# GATE Chemical Engineering Syllabus

## Subject Code: CH

### Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential equations
Unit 4 Complex variables
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B Process Calculations and Thermodynamics
Section C Fluid Mechanics and Mechanical Operations
Section D Heat Transfer
Section E Mass Transfer
Section F Chemical Reaction Engineering
Section G Instrumentation and Process Control
Section H Plant Design and Economics
Section I Chemical Technology

### Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

• Matrix algebra
• Systems of linear equations
• Eigen values
• Eigenvectors

Unit 2: Calculus

• Functions of single variable
• Limit
• Continuity and differentiability
• Taylor series, Mean value theorems
• Evaluation of definite and improper integrals
• Partial derivatives
• Total derivative
• Maxima and minima
• Divergence and Curl
• Vector identities
• Directional derivatives
• Line, Surface and Volume integrals
• Stokes
• Gauss and Green’s theorems

Unit 3: Differential Equations

• First order equations (linear and nonlinear)
• Higher order linear differential equations with constant coefficients
• Cauchy’s and Euler’s equations
• Initial and boundary value problems
• Laplace transforms
• Solutions of one dimensional heat and wave equations and Laplace equation

Unit 4: Complex variables

• Complex number
• Polar form of complex number
• Triangle inequality

Unit 5: Probability and Statistics

• Definitions of probability and sampling theorems
• Conditional probability
• Mean, median, mode and standard deviation
• Random variables, Poisson, Normal and Binomial distributions
• Linear regression analysis

Unit 6: Numerical Methods

• Numerical solutions of linear and non-linear algebraic equations
• Integration by trapezoidal and Simpson’s rule
• Single and multi-step methods for numerical solution of differential equations

Section B: Process Calculations and Thermodynamics

• Steady and unsteady state mass and energy balances including multiphase −
• Multicomponent
• Reacting and non-reacting systems
• Use of tie components −
• Recycle
• Bypass
• Purge calculations
• Gibb’s phase rule and degree of freedom analysis

First and Second laws of thermodynamics

• Applications of first law to close and open systems
• Second law and Entropy
• Thermodynamic properties of pure substances
• Equation of State and residual properties −
• Properties of mixtures Partial molar properties
• Fugacity
• Excess properties
• Activity coefficients
• Phase equilibria −
• Predicting VLE of systems
• Chemical reaction equilibrium

Section C: Fluid Mechanics and Mechanical Operations

• Fluid statics

• Newtonian and non-Newtonian fluids

• Shell-balances including differential form of Bernoulli equation and energy balance

• Macroscopic friction factors

• Dimensional analysis and similitude

• Flow through pipeline systems

• Flow meters

• Pumps and compressors

• Elementary boundary layer theory

• Flow past immersed bodies including packed and fluidized beds

• Turbulent flow

• Fluctuating velocity

• Universal velocity profile

• Pressure drop

• Particle size and shape

• Particle size distribution

• Size reduction and classification of solid particles

• Free and hindered settling

• Centrifuge and cyclones

• Thickening and classification, filtration, agitation and mixing

• Conveying of solids

Section D: Heat Transfer

• Convection and radiation
• Thermal boundary layer and heat transfer coefficients
• Boiling, condensation and evaporation
• Types of heat exchangers and evaporators and their process calculations
• Design of double pipe, shell and tube heat exchangers
• Single and multiple effect evaporators

Section E: Mass Transfer

• Fick’s laws
• Molecular diffusion in fluids
• Mass transfer coefficients
• Film
• Penetration
• Surface renewal theories
• Momentum, heat and mass transfer analogies
• Stage-wise and continuous contacting and stage efficiencies
• HTU & NTU concepts −
• Design and operation of equipment for distillation
• Absorption
• Leaching
• Liquid-liquid extraction
• Drying
• Humidification
• Dehumidification

Section F: Chemical Reaction Engineering

• Theories of reaction rates
• Kinetics of homogeneous reactions
• Interpretation of kinetic data
• Single and multiple reactions in ideal reactors
• Non-ideal reactors
• Residence time distribution
• Single parameter model
• Non-isothermal reactors
• Kinetics of heterogeneous catalytic reactions
• Diffusion effects in catalysis

Section G: Instrumentation and Process Control

• Measurement of process variables
• Sensors
• Transducers and their dynamics
• Process modeling and linearization
• Transfer functions and dynamic responses of various systems
• Systems with inverse response
• Process reaction curve
• Controller modes (P, PI, and PID)
• Control valves
• Analysis of closed loop systems including stability
• Frequency response
• Controller tuning
• Cascade and feed forward control

Section H: Plant Design and Economics

• Principles of process economics and cost estimation including depreciation and total annualized cost

• Cost indices

• Rate of return

• Payback period

• Discounted cash flow

• Optimization in process design and sizing of chemical engineering equipment such as compressors

• Heat exchangers

• Multistage contactors

Section I: Chemical Technology

• Inorganic chemical industries (sulfuric acid, phosphoric acid, chlor-alkali industry)

• Fertilizers (Ammonia, Urea, SSP and TSP)

• Natural products industries (Pulp and Paper, Sugar, Oil, and Fats)

• Petroleum refining and petrochemicals

• Polymerization industries (polyethylene, polypropylene, PVC and polyester synthetic fibers)