Thermodynamics
Thermodynamics covers temperature and heat, calorimetry, gas laws, the first and second laws, and engine efficiency. Expect calorimetry calculations and PV-diagram reasoning.
Core rules
- Calorimetry. Q = mcΔT for a temperature change; Q = mL during a phase change, where temperature stays constant.
- Ideal gas. PV = nRT with T in kelvin; R = 8.31 J/(mol·K).
- First law. ΔU = Q − W, where W is work done by the gas. On a PV diagram, work is the area under the curve.
- Second law. Entropy of an isolated system increases; no engine beats the Carnot limit e = 1 − T_c/T_h, with temperatures in kelvin.
- Heat transfer. Conduction rate scales as A ΔT/L; spontaneous flow is hot to cold.
Worked example
A 0.20 kg aluminum block (c = 900 J/kg·K) at 100 °C is dropped into 0.50 kg of water (c = 4186 J/kg·K) at 20 °C. Setting heat lost equal to heat gained: 0.20(900)(100 − T) = 0.50(4186)(T − 20), so 180(100 − T) = 2093(T − 20). Expanding gives 18,000 − 180T = 2093T − 41,860, hence T ≈ 26 °C. The water's larger mass and specific heat pull the equilibrium close to its starting temperature.
Traps
- Using Celsius in PV = nRT or in Carnot efficiency.
- Applying Q = mcΔT across a melting or boiling plateau.
- Reversing the sign of W in the first law; gas expansion means the gas does positive work.
- Assuming added heat always raises temperature when a phase change is possible.