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# GATE 2019 Syllabus for Chemical Engineering

#### Engineering Mathematics

Linear Algebra
• Matrix algebra

• Systems of linear equations

• Eigen values and Eigen vectors

Ordinary Differential Equation ( ODE )
• First order ( linear and non – linear ) equations

• higher order linear equations with constant coefficients

• Euler – Cauchy equations

• Laplace transform and its application in solving linear ODEs

• Initial and boundary value problems.

Calculus
• Functions of single variable

• Limit, continuity and differentiability

• Mean value theorems

• local maxima and minima

• Taylor and Maclaurin series

• Evaluation of definite and indefinite integrals

• application of definite integral to obtain area and volume

• Partial derivatives

• Total derivative

• Divergence and Curl, Vector identities

• Directional derivatives

• Line, Surface and Volume integrals

• Stokes

• Gauss and Green's theorems.

Partial Differential Equation ( PDE ) : Fourier series
• separation of variables

• solutions of onedimensional diffusion equation

• first and second order one – dimensional wave equation and two-dimensional Laplace equation.

Probability and Statistics
• Definitions of probability and sampling theorems

• Conditional probability

• Discrete Random variables

• Poisson and Binomial distributions

• Continuous random variables

• normal and exponential distributions

• Descriptive statistics – Mean, median, mode and standard deviation

• Hypothesis testing.

Numerical Methods
• Accuracy and precision

• error analysis

• Numerical solutions of linear and non – linear algebraic equations

• Least square approximation

• Newton's and Lagrange polynomials

• numerical differentiation

• Integration by trapezoidal and Simpson's rule

• single and multi – step methods for first order differential equations.

#### 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 and 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 and activity coefficients

• phase equilibria

• predicting VLE of systems; chemical reaction equilibrium.

#### 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 and 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.

#### 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, and

• single and multiple effect evaporators.

• Fick's laws,

• molecular diffusion in fluids

• mass transfer coefficients

• film

• penetration and 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

• dehumidification

• dehumidification and adsorption.

#### 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.

#### 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.

#### 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 equipments such as compressors, heat exchangers, multistage contactors.

#### 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 ).