GATE Metallurgical Engineering Metallurgical Thermodynamics Syllabus

Metallurgical Thermodynamics syllabus — full chapter and topic list

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

1. 1

   Laws of Thermodynamics

   2 topics

   • First Law - Energy Conservation
   • Second Law - Entropy
2. 2

   Thermodynamic Properties

   5 topics

   • Enthalpy
   • Gibbs Free Energy
   • Helmholtz Free Energy
   • Maxwell’s Relations
   • Chemical Potential
3. 3

   Applications to Metallurgical Systems

   1 topic

   • Solutions
     • Ideal Solutions
     • Regular Solutions
4. 4

   Phase Equilibria

   6 topics

   • Gibbs Phase Rule
   • Binary Phase Diagram and Lever Rule
   • Free-Energy vs. Composition Diagrams
   • Equilibrium Constant
   • Activity
   • Ellingham and Phase Stability Diagrams
5. 5

   Thermodynamics of Point Defects

   1 topic

   • Surfaces and Interfaces
6. 6

   Adsorption and Segregation Phenomena

   overview

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

Metallurgical Thermodynamics flashcards for GATE Metallurgical Engineering

21 of 50 cards from the Metallurgical Thermodynamics deck — real questions with worked answers.

1. State the First Law of Thermodynamics in differential form for a closed system.

   $$dU = \delta q - \delta w$$ where $dU$ is the change in internal energy, $\delta q$ is heat added to the system, and $\delta w$ is work done by the system. For $PV$ work only, $dU = \delta q - P\,dV$.

2. For a constant-volume process, how does heat relate to internal energy?

   At constant volume the work term vanishes ($dV=0$), so $\delta q_V = dU$. Thus $q_V = \Delta U$, and the heat capacity is $C_V = \left(\frac{\partial U}{\partial T}\right)_V$.

3. Define enthalpy and give its differential form.

   Enthalpy is $H = U + PV$. Its differential is $$dH = dU + P\,dV + V\,dP.$$ At constant pressure, $\delta q_P = dH$, so $q_P = \Delta H$.

4. Express the constant-pressure heat capacity in terms of enthalpy, and relate $C_P$ and $C_V$ for an ideal gas.

   $C_P = \left(\frac{\partial H}{\partial T}\right)_P$. For an ideal gas, $C_P - C_V = R$ (per mole).

5. What is Hess's Law and what state function does it rely on?

   Hess's Law states that the total enthalpy change of a reaction is the same regardless of the pathway taken, because $H$ is a state function. Reaction enthalpies can therefore be added algebraically: $\Delta H_{rxn} = \sum \Delta H_{steps}$.

6. State the Second Law of Thermodynamics using entropy for an isolated system.

   For any spontaneous process in an isolated system, the total entropy increases: $$dS_{univ} \geq 0.$$ Equality holds only for reversible (equilibrium) processes.

7. Give the thermodynamic (Clausius) definition of an entropy change for a reversible process.

   $$dS = \frac{\delta q_{rev}}{T}$$ For an irreversible process, $dS > \frac{\delta q}{T}$ (the Clausius inequality).

8. Write Boltzmann's statistical definition of entropy.

   $$S = k_B \ln \Omega$$ where $k_B$ is Boltzmann's constant and $\Omega$ is the number of accessible microstates of the system.

9. Calculate the entropy change when $n$ moles of an ideal gas expand isothermally and reversibly from $V_1$ to $V_2$.

   $$\Delta S = nR \ln\!\left(\frac{V_2}{V_1}\right)$$ Since $T$ is constant, $\Delta U = 0$ and $q_{rev} = w = nRT\ln(V_2/V_1)$, giving $\Delta S = q_{rev}/T$.

10. Define the Gibbs free energy and give its differential form.

    Gibbs free energy is $G = H - TS = U + PV - TS$. Its differential is $$dG = V\,dP - S\,dT.$$

11. What is the criterion for spontaneity and equilibrium at constant $T$ and $P$ using Gibbs free energy?

    At constant $T$ and $P$: a process is spontaneous if $dG < 0$, at equilibrium if $dG = 0$, and non-spontaneous if $dG > 0$. The system minimizes $G$.

12. How does $\Delta G$ relate to $\Delta H$ and $\Delta S$, and what does the sign of each tell you about spontaneity?

    $$\Delta G = \Delta H - T\Delta S$$ A negative $\Delta H$ (exothermic) and positive $\Delta S$ favour spontaneity. At high $T$, the $-T\Delta S$ term dominates.

13. Define the Helmholtz free energy and give its differential form.

    Helmholtz free energy is $A = U - TS$ (also written $F$). Its differential is $$dA = -P\,dV - S\,dT.$$

14. What is the equilibrium criterion using Helmholtz free energy, and when is it the natural potential to use?

    At constant $T$ and $V$, a process is spontaneous if $dA < 0$ and at equilibrium when $dA = 0$. It is the natural potential for systems held at constant temperature and volume.

15. List the natural (characteristic) variables of $U$, $H$, $A$, and $G$.

    $U(S,V)$, $H(S,P)$, $A(T,V)$, and $G(T,P)$. Each potential is minimized at equilibrium when its natural variables are held fixed.

16. Write the four fundamental thermodynamic (Gibbs) equations for $U$, $H$, $A$, and $G$.

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

17. State Maxwell's relation derived from the Gibbs free energy $dG = -S\,dT + V\,dP$.

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

18. State Maxwell's relation derived from the Helmholtz free energy $dA = -S\,dT - P\,dV$.

    $$\left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial P}{\partial T}\right)_V$$

19. State the two Maxwell relations derived from $U$ and $H$.

    From $dU = T\,dS - P\,dV$: $\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V$. From $dH = T\,dS + V\,dP$: $\left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P$.

20. What mathematical property of state functions are Maxwell relations based on?

    They are based on the equality of mixed second partial derivatives (exactness of differentials): for an exact differential $dz = M\,dx + N\,dy$, $\left(\frac{\partial M}{\partial y}\right)_x = \left(\frac{\partial N}{\partial x}\right)_y$.

21. Define the chemical potential of component $i$ in terms of Gibbs free energy.

    $$\mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{T,P,n_{j\neq i}}$$ It is the partial molar Gibbs free energy of component $i$.

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