First Hour Exam Review
Chapters 1, 2, and 3

(majority courtesy of Prof. R. Poshusta, Chem331/2002)

1. Zeroth Law and Equations of State

• System vs. Surroundings. State of a system.
• Thermometer principle: If A is in thermal equilibrium with B, and if B is in thermal equilibrium with C, then A is also in thermal equilibrium with C. [B is the "thermometer". A has the same temperature as C. If B is not in thermal equilibrium with C then when they touch there will be a conspicuous visible change in B.]
• Absolute temperature scale. Ideal gas thermometer. -273.15°C.
• Ideal gas equation of state: PV=nRT. R=8.31451 J K^-1 mol^-1.
• Mole fractions and partial pressures in mixtures of gases. n_tot = n₁ + n₂ + etc. ,  y_i = n_i/n_tot ,   P_i = y_i P_tot.
• Virial equation of state for real gases. Z=PV/nRT
  pressure form: Z = 1 + B_pP + C_pP² + ... ; second, third, etc. virial coefficients are temperature dependent: B_p(T), C_p(T), etc.
  volume form:  Z = 1 + B(1/V) + C(1/V)² + ... ; B=B(T), etc.
• Boyle temperature, T_B: B = 0 at T_B. [The gas behaves ideally over largest pressure (or volume) range at this temperature.]
• van der Waals' empirical equation of state for gases: (P+a/V²) (V-b)= RT [where V is molar volume], a and b chosen to fit behavior of some gas.
• Critical point: P_c, V_c, T_c.

2. First Law of thermodynamics

• Work, pressure-volume type work: dw = -P_ext dV; electrical work, magnetic work, surface work, etc.
• Heat; heat capacity; dq = CdT
• Internal energy, the first law: dU = dq + dw; DU = q + w; integral on a closed path of dU is zero.
• Exact differentials: dz = Mdx + Ndy is exact if and only if (dM/dy)_x = (dN/dx)_y.
• P-V type work on a gas: dw = -P_ext dV.
• Joule's experiment showing dU/dV)_T = 0 for an ideal gas. Hence, for ideal gas also dU = C_vdT.
• Reversible process definition. Irreversible process. E.g., Reversible P-V work on an ideal gas: dw_rev = -(nRT/V)dV.
• Define ENTHALPY, H = U + PV. [Any substance] New state function. dH = dU + PdV + VdP; DH = DU + D(PV); DH = DU + (P₂V₂ - P₁V₁);
• Heat capacity at constant pressure, C_P = (dH/dT)_P, heat capacity at constant volume, C_v = (dU/dT)_V
  Relation for C_P - C_V.
• DH for heating pure substance at constant pressure: dH = C_P(T) dT, DH = Integral[C_P(T) dT].
• Adiabatic process. dq = 0.
• Thermochemistry. DH of formation, DH of reaction.
  DH_rx = DH_f(products) - DH_f(reactants); DH_rx,T2 = DH_rx,T1 + Integral[C_P,r(T) dT].
• Calorimetry experiments to measure enthalpy change. 

3. Second and Third Laws

• Entropy define and interpret. dS = dq_rev/T; integral around a closed path of dS is zero.
• Criterion of spontaneous process on a isolated system: DS > 0 or DS_univ>0. Criterion of reversible process on isolated system: DS = 0.
• Examples: reversible isothermal expansion of an ideal gas;
  irreversible isothermal expansion of an ideal gas;
  reversible adiabatic expansion of an ideal gas;
  irreversible adiabatic expansion of an ideal gas;
  transfer of heat from a hot to a cold body;
  phase change (melting, evaporation);
  etc.
• DS of mixing for ideal gases.
• Absolute entropy by integration from absolute zero temperature. Debye theory for C_P(T) at very low T.
• Third Law
• Heat Engines: Carnot cycle. Efficiency of converting heat to work using the ideal Carnot engine: e=(T_H-T_C)/T_H. Refrigeration and heat pumps.