# 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
- Gradient
- 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**

- Steady and unsteady heat conduction
- 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
- Adsorption

**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)

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