Sources and References

Primary texts — Felder, R.M., Rousseau, R.W., and Bullard, L.G., Elementary Principles of Chemical Processes, 4th ed., Wiley, 2016; Smith, J.M., Van Ness, H.C., Abbott, M.M., and Swihart, M.T., Introduction to Chemical Engineering Thermodynamics, 9th ed., McGraw-Hill, 2022.

Supplementary texts — Himmelblau, D.M. and Riggs, J.B., Basic Principles and Calculations in Chemical Engineering, 9th ed.; Seader, J.D., Henley, E.J., and Roper, D.K., Separation Process Principles, 4th ed., Wiley, 2016.

Online resources — MIT OCW 10.40 “Chemical Engineering Thermodynamics”; DIPPR project public summary; NIST WebBook; AIChE open concept videos.

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Chapter 1: Energy Balances for Non-Reacting Systems

1.1 Forms of Energy

Total energy in a flowing stream comprises internal (\( U \)), kinetic (\( v^2/2 \)), and potential (\( gz \)) contributions. Work modes are mechanical (shaft work, boundary work) and flow work (\( Pv \)). The combination \( H = U + Pv \) (enthalpy) absorbs flow work in open-system accounting, giving the reason why enthalpy, not internal energy, appears naturally in steady-flow balances.

1.2 First Law for Open Systems

For a steady-flow control volume with one inlet and one outlet and negligible kinetic and potential terms:

\[ \dot Q - \dot W_s = \dot m \Delta H. \]

For multiple streams:

\[ \dot Q - \dot W_s = \sum_{out} \dot n_i H_i - \sum_{in} \dot n_i H_i. \]

A reference state is chosen for each species; common choices are 25 °C and 1 atm, or the inlet condition.

1.3 Sensible Heat

Between phases, \( \Delta H = \int C_p\, dT \). Heat capacities are correlated polynomially:

\[ C_p(T) = a + bT + cT^2 + dT^3. \]

For ideal gases, \( C_p - C_v = R \). Mean heat capacities \( \bar C_p = \frac{1}{T_2 - T_1}\int_{T_1}^{T_2} C_p\, dT \) streamline hand calculations.

1.4 Latent Heat

At a phase transition, temperature is fixed and the enthalpy changes by \( \Delta H_{vap} \), \( \Delta H_{fus} \), or \( \Delta H_{sub} \). The Clausius–Clapeyron equation

\[ \frac{dP^{sat}}{dT} = \frac{\Delta H_{vap}}{T \Delta V_{vap}} \approx \frac{\Delta H_{vap} P^{sat}}{R T^2} \]

connects vapor pressure to latent heat under the ideal-gas, negligible-liquid-volume approximation.

Chapter 2: Energy Balances with Reaction

2.1 Heat of Reaction

Standard heat of reaction \( \Delta H_{rxn}^\circ \) at 25 °C is computed from heats of formation:

\[ \Delta H_{rxn}^\circ = \sum_{prod} \nu_i \Delta H_{f,i}^\circ - \sum_{react} |\nu_j| \Delta H_{f,j}^\circ. \]

Hess’s law exploits \( H \) as a state function: any thermodynamic path connecting reactants to products gives the same overall \( \Delta H \).

2.2 Adiabatic Reactor Balance

The adiabatic flame temperature results from \( \dot Q = 0 \):

\[ \sum_{react,in} \dot n_i H_i(T_{in}) = \sum_{prod,out} \dot n_j H_j(T_{ad}) + \xi \Delta H_{rxn}^\circ (25^\circ\text{C}). \]

Solving requires iteration because \( H_j(T_{ad}) \) is nonlinear in temperature.

2.3 Heats of Solution and Mixing

For nonideal mixtures, enthalpy of mixing \( \Delta H_{mix} \) is nonzero. Dissolving H\(_2\)SO\(_4\) in water is famously exothermic; enthalpy-concentration charts for such systems are engineering staples.

Chapter 3: Phase Equilibria

3.1 Gibbs Phase Rule

For a non-reacting system with \( C \) components and \( \pi \) phases,

\[ F = C - \pi + 2 \]

independent intensive variables specify the state. A binary vapor-liquid system (C=2, π=2) has F=2: choose \( T \) and \( P \), and all compositions follow.

3.2 Vapor-Liquid Equilibrium

Raoult’s law for ideal solutions:

\[ y_i P = x_i P_i^{sat}(T). \]

For nonideal liquid mixtures, activity coefficients \( \gamma_i \) modify the relation: \( y_i P = x_i \gamma_i P_i^{sat} \). Correlations (Wilson, NRTL, UNIQUAC, UNIFAC) estimate \( \gamma_i \) from binary data or group contributions. Azeotropes arise where \( \gamma_i \) departs enough from unity that \( y_i = x_i \) at some composition different from pure components.

3.3 Bubble and Dew Points

• Bubble-point at fixed \( x \) and \( P \): find \( T \) satisfying \( \sum_i K_i x_i = 1 \), \( K_i = P_i^{sat}/P \).
• Dew-point at fixed \( y \) and \( P \): find \( T \) satisfying \( \sum_i y_i/K_i = 1 \).

Flash calculations solve the Rachford–Rice equation for the vapor fraction \( \psi \):

\[ \sum_i \frac{z_i(K_i - 1)}{1 + \psi(K_i - 1)} = 0. \]

3.4 Liquid-Liquid and Liquid-Solid Equilibria

Partially miscible liquids form two phases; tie-lines and binodal curves on ternary diagrams guide extraction design. Liquid-solid equilibria underlie crystallization, with eutectics and peritectics analogous to azeotropes.

Chapter 4: Unit Operations: Separation

4.1 Flash Distillation

A single-stage partial vaporization separates based on volatility differences. Mass and energy balances with VLE close the problem. The degree of separation depends on relative volatility \( \alpha_{ij} = K_i/K_j \); \( \alpha \) close to 1 demands many stages.

4.2 Multistage Distillation

Multiple equilibrium stages stacked with countercurrent flow approach near-complete separation. The McCabe–Thiele graphical method on an \( x \)–\( y \) diagram constructs operating lines (rectifying, stripping) and steps off equilibrium stages. Minimum reflux corresponds to pinch at the feed; infinite stages at minimum reflux, or infinite reflux at minimum stages (Fenske equation):

\[ N_{min} = \frac{\log\!\left[\frac{x_D/(1-x_D)}{x_B/(1-x_B)}\right]}{\log \alpha_{avg}}. \]

4.3 Absorption, Stripping, and Extraction

Absorption transfers a solute from gas to liquid; stripping reverses it. The operating line \( y = (L/V)x + b \) and equilibrium line \( y = mx \) together define Kremser-equation estimates of stage count. Liquid-liquid extraction uses an immiscible solvent to remove a solute; stage counting on ternary tie-line diagrams extends distillation reasoning to LLE.

4.4 Solid-Fluid Separations

Leaching, adsorption, and crystallization each rest on equilibrium between a solid phase and a fluid. Design considers solubility curves, crystal size distribution (important for filtration), and mass transfer coefficients to the particle surface.

Chapter 5: Fluid Movement and Heat Transfer

5.1 Pumps and Compressors

The mechanical energy balance identifies the shaft work requirement of a pump:

\[ W_s = \frac{\Delta P}{\rho} + F. \]

Net positive suction head (NPSH) must exceed the fluid’s vapor pressure margin to avoid cavitation. Compressors are categorized as centrifugal, axial, reciprocating, or rotary; each has a characteristic efficiency–pressure ratio map.

5.2 Modes of Heat Transfer

Conduction: \( q = -k \nabla T \). Convection: \( q = h (T_s - T_\infty) \). Radiation: \( q = \varepsilon \sigma (T_s^4 - T_{sur}^4) \). The overall heat transfer coefficient for a composite wall,

\[ \frac{1}{UA} = \sum_i R_i = \sum_i \frac{L_i}{k_i A_i} + \sum_j \frac{1}{h_j A_j}, \]

frames the design of exchangers.

5.3 Heat Exchanger Design

For counterflow and parallel-flow exchangers the log-mean temperature difference (LMTD) is

\[ \Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)}, \quad Q = UA\Delta T_{lm}. \]

Shell-and-tube geometry and multi-pass configurations require a correction factor \( F \). The effectiveness-NTU method is preferred when outlet temperatures are unknown.

5.4 Correlations for Convection

Dimensionless numbers—Reynolds, Prandtl (\( Pr = C_p\mu/k \)), Nusselt (\( Nu = hD/k \))—structure correlations. Dittus-Boelter for turbulent pipe flow:

\[ Nu = 0.023 Re^{0.8} Pr^n, \]

with \( n = 0.4 \) (heating) or 0.3 (cooling). Condensation (Nusselt’s film theory) and boiling (Rohsenow, Zuber) have their own correlations with much larger \( h \) values.