GATE Chemical Engineering Process Calculations and Thermodynamics Syllabus

Process Calculations and Thermodynamics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Process Calculations and Thermodynamics in GATE Chemical Engineering, not a summary of it.

1. 1

   Steady and unsteady state mass and energy balances

   4 topics

   • Multiphase systems
   • Multi-component systems
   • Reacting systems
   • Non-reacting systems
2. 2

   Use of tie components; recycle, bypass and purge calculations

   overview

   Examined as a single unit within Process Calculations and Thermodynamics — no further topic split in the official outline.

3. 3

   Gibb’s phase rule and degree of freedom analysis

   overview

   Examined as a single unit within Process Calculations and Thermodynamics — no further topic split in the official outline.

4. 4

   First Law of Thermodynamics

   2 topics

   • Applications of first law to close systems
   • Applications of first law to open systems
5. 5

   Second Law of Thermodynamics

   1 topic

   • Entropy
6. 6

   Thermodynamic properties of substances

   2 topics

   • Equation of State and residual properties
   • Properties of mixtures
     • Partial molar properties
     • Fugacity
     • Excess properties
     • Activity coefficients
7. 7

   Phase equilibria

   2 topics

   • Predicting VLE of systems
   • Chemical reaction equilibrium

Process Calculations and Thermodynamics flashcards for GATE Chemical Engineering

25 of 50 cards from the Process Calculations and Thermodynamics deck — real questions with worked answers.

1. In a multiphase system at equilibrium, what three conditions must hold between coexisting phases?

   Thermal, mechanical, and chemical equilibrium: equal temperature ($T^{\alpha}=T^{\beta}$), equal pressure ($P^{\alpha}=P^{\beta}$), and equal chemical potential of each species ($\mu_i^{\alpha}=\mu_i^{\beta}$ for all $i$).

2. State the Gibbs phase rule for a non-reacting system and define each term.

   $$F = C - \pi + 2$$ where $F$ = degrees of freedom, $C$ = number of components, $\pi$ = number of phases, and $2$ accounts for $T$ and $P$.

3. How is the Gibbs phase rule modified when $r$ independent chemical reactions occur at equilibrium?

   $$F = C - r - \pi + 2$$ The number of independent reactions $r$ reduces the degrees of freedom.

4. For a multi-component mixture, write the definition of the mole fraction of species $i$ and the constraint it satisfies.

   $$x_i = \frac{n_i}{\sum_j n_j}, \qquad \sum_i x_i = 1$$

5. In material balances on a reacting system, define the extent of reaction $\xi$ and relate it to moles.

   $$n_i = n_{i,0} + \nu_i\,\xi$$ where $\nu_i$ is the stoichiometric coefficient (negative for reactants, positive for products) and $\xi$ is the extent of reaction.

6. Define fractional conversion of a limiting reactant $A$ in a reacting system.

   $$X_A = \frac{n_{A,0} - n_A}{n_{A,0}} = \frac{\text{moles of } A \text{ reacted}}{\text{moles of } A \text{ fed}}$$

7. Distinguish 'excess air' and 'theoretical air' in combustion calculations.

   Theoretical (stoichiometric) air is the exact amount needed to completely burn the fuel. Excess air is the amount supplied beyond theoretical: $$\%\text{ excess} = \frac{\text{air supplied} - \text{theoretical air}}{\text{theoretical air}}\times 100$$

8. For a non-reacting steady-state process with recycle, what is the purpose of a purge stream?

   A purge stream removes inert or accumulating species from a recycle loop to prevent their unlimited buildup, keeping the system at steady state.

9. State the first law of thermodynamics for a closed system in differential form.

   $$dU = \delta Q - \delta W$$ where $U$ is internal energy, $Q$ is heat added to the system, and $W$ is work done by the system.

10. For a closed-system reversible process with only $PV$ work, write the work expression.

    $$W = \int_{V_1}^{V_2} P\,dV$$

11. For a closed system undergoing a constant-volume process, how does the first law simplify?

    With $W=0$ (no $PV$ work), $$Q_V = \Delta U = n C_V \Delta T$$ (for an ideal gas with constant $C_V$).

12. For a closed system at constant pressure, relate heat to enthalpy.

    $$Q_P = \Delta H = \Delta U + P\Delta V$$ and for an ideal gas $Q_P = n C_P \Delta T$.

13. Write the relation between $C_P$ and $C_V$ for an ideal gas.

    $$C_P - C_V = R$$

14. For a reversible adiabatic (isentropic) process of an ideal gas, give the $P$–$V$ relation.

    $$P V^{\gamma} = \text{constant}, \qquad \gamma = \frac{C_P}{C_V}$$

15. State the steady-state energy balance (first law) for an open system.

    $$\dot{Q} - \dot{W}_s = \Delta\left[\left(H + \frac{u^2}{2} + gz\right)\dot{m}\right]$$ where $\dot{W}_s$ is shaft work and $H$ is specific enthalpy.

16. For an adiabatic steady-flow nozzle (no shaft work), how does the energy balance simplify (neglecting potential energy)?

    $$\Delta H + \frac{\Delta u^2}{2} = 0 \quad\Rightarrow\quad H_1 + \frac{u_1^2}{2} = H_2 + \frac{u_2^2}{2}$$

17. For a steady-flow throttling process (valve), what property is conserved?

    Enthalpy: $H_1 = H_2$ (isenthalpic process), since $\dot Q=0$, $\dot W_s=0$, and kinetic/potential changes are negligible.

18. Define the Joule–Thomson coefficient and state its sign for cooling on throttling.

    $$\mu_{JT} = \left(\frac{\partial T}{\partial P}\right)_H$$ Cooling on throttling requires $\mu_{JT} > 0$ (since $dP<0$).

19. State the second law via the Clausius inequality for a cyclic process.

    $$\oint \frac{\delta Q}{T} \leq 0$$ with equality for a reversible cycle.

20. Define entropy change in terms of reversible heat transfer.

    $$dS = \frac{\delta Q_{rev}}{T}$$

21. Write the entropy change of an ideal gas between two states in terms of $T$ and $P$.

    $$\Delta S = C_P \ln\frac{T_2}{T_1} - R \ln\frac{P_2}{P_1}$$

22. State the entropy balance for a steady-flow open system.

    $$\Delta(S\dot m) = \sum \frac{\dot Q_j}{T_j} + \dot S_{gen}, \qquad \dot S_{gen} \geq 0$$

23. Give the efficiency of a Carnot engine operating between $T_H$ and $T_C$.

    $$\eta_{Carnot} = 1 - \frac{T_C}{T_H}$$ (temperatures in absolute units).

24. Write the four fundamental property (Gibbs) relations for a closed system of constant composition.

    $$dU = T\,dS - P\,dV$$ $$dH = T\,dS + V\,dP$$ $$dA = -S\,dT - P\,dV$$ $$dG = -S\,dT + V\,dP$$

25. State the four Maxwell relations.

    $$\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V,\quad \left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P$$ $$\left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial P}{\partial T}\right)_V,\quad \left(\frac{\partial S}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_P$$

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