross-section stretches 1.0 mm under a 100 N load. Find Young's modulus. A = 1.0×10⁻⁶ m² and ΔL = 1.0×10⁻³ m. Y = FL/(AΔL) = (100 × 2.0)/[(1.0×10⁻⁶)(1.0×10⁻³)] = 200/(1.0×10⁻⁹) = 2.0×10¹¹ Pa, a typical value for steel.
Traps that cost marks
- Forgetting to square the radius when finding area from a wire's diameter.
- Attaching units to strain; it is a pure ratio.
- Mixing specific heat capacity c with latent heat L.
- Substituting Celsius temperatures into the Carnot formula.