T-2 Phase Changes & Ideal Gas Law

State Variables:

• volume (V), [m³]
• pressure (p), [Pa]
• mass (M), [kg]
• temperature (T) [K]: related to thermal energy (E_th)
• Derived: ρ = M/V (mass density) [kg m-3]

Molecules (分子) & Moles (摩爾^mo2er3)

• N: Number of molecules [-]
• N_A: 6.02 x 10²³ [mol^-1]
• n = N/N_A [mol] (Why? For convenience)

Basic phases of matter and phase diagrams

Ideal Gas Law & Processes

• Incompatable assumptions:
  1. molecules don't touch each other;
  2. gases in thermal equilibrium (requires contact)
• → Valid away from phase transition boundary (see phase diagram)
• Equation:.
  • pV = n R T where R= 8.31 [J mol^-1 K ^-1]
  • pV = N k_B T where k_B=1.nt04 x 10^-23 [J K ^-1]
• p-V diagrams (p,V → T, only concern Δ) for Quasi-Static Processes

  isochoric: Vf = Vi isobaric: pf = pi isothermal: Tf = Ti

Ref: A Macroscopic Description of Matter(Slides)

• Ref: Knight Version 3 Chapter 16
• Ref: Knight Version 4 Chapter 18

FAQ

1. Why are the the quantities such are R and N_A not simple numbers? ANS: This is due to history and the way units were first defined. For example, we could define a new unit of temperature the [bai]. If 10 [bai] = 8.31 [K] then R=10. (Water would freeze at 328.7 bai, and boil at 448 bai. I could then define a scale for daily use T [xiaobai] = T[bai] -328.7 so that the freezing point of water would be 0 [xiaobai] and boiling point would be 106.5 [xiaobai] ) Similarily we could define a new unit of mass, the [white] such that so that Avrogadro's number is 10²⁴!
2. Why can we only consider quasi-static processes in thermodynamics? ANS: P,V and T are only defined for thermodynamic equilibrium. If things move fast we leave this equilibrium → the state variables are not defined. i.e. T is not constant in the system, P is not constant everywhere. To draw a path on the pV diagram we need to go ∞ slow. See Quasistatic and Reversible Processes (Khan Academy) for more information.