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Laws of Thermodynamics and Solutions(33)Electrochemistry(4)

Laws of Thermodynamics and Solutions

33 Questions

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q1

MCQ[1 Mark]

Which one of the following is NOT a state function? (A) Enthalpy (B) Entropy (C) Work (D) Internal Energy

(A)

Enthalpy

(B)

Entropy

(C)

Work

(D)

Internal Energy

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q2

MCQ[1 Mark]

For a regular solution, which one of the following statements is correct? ($\Delta H_{mix}$ is the enthalpy of mixing and $\Delta S_{mix}$ is the entropy of mixing) (A) Both $\Delta H_{mix}$ and $\Delta S_{mix}$ are finite (B) $\Delta H_{mix}$ is zero and $\Delta S_{mix}$ is finite (C) $\Delta H_{mix}$ is finite and $\Delta S_{mix}$ is zero (D) Both $\Delta H_{mix}$ and $\Delta S_{mix}$ are zero

(A)

Both \Delta H_{mix} and \Delta S_{mix} are finite

(B)

\Delta H_{mix} is zero and \Delta S_{mix} is finite

(C)

\Delta H_{mix} is finite and \Delta S_{mix} is zero

(D)

Both \Delta H_{mix} and \Delta S_{mix} are zero

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q3

MSQ[1 Mark]

Choose the correct option(s). Here $A$ is the Helmholtz free energy and $G$ is the Gibbs free energy. (A) $A$ provides a criterion for equilibrium in a system with constant temperature and constant pressure (B) $G$ provides a criterion for equilibrium in a system with constant temperature and constant pressure (C) $A$ provides a criterion for equilibrium in a system with constant temperature and constant volume (D) $G$ provides a criterion for equilibrium in a system with constant temperature and constant volume

(A)

'A' provides a criterion for equilibrium in a system with constant temperature and constant pressure

(B)

'G' provides a criterion for equilibrium in a system with constant temperature and constant pressure

(C)

'A' provides a criterion for equilibrium in a system with constant temperature and constant volume

(D)

'G' provides a criterion for equilibrium in a system with constant temperature and constant volume

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q4

NAT[1 Mark]

For an equilibrium phase diagram of a binary A-B alloy at a constant pressure as shown in the figure, the degree of freedom at 'X' is (answer in integer)

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q5

NAT[2 Marks]

$20\text{ g}$ of Au and $20\text{ g}$ of Ag form an ideal solid solution. Total entropy of mixing is ___ $\text{J/K}$.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q6

NAT[2 Marks]

$2$ moles of an ideal gas are reversibly expanded from $10\text{ L}$ to $20\text{ L}$ isothermally at $27^\circ\text{C}$. Magnitude of work done is ___ Joules.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q7

NAT[2 Marks]

For $2$ moles of metal with $C_p = 20 + 5 \times 10^{-3}T$, change in enthalpy upon heating from $300\text{ K}$ to $600\text{ K}$ is ___ Joules.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q8

NAT[2 Marks]

Given Ellingham oxidation equations for solid and liquid metal M, the melting point of metal M is ___ Kelvin.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q9

NAT[2 Marks]

For the combustion of methane with stoichiometric air, estimated adiabatic flame temperature is ___ Kelvin.

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q10

MCQ[1 Mark]

For an isobaric process, the heat transferred is equal to the change in _______ of the system. (A) enthalpy (B) entropy (C) Helmholtz free energy (D) Gibbs free energy

(A)

enthalpy

(B)

entropy

(C)

Helmholtz free energy

(D)

Gibbs free energy

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q11

MCQ[1 Mark]

Which one of the following is an intensive property? (A) Chemical potential (B) Volume (C) Mass (D) Entropy

(A)

Chemical potential

(B)

Volume

(C)

Mass

(D)

Entropy

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q12

MCQ[1 Mark]

Consider the following gas-phase reaction: $$2SO_{2}+O_{2}\rightleftharpoons 2SO_{3}$$\nIf the enthalpy of reaction is negative, which one of the following conditions promotes a higher equilibrium concentration of $SO_{3}$? (A) Higher pressure and higher temperature (B) Higher pressure and lower temperature (C) Lower pressure and higher temperature (D) Lower pressure and lower temperature

(A)

Higher pressure and higher temperature

(B)

Higher pressure and lower temperature

(C)

Lower pressure and higher temperature

(D)

Lower pressure and lower temperature

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q13

MSQ[1 Mark]

Standard Gibbs free energies of formation of some solid oxides per mole of $O_2$ at $1000\text{ K}$ are given below: $SiO_2$: $-728\text{ kJ}$, $TiO_2$: $-737\text{ kJ}$, $VO$: $-712\text{ kJ}$, $MnO$: $-624\text{ kJ}$\nRegarding thermodynamic feasibility of oxide reduction, which of the following statements is/are CORRECT under standard conditions at $1000\text{ K}$? (A) Si can reduce $TiO_2$ (B) Mn can reduce VO (C) Ti can reduce MnO (D) V can reduce $SiO_2$

(A)

Si can reduce TiO_{2}

(B)

Mn can reduce VO

(C)

Ti can reduce MnO

(D)

V can reduce SiO_{2}

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q14

NAT[1 Mark]

Consider the gas phase reaction: $$CO + \frac{1}{2}O_2 \rightleftharpoons CO_2$$\nAt equilibrium for a particular temperature, the partial pressures of $CO$, $O_2$, and $CO_2$ are found to be $10^{-6}\text{ atm}$, $10^{-6}\text{ atm}$, and $16\text{ atm}$, respectively. The equilibrium constant for the reaction is ___ $\times 10^{10}$ (rounded off to one decimal place).

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q15

MCQ[2 Marks]

Consider the phase diagram of a one component system given below. $V_{\alpha}$, $V_{\beta}$, and $V_{Liquid}$ are the molar volumes of $\alpha$, $\beta$, and liquid phases, respectively. Which one of the following statements is TRUE?\nGiven: The change in molar enthalpies, $\Delta H^{\alpha\rightarrow\beta}$ and $\Delta H^{\beta\rightarrow Liquid}$, are positive. (A) $V_{\alpha} < V_{\beta}$ and $V_{\beta} < V_{Liquid}$ (B) $V_{\alpha} > V_{\beta}$ and $V_{\beta} < V_{Liquid}$ (C) $V_{\alpha} < V_{\beta}$ and $V_{\beta} > V_{Liquid}$ (D) $V_{\alpha} > V_{\beta}$ and $V_{\beta} > V_{Liquid}$

(A)

V_{\alpha}<V_{\beta} and V_{\beta}<V_{Liquid}

(B)

V_{\alpha}>V_{\beta} and V_{\beta}<V_{Liquid}

(C)

V_{\alpha}<V_{\beta} and V_{\beta}>V_{Liquid}

(D)

V_{\alpha}>V_{\beta} and V_{\beta}>V_{Liquid}

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q16

NAT[2 Marks]

The excess molar Gibbs free energy of a solution of element A and B at $1000\text{ K}$ is given by $G^{XS} = -3000\text{ }X_A X_B\text{ J mol}^{-1}$, where $X_A$ and $X_B$ are mole fractions of A and B, respectively. The activity of B in a solution of A and B containing $40\text{ mol}\%$ of B at $1000\text{ K}$ is ___ (rounded off to two decimal places). (Given: $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$)

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q17

NAT[2 Marks]

Consider the following reactions and their standard Gibbs free energies (in J): $Fe(s) + \frac{1}{2}O_2(g) \rightleftharpoons FeO(s)$, $\Delta G^\circ = -264900 + 65T$ $2H_2(g) + O_2(g) \rightleftharpoons 2H_2O(g)$, $\Delta G^\circ = -492900 + 109T$\nThe value of $\frac{p_{H_2O}}{p_{H_2}}$ required to reduce solid FeO to solid Fe at $1000\text{ K}$ is ___ (rounded off to two decimal places).

Explanation

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q18

MCQ[1 Mark]

If in an A-B solid solution, the activity and mole fraction of A are given by $a_{A}$ and $X_{A}$ respectively, then the activity coefficient of A is given by (A) $\frac{a_{A}}{X_{A}}$ (B) $\frac{X_{A}}{a_{A}}$ (C) $a_{A}$ (D) $a_{A}X_{A}^{2}$

(A)

\frac{a_{A}}{X_{A}}

(B)

\frac{X_{A}}{a_{A}}

(C)

a_{A}

(D)

a_{A}{X_{A}}^{2}

Explanation

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q19

MSQ[1 Mark]

Which of the following is/are criterion/criteria for equilibrium of an isolated system? (A) Maximum entropy (B) Minimum internal energy (C) Minimum Helmholtz free energy (D) Minimization of Gibbs free energy

(A)

Maximum entropy

(B)

Minimum internal energy

(C)

Minimum Helmholtz free energy

(D)

Minimization of Gibbs free energy

Explanation

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q20

NAT[2 Marks]

An ideal solution is formed by mixing $10\text{ grams}$ of A and $50\text{ grams}$ of B at $673\text{ K}$. The molar free energy of mixing is ___ $\text{J mol}^{-1}$ (Round off to one decimal place).\nGiven: Universal gas constant $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$, atomic weight of $\text{A} = 40\text{ g mol}^{-1}$, atomic weight of $\text{B} = 60\text{ g mol}^{-1}$

Explanation

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q21

NAT[2 Marks]

800 grams of A-B alloy containing $20\text{ wt.}\%$ B is held at temperature $T_1$. The weight of B dissolved in $\alpha$ at that temperature is ___ grams (Round off to the nearest integer).

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q22

MCQ[1 Mark]

At one atmosphere pressure, $\alpha$-Fe transforms to $\gamma$-Fe above $912^{\circ}\text{C}$. Density of $\gamma$-Fe is more than that of $\alpha$-Fe. Choose the correct statement. (A) Increasing the pressure above one atmosphere lowers the $\alpha$-Fe to $\gamma$-Fe transformation temperature. (B) Increasing the pressure above one atmosphere raises the $\alpha$-Fe to $\gamma$-Fe transformation temperature. (C) Molar volume of $\gamma$-Fe is higher than the molar volume of $\alpha$-Fe. (D) Pressure change will not have any effect on the $\alpha$-Fe to $\gamma$-Fe transformation temperature.

(A)

Increasing the pressure above one atmosphere lowers the \alpha-Fe to \gamma-Fe transformation temperature.

(B)

Increasing the pressure above one atmosphere raises the \alpha-Fe to \gamma-Fe transformation temperature.

(C)

Molar volume of \gamma-Fe is higher than the molar volume of \alpha-Fe.

(D)

Pressure change will not have any effect on the \alpha-Fe to \gamma-Fe transformation temperature.

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q23

MCQ[1 Mark]

Formation of an ideal solution leads to (A) increase in entropy (B) decrease in volume (C) increase in enthalpy (D) decrease in entropy

(A)

increase in entropy

(B)

decrease in volume

(C)

increase in enthalpy

(D)

decrease in entropy

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q24

MCQ[1 Mark]

At one atmosphere pressure, iron (Fe) and nickel (Ni) oxidize as: $2Fe + O_{2} \leftrightarrow 2FeO$, $\Delta G^{\circ} = -527400 + 128T\text{ Joules}$ $2Ni + O_{2} \leftrightarrow 2NiO$, $\Delta G^{\circ} = -471200 + 172T\text{ Joules}$\nIdentify the correct statement. Given: Temperature $T$ is in Kelvin. (A) Fe can reduce NiO at all temperatures (B) Fe can reduce NiO only above 1000 K (C) Ni can reduce FeO at all temperatures (D) Ni can reduce FeO only above 1000 K

(A)

Fe can reduce NiO at all temperatures

(B)

Fe can reduce NiO only above 1000 K

(C)

Ni can reduce FeO at all temperatures

(D)

Ni can reduce FeO only above 1000 K

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q25

NAT[1 Mark]

Maximum number of phases that can be in equilibrium for a 5-component system at constant temperature and pressure is ___ (in integer).

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q26

MCQ[2 Marks]

Taking $S$ as entropy, $T$ as temperature, $P$ as pressure, and $V$ as volume, match Column I with Column II.\nColumn I: (A) Gibbs Free Energy (B) Helmholtz Free Energy (C) Enthalpy (D) Internal Energy\nColumn II: (1) depends on $T, V$ and composition (2) depends on $T, P$ and composition (3) depends on $S, P$ and composition (4) depends on $S, V$ and composition (A) A-2, B-1, C-3, D-4 (B) A-4, B-3, C-2, D-1 (C) A-3, B-1, C-4, D-2 (D) A-2, B-1, C-4, D-3

(A)

A-2, B-1, C-3, D-4

(B)

A-4, B-3, C-2, D-1

(C)

A-3, B-1, C-4, D-2

(D)

A-2, B-1, C-4, D-3

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q27

MSQ[2 Marks]

Concerning the chemical potentials of components in a binary system at constant pressure, the correct statement(s) is/are (A) For single-phase equilibrium at a given temperature, chemical potentials of the components change with alloy composition. (B) For two-phase equilibrium at a given temperature, chemical potential of any component in both phases is same. (C) For two-phase equilibrium at a given temperature, chemical potentials of the components change with alloy composition. (D) For single-phase equilibrium of a given composition, chemical potentials of the components do not change with temperature.

(A)

For single-phase equilibrium at a given temperature, chemical potentials of the components change with alloy composition.

(B)

For two-phase equilibrium at a given temperature, chemical potential of any component in both phases is same.

(C)

For two-phase equilibrium at a given temperature, chemical potentials of the components change with alloy composition.

(D)

For single-phase equilibrium of a given composition, chemical potentials of the components do not change with temperature.

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q28

NAT[2 Marks]

Enthalpy of formation of an A-B regular solution containing $80\text{ atomic percent A}$ is $3.36\text{ kJ mol}^{-1}$. The activity coefficient of A at $500\text{ K}$ for the solution containing $40\text{ atomic percent A}$ is ___ (round off to 1 decimal place).\nGiven: Universal gas constant, $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$

Explanation

GATE→2023→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q29

NAT[2 Marks]

The alloy A (given in the phase diagram) is cooled slowly from the liquid state to just below the eutectic temperature. The ratio of weight fractions of pro-eutectic $\alpha$ to eutectic $\alpha$ is ___ (round off to 1 decimal place).

Explanation

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q30

NAT[2 Marks]

What is the equilibrium $\frac{p_{CO}}{p_{CO_{2}}}$ ratio for the given reaction at $1873\text{ K}$? (round off to 2 decimal places) $$Mo(s) + O_{2}(g) \leftrightarrow MoO_{2}(s)$$\nGiven: $\Delta_{f}G^{\circ}_{1873} = -262300\text{ J}$; $a_{MoO_{2}(s)} = 0.5$ and $\Delta_{r}G^{\circ}_{1873} = -120860\text{ J}$ for the reaction $CO(g) + 0.5O_{2}(g) \leftrightarrow CO_{2}(g)$; $R = 8.314\text{ J K}^{-1}\text{mol}^{-1}$.

Explanation

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q31

NAT[2 Marks]

The partial molar enthalpy of Au in Ag-Au melt containing $25\text{ mol}\%$ Au at $1400\text{ K}$ is $-8300\text{ J}\cdot\text{mol}^{-1}$. Assuming regular solution behavior, the activity of Au in the melt is ___ (round off to 3 decimal places).\nGiven: $R = 8.314\text{ J}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}$

Explanation

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q32

NAT[2 Marks]

Assuming that Dulong-Petit law is valid for a monoatomic solid, the ratio of heat capacities $\frac{C_p}{C_v}$ at $500\text{ K}$ is ___ (round off to 3 decimals).\nGiven: molar volume $= 7 \times 10^{-6}\text{ m}^3\cdot\text{mol}^{-1}$, isothermal compressibility $\beta = 8 \times 10^{-12}\text{ Pa}^{-1}$, isobaric expansivity $\alpha = 6 \times 10^{-5}\text{ K}^{-1}$, and $R = 8.314\text{ J}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}$.

Explanation

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q33

NAT[2 Marks]

The equilibrium microstructure of an alloy A-B consists of two phases $\alpha$ and $\beta$ in the molar proportion $2:1$. If the overall composition of the alloy is $70\text{ mol}\%$ B and the composition of $\beta$ is $90\text{ mol}\%$ B, the composition of $\alpha$ is ___ (in mol% B) (round off to the nearest integer).

Explanation

Electrochemistry

4 Questions

GATE→2025→Metallurgical Thermodynamics→Electrochemistry

Q34

NAT[2 Marks]

Consider the following cell reaction: $$Mg + Cd^{2+} \rightleftharpoons Mg^{2+} + Cd$$\nThe standard Gibbs free energy change for the reaction is ___ $\text{kJ}$ (rounded off to an integer).\nGiven: Standard oxidation potentials are $Mg \rightleftharpoons Mg^{2+} + 2e^-$, $E^\circ = 2.37\text{ V}$; $Cd \rightleftharpoons Cd^{2+} + 2e^-$, $E^\circ = 0.403\text{ V}$. Faraday's constant $= 96500\text{ C mol}^{-1}$

Explanation

GATE→2024→Metallurgical Thermodynamics→Electrochemistry

Q35

NAT[2 Marks]

The cupric ion ($Cu^{2+}$) concentration in the electrolyte (at $298\text{ K}$) required to make the potential of pure copper equal to $0.17\text{ V}$ is ___ $\times 10^{-6}\text{ gram-mol (litre)}^{-1}$ (Round off to two decimal places). (Given: $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$, $F = 96500\text{ C mol}^{-1}$, standard reduction potential $E^\circ = 0.34\text{ V}$)

Explanation

GATE→2023→Metallurgical Thermodynamics→Electrochemistry

Q36

NAT[2 Marks]

In an aqueous solution of $Fe^{2+}$ ions with concentration of $10^{-4}\text{ M}$ at $298\text{ K}$ and atmospheric pressure, the reduction potential of Fe in volt is ___ (round off to 2 decimal places).\nGiven: Standard reduction potential, $E^{\circ}_{Fe^{2+}/Fe} = -0.44\text{ V}$, Faraday's constant $F = 96500\text{ C mol}^{-1}$, Universal gas constant $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$

Explanation

GATE→2022→Metallurgical Thermodynamics→Electrochemistry

Q37

NAT[2 Marks]

The emf of the cell $$\text{Au-Pb(liquid) } | \text{ PbCl}_2\text{-KCl(liquid) } | \text{ Cl}_2\text{(gas, } 0.5\text{ atm), C(graphite)}$$\nis $1.2327\text{ V}$ at $873\text{ K}$. Activity of Pb in the Au-Pb alloy is $0.72$ and the activity of $\text{PbCl}_2$ in the electrolyte is $0.18$. The standard Gibbs energy of formation of $\text{PbCl}_2\text{(liquid)}$ at $873\text{ K}$ is ___ $\text{kJ}\cdot\text{mol}^{-1}$ (round off to 1 decimal place).\nGiven: $R = 8.314\text{ J}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}$ and $F = 96500\text{ C}\cdot\text{mol}^{-1}$.

Explanation