Thermodynamics
Scope
Thermodynamics appears as property estimation, phase equilibrium, and work/heat device calculations: compressors, turbines, refrigeration, and power cycles.
Concepts to own
- First and second laws; entropy generation; Carnot limits (efficiency = 1 − Tc/Th; refrigerator COP = Tc/(Th − Tc)).
- Equations of state and departure functions: ideal-gas enthalpy depends only on temperature, while real-gas enthalpy also depends on pressure.
- Phase equilibrium: Raoult's law for ideal mixtures, modified Raoult with activity coefficients, Henry's law for dilute solutes, K-values y/x, bubble- and dew-point calculations.
- Chemical equilibrium: ΔG° = −RT ln K; Kp uses partial pressures or fugacities with a consistent standard state; K depends only on T for ideal gases.
- Isentropic compression: T2 = T1 (P2/P1)^((k−1)/k), corrected by isentropic efficiency.
- Joule-Thomson: throttling is isenthalpic, not isentropic; most gases cool, hydrogen and helium warm.
Traps
- Mixing bar and atm inside Kp.
- Treating a gas as ideal when reduced temperature is near 1 and reduced pressure is high.
- Applying Carnot efficiency to a real cycle, or using adiabatic efficiency in the wrong direction.
- Confusing refrigerator COP with heat-pump COP, which is larger by exactly 1.
Worked example
Compress air from 300 K and 1 bar to 10 bar with k = 1.4 and efficiency 0.75. Ideal: T2s = 300(10)^0.2857 = 579 K. Actual: T2 = 300 + (579 − 300)/0.75 = 672 K.
Rule of thumb: for k near 1.4, each doubling of pressure raises the ideal outlet temperature by about 0.22 T1.