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Chemical Engineering Cheatsheet

A comprehensive cheat sheet covering essential concepts and formulas in Chemical Engineering, useful for quick reference and exam preparation.

Thermodynamics

Fundamental Concepts

First Law of Thermodynamics

ΔU = Q - W

  • ΔU: Change in internal energy
  • Q: Heat added to the system
  • W: Work done by the system

Enthalpy (H)

H = U + PV

  • U: Internal energy
  • P: Pressure
  • V: Volume

Second Law of Thermodynamics

ΔS ≥ 0 (for a closed system)

  • ΔS: Change in entropy

Gibbs Free Energy (G)

G = H - TS

  • T: Temperature
  • S: Entropy
  • At constant T and P, ΔG < 0 for a spontaneous process.

Helmholtz Free Energy (A)

A = U - TS

  • At constant T and V, ΔA < 0 for a spontaneous process.

Heat Capacity

Cv = (∂U/∂T)v
Cp = (∂H/∂T)p

Equations of State

Ideal Gas Law

PV = nRT

  • P: Pressure
  • V: Volume
  • n: Number of moles
  • R: Ideal gas constant
  • T: Temperature

Van der Waals Equation

(P + a(n/V)^2)(V - nb) = nRT

  • a, b: Van der Waals constants

Peng-Robinson Equation

P = (RT)/(V_m - b) - (aα)/(V_m2 + 2bV_m - b2)

  • V_m: Molar volume
  • a, b, α: Peng-Robinson parameters

Thermodynamic Cycles

Carnot Cycle

η = 1 - (Tc/Th)

  • η: Efficiency
  • Tc: Cold reservoir temperature
  • Th: Hot reservoir temperature

Rankine Cycle

Used in steam power plants. Includes pump, boiler, turbine, and condenser.

Fluid Mechanics

Fluid Properties

Density (ρ)

ρ = m/V

  • m: Mass
  • V: Volume

Viscosity (μ)

Measure of a fluid’s resistance to flow.

Surface Tension (σ)

Energy required to increase the surface area of a liquid.

Fluid Statics

Pressure (P)

P = F/A

  • F: Force
  • A: Area

Hydrostatic Pressure

P = ρgh

  • ρ: Density
  • g: Acceleration due to gravity
  • h: Height

Buoyancy

Archimedes’ principle: Buoyant force equals the weight of the fluid displaced.

Fluid Dynamics

Continuity Equation

A1V1 = A2V2 (for incompressible fluids)

  • A: Cross-sectional area
  • V: Velocity

Bernoulli’s Equation

P + (1/2)ρV^2 + ρgh = constant

  • P: Pressure
  • ρ: Density
  • V: Velocity
  • g: Acceleration due to gravity
  • h: Height

Navier-Stokes Equations

Equations describing the motion of viscous fluid substances.

Reynolds Number (Re)

Re = (ρVD)/μ

  • ρ: Density
  • V: Velocity
  • D: Diameter
  • μ: Viscosity

Friction Factor (f)

Used to calculate pressure drop in pipes.

Mass Transfer

Diffusion

Fick’s First Law

J = -D (dC/dx)

  • J: Diffusion flux
  • D: Diffusion coefficient
  • C: Concentration
  • x: Distance

Fick’s Second Law

∂C/∂t = D (∂2C/∂x2)

  • C: Concentration
  • t: Time
  • D: Diffusion coefficient
  • x: Distance

Mass Transfer Coefficient

Mass Transfer Coefficient (k)

Relates the mass transfer rate to the concentration difference.
N = kΔC

  • N: Mass transfer rate
  • k: Mass transfer coefficient
  • ΔC: Concentration difference

Distillation

Relative Volatility (α)

α = (yA/xA) / (yB/xB)

  • yA, yB: Vapor mole fractions of components A and B
  • xA, xB: Liquid mole fractions of components A and B

McCabe-Thiele Method

Graphical method for designing distillation columns.

Fenske Equation

N_min = log( (xA,D/xB,D) * (xB,B/xA,B) ) / log(α)

  • N_min: Minimum number of trays
  • xA,D, xB,D: mole fractions of A and B in distillate
  • xA,B, xB,B: mole fractions of A and B in bottoms

Absorption

Stripping Factor (S)

S = (mG)/L

  • m: Slope of equilibrium line
  • G: Gas flow rate
  • L: Liquid flow rate

Chemical Reaction Engineering

Reaction Kinetics

Rate Law

-rA = k CA^n

  • -rA: Rate of disappearance of reactant A
  • k: Rate constant
  • CA: Concentration of A
  • n: Order of reaction

Arrhenius Equation

k = A exp(-Ea/RT)

  • k: Rate constant
  • A: Pre-exponential factor
  • Ea: Activation energy
  • R: Gas constant
  • T: Temperature

Reactor Types

Batch Reactor

Closed system; reactants are mixed and allowed to react for a certain time.

Continuous Stirred-Tank Reactor (CSTR)

Continuous flow of reactants and products; perfectly mixed.

Plug Flow Reactor (PFR)

Continuous flow; no mixing in the axial direction.

Reactor Design Equations

CSTR Design Equation

V = (FA0 XA) / (-rA)

  • V: Reactor volume
  • FA0: Molar flow rate of A at inlet
  • XA: Conversion of A
  • -rA: Rate of disappearance of A

PFR Design Equation

V = ∫(FA0 dXA) / (-rA)

  • V: Reactor volume
  • FA0: Molar flow rate of A at inlet
  • XA: Conversion of A
  • -rA: Rate of disappearance of A
  • Integration is performed over the range of conversion.
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