##
**GATE Chemical
Engineering (CH) syllabus:**

**Section 1: Engineering Mathematics**

**Linear Algebra**

*:*Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

**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.

**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.

**Complex variables**

*:*Complex number, polar form of complex number, triangle inequality.

**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.

**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 2: Process Calculations and Thermodynamics**

Steady and
unsteady state mass and energy balances including multiphase, multi-component, 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 equilibrium:
predicting VLE of systems; chemical reaction equilibrium.

**Section 3: 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.

**Section 4: 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, and single and multiple effect
evaporators.

**Section 5: Mass Transfer**

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, humidification, dehumidification and
adsorption.

**Section 6: 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 7: 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 8: 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.

**Section 9: Chemical Technology**

Inorganic
chemical industries (sulphuric acid, phosphoric acid, chloro-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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