Chemegate
Home/Topics/Reactions & Control/Thermodynamics
Topic Guide

Thermodynamics
GATE CH Guide

Laws, equations of state, fugacity, VLE, phase rule, and reaction equilibria for the GATE Chemical Engineering paper.

Linked Calculator

Antoine →

Overview

Chemical Engineering Thermodynamics is the framework that tells you which direction a process can go and how far, whether a reaction will proceed, how much work a compressor needs, or what composition a vapor and liquid settle into at equilibrium. In the GATE CH syllabus it's one of the broadest sections, spanning the first and second laws, pure-component and mixture properties, and reaction/phase equilibria, and it underpins later sections like Distillation and Reaction Engineering that assume you can already compute an equilibrium constant or a fugacity coefficient.

The section builds in three layers. First come the laws themselves, energy and entropy balances for closed and open systems, and the property relationships (Maxwell relations, departure functions) that connect measurable quantities like P, V, T to unmeasurable ones like internal energy and entropy. Second comes non-ideal behavior: equations of state (virial, Redlich-Kwong-type cubic EOS) that correct the ideal-gas law, and activity coefficient models that correct Raoult's law for non-ideal liquid mixtures. Third comes equilibrium itself, vapor-liquid equilibrium (VLE) via K-values and relative volatility, and chemical reaction equilibrium via the equilibrium constant and Gibbs free energy of reaction.

GATE draws heavily on the ideal-gas and single-component property side (polytropic processes, heat engines, phase rule) as reliable easy marks, then tests VLE and reaction equilibrium as the harder numericals. Grounding vapor pressure calculations first, via the Antoine equation, covered on this site's dedicated calculator, makes every VLE and K-value problem in this section far faster to set up.

Real GATE CH PYQ Frequency (2024–2026)

2024202520263-Yr Avg
6666

Computed directly from 18 real questions tagged to this topic across our GATE CH 2024–2026 archive, averaging 6 questions/year. Browse the underlying 18 questions for this topic in the PYQ archive, or see the full topic weightage comparison across all topics.

GATE Weightage

Thermodynamics typically contributes 5–7 questions (about 9–12 marks) to the GATE CH paper, one of the highest-weightage sections, spread across the laws/property relations, non-ideal mixture behavior, and equilibrium calculations.

Sub-areaApprox. Marks
Laws of thermodynamics & property relations~2–3
Equations of state & non-ideal behavior~1–2
Vapor-liquid equilibrium (VLE) & fugacity~2–3
Reaction equilibria & phase rule~2–3

Sub-area split is a directional estimate (our archive doesn't tag marks at this granularity), for the real, computed topic-level total, see "Real GATE CH PYQ Frequency" above.

Key Subtopics

1

First & second laws

Energy balances for closed and open (flow) systems, and entropy generation as the mathematical statement of the second law and process irreversibility.

2

Pure-substance properties

P-V-T behavior, phase diagrams, and property tables/charts for pure substances, including polytropic and other ideal-gas process paths.

3

Equations of state

The virial equation (truncated at the second coefficient) and cubic equations of state (Redlich-Kwong, Peng-Robinson family) that correct the ideal-gas law for real-gas behavior.

4

Departure functions & property relations

Maxwell relations and generalized correlations (Lee-Kesler-type) used to compute enthalpy and entropy departures from ideal-gas behavior at a given reduced temperature and pressure.

5

Fugacity & activity coefficients

Fugacity as a corrected pressure for real gases, and activity coefficients (via models like van Laar or Margules) as a correction to Raoult's law for non-ideal liquid mixtures.

6

Vapor-liquid equilibrium (VLE)

K-values (K = y/x), relative volatility, and bubble/dew point calculations for both ideal and non-ideal systems, the direct bridge to distillation design.

7

Chemical reaction equilibrium

The equilibrium constant K from the standard Gibbs free energy of reaction, and how K shifts with temperature via the van't Hoff equation.

8

Phase rule & phase equilibria

Gibbs' phase rule (F = C − P + 2) for counting degrees of freedom in multi-phase, multi-component systems.

Essential Formulas

Full formula reference →

ΔU=Q−W\Delta U = Q - W

First law for a closed system (W = work done by the system)

ΔH=ΔU+Δ(PV)\Delta H = \Delta U + \Delta(PV)

Enthalpy, the natural energy variable for steady-flow open systems

dS≥δQTdS \geq \dfrac{\delta Q}{T}

Second law, equality for reversible processes, strict inequality for irreversible ones

PV=ZRTPV = ZRT

Real-gas equation of state with compressibility factor Z (Z = 1 for ideal gas)

Z=1+BPRTZ = 1 + \dfrac{BP}{RT}

Truncated virial equation of state using the second virial coefficient B

fi=ϕiPf_i = \phi_i P

Fugacity of a pure gas via the fugacity coefficient φ (φ → 1 as P → 0)

f^iL=xiγifi∘\hat{f}_i^{L} = x_i \gamma_i f_i^{\circ}

Fugacity of component i in a non-ideal liquid mixture using activity coefficient γ_i

Ki=yixiK_i = \dfrac{y_i}{x_i}

Vapor-liquid equilibrium K-value for component i

F=C−P+2F = C - P + 2

Gibbs' phase rule, degrees of freedom F for C components and P phases

ΔGrxn∘=−RTln⁡K\Delta G_{rxn}^{\circ} = -RT\ln K

Standard Gibbs free energy of reaction and the equilibrium constant K

dln⁡KdT=ΔHrxn∘RT2\dfrac{d\ln K}{dT} = \dfrac{\Delta H_{rxn}^{\circ}}{RT^2}

Van't Hoff equation, how K shifts with temperature (integrate for a two-point estimate)

PVn=const.PV^{n} = \text{const.}

Polytropic process path for an ideal gas (n = 1 isothermal, n = γ isentropic, n = 0 isobaric)

Visual Reference

0°C20°C40°C60°C80°C100°C0200400600760800TemperatureVapor pressure (mmHg)normal boiling point20°C: 17 mmHg
log₁₀P = A − B/(C+T) plotted over water's fitted range — vapor pressure climbs far faster than linearly with temperature, which is the whole reason boiling at 20°C takes real effort.
A decommissioned low-pressure steam turbine rotor from a power plant
A real steam turbine rotor — the hardware a Rankine-cycle thermodynamics problem is ultimately describing when it asks for turbine work output. AlfvanBeem, CC0, via Wikimedia Commons.

Derivations & Physical Insight

From the Second Law to the Equilibrium Constant

Chemical reaction equilibrium is where thermodynamics stops being descriptive and starts being predictive: instead of just tracking energy and entropy, it tells you exactly how far a reaction goes. The starting point is that at constant T and P, a system reaches equilibrium when its Gibbs free energy is at a minimum, equivalently, when the total Gibbs free energy of reaction, summed over all species weighted by their stoichiometric coefficients and chemical potentials, is zero.

Writing each species' chemical potential in terms of its standard-state value plus RT ln(activity), and setting the sum to zero at equilibrium, collapses the reaction's entire equilibrium condition into a single number, the equilibrium constant K, multiplied by RT:

∑νiμi=0  ⇒  ΔGrxn∘=−RTln⁡K,K=∏i(a^i)νi\sum \nu_i \mu_i = 0 \;\Rightarrow\; \Delta G_{rxn}^{\circ} = -RT\ln K, \qquad K = \prod_i (\hat a_i)^{\nu_i}

Why Fugacity Replaces Pressure in Real-Gas Equilibrium

For an ideal gas, chemical potential is a clean logarithmic function of pressure: μ = μ° + RT ln(P/P°). Real gases deviate from this because molecular interactions (attraction and finite molecular volume) change how the Gibbs free energy actually responds to pressure, the ideal-gas expression would predict the wrong equilibrium composition if used directly with real pressures.

Fugacity is defined precisely so the ideal-gas-style equation still works exactly, just with f substituted for P: μ = μ° + RT ln(f/P°). It's not a separate physical quantity, it's a bookkeeping device, a "corrected pressure," whose ratio to the actual pressure (the fugacity coefficient φ = f/P) captures all of the real-gas non-ideality in one number, calculable from an equation of state or a generalized (Lee-Kesler-type) correlation using only the reduced temperature and pressure.

Worked Practice Problems

Original practice problems in the GATE CH style, not copied from any question bank. Work them before reading the solution.

1-mark · NAT

Phase Rule for a Binary VLE System

Problem: A binary liquid mixture is in equilibrium with its vapor (two phases, two components, no reaction). Find the number of degrees of freedom.

Given: C = 2 components, P = 2 phases (liquid + vapor).

F=C−P+2=2−2+2F = C - P + 2 = 2 - 2 + 2

Answer: F = 2 (e.g., fixing temperature and liquid composition fully determines the system).

2-mark · NAT

Equilibrium Constant from Standard Gibbs Free Energy

Problem: A reaction has a standard Gibbs free energy of reaction ΔG°_rxn = −5000 J/mol at 400 K. Find the equilibrium constant K.

Given: ΔG°_rxn = −5000 J/mol, T = 400 K, R = 8.314 J/mol·K.

ΔGrxn∘=−RTln⁡K  ⇒  ln⁡K=−ΔGrxn∘RT=50008.314×400\Delta G_{rxn}^{\circ} = -RT\ln K \;\Rightarrow\; \ln K = \dfrac{-\Delta G_{rxn}^{\circ}}{RT} = \dfrac{5000}{8.314 \times 400}
ln⁡K=1.503  ⇒  K=e1.503\ln K = 1.503 \;\Rightarrow\; K = e^{1.503}

Answer: K ≈ 4.50 (reaction favors products at this temperature since K > 1).

Topic-wise PYQ Frequency

High

Ideal-gas processes & polytropic paths

A dependable easy numerical, GATE 2024 Q56 and GATE 2025 Q48 both tested ideal-gas process work/heat calculations directly.

Medium

Phase rule & phase equilibria

A quick conceptual/numerical staple, tested in GATE 2025 Q15 and GATE 2026 Q16.

Medium

VLE & K-values

Recurring in some form nearly every year, GATE 2024 Q18 and GATE 2026 Q36 both tested VLE/K-value calculations.

Medium

Fugacity & non-ideal mixture properties

GATE 2025 Q32 (fugacity) and Q33 (entropy of mixing) show this is tested regularly, if less often than VLE basics.

Medium

Reaction equilibrium

GATE 2026 Q54 tested chemical equilibrium (methanol synthesis), a realistic style for this subtopic.

Low

Virial equation & equations of state

GATE 2024 Q57 tested the virial equation of state directly; less frequent than ideal-gas or VLE questions.

Recommended Study Order

  1. 1

    1. First & second laws, property relations

    The conceptual foundation, energy and entropy balances recur in every later subtopic.

  2. 2

    2. Pure-substance & ideal-gas process behavior

    The highest-frequency, easiest-marks subtopic, master polytropic processes and property-table lookups first.

  3. 3

    3. Phase rule

    Quick to learn and frequently tested as a standalone conceptual question.

  4. 4

    4. Equations of state & fugacity

    Needed before tackling non-ideal VLE, since fugacity coefficients come directly from an equation of state.

  5. 5

    5. VLE & activity coefficients

    The highest-weightage applied subtopic, and a direct prerequisite for the Distillation topic guide.

  6. 6

    6. Reaction equilibrium

    Builds on Gibbs free energy concepts from the laws and connects directly to Chemical Reaction Engineering.

Common Pitfalls

✗ Using the ideal-gas law when a problem explicitly gives a compressibility factor Z or reduced properties.

✓ Any mention of Z, reduced temperature/pressure, or a generalized correlation is a signal to use PV = ZRT, not the plain ideal-gas law.

✗ Confusing fugacity coefficient (real-gas correction) with activity coefficient (non-ideal-mixture correction).

✓ φ corrects pure-component or mixture vapor-phase pressure for real-gas behavior; γ corrects liquid-phase composition for non-ideal mixing, they apply to different phases and different physics.

✗ Forgetting that ΔG°_rxn depends on the temperature at which K is evaluated, and using a 298 K value at a different reaction temperature without correction.

✓ Use the van't Hoff equation to adjust K (or ΔG°) to the actual reaction temperature before proceeding.

✗ Misapplying the phase rule by miscounting independent components (e.g., not accounting for a reaction constraint).

✓ If a chemical reaction links species concentrations, subtract one degree of freedom per independent reaction from the naive component count.

Put It Into Practice

Work the phase-rule and equilibrium-constant problems above, then apply the same Gibbs-free-energy and VLE reasoning to the thermodynamics questions in the full GATE previous-year test set.

Open the Antoine Equation Calculator →Take a Practice Test →

Keep Exploring

Related

Chemical Reaction Engineering

Rate laws, ideal reactors (batch, CSTR, PFR), RTD, non-ideal flow, and catalysis for GATE CH.

Open →

Process Calculations

Material & energy balances, recycle/bypass/purge systems, and combustion stoichiometry for GATE CH.

Open →

Antoine Equation

Calculate P* = 10^(A − B/(C+T)) for Benzene and Water. Includes GATE 2025 Q47 dew point solution.

Open →

GATE CH Formula Sheet

Every core GATE Chemical Engineering formula in one place, grouped by topic with variable definitions.

Open →

GATE Practice Tests by Year

Full-length, timed GATE CH practice tests (2024–2026) with instant, step-by-step-explained results.

Open →