List of top Metallurgical Thermodynamics Questions asked in GATE MT

Copper is being electrodeposited from a CuSO\(_4\) bath onto a stainless steel cathode of total surface area of 2 m\(^2\) in an electrolytic cell operated at a current density of 200 A m\(^{-2}\) with a current efficiency of 90%. The mass of copper deposited in 24 h is _________ kg (rounded off to two decimal places). Given: Faraday's constant = 96500 C mol\(^{-1}\), Atomic mass of copper = 63.5 g mol\(^{-1}\).
Consider the following cell reaction: \[ {Mg} + {Cd}^{2+} \rightleftharpoons {Mg}^{2+} + {Cd} \] The standard Gibbs free energy change for the reaction is _________ kJ (rounded off to an integer). Given: Standard oxidation potentials for the reactions with respect to the standard hydrogen electrode are: Mg \( \rightleftharpoons \) Mg\(^{2+}\) + 2e\(^-\) \( E^\circ = 2.37 \, {V} \) Cd \( \rightleftharpoons \) Cd\(^{2+}\) + 2e\(^-\) \( E^\circ = 0.403 \, {V} \) Faraday’s constant = 96500 C mol\(^{-1}\)
The excess molar Gibbs free energy of a solution of element A and B at 1000 K is given by \( G^{XS} = -3000 X_A X_B \) 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 mol% of B at 1000 K is ......... (rounded off to two decimal places). Given: Ideal gas constant \( R = 8.314 \, {J mol}^{-1} {K}^{-1} \)
Temperatures at two sides of a 0.4 m thick copper plate are 1000 and 500 °C. Assuming steady state, one-dimensional conductive heat transfer through the wall and ignoring end-effects, the magnitude of the heat flux through the wall is ............... × 10$^5$ W m$^{-2$ (in integer).} Given: Thermal conductivity of copper = 400 W m$^{-1}$ K$^{-1}$
Consider the following cell reaction: Mg + Cd$^{2+}$ ⇌ Mg$^{2+}$ + Cd The standard Gibbs free energy change for the reaction is ........... kJ (rounded off to an integer). Given: Standard oxidation potentials with respect to standard hydrogen electrode are: Mg ⇌ Mg$^{2+}$ + 2e$^-$, E° = 2.37 V
Cd ⇌ Cd$^{2+}$ + 2e$^-$, E° = 0.403 V
Faraday's constant = 96500 C mol$^{-1}$
The excess molar Gibbs free energy of a solution of element A and B at 1000 K is given by $G^{XS = -3000 X_A X_B$ 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 mol percent of B at 1000 K is ........... (rounded off to two decimal places).}
Consider the following reactions and their standard Gibbs free energies (in J): Fe(s) + $\tfrac{1}{2}$ O$_2$(g) ⇌ FeO(s) \quad ΔG° = −264900 + 65T
2 H$_2$(g) + O$_2$(g) ⇌ 2 H$_2$O(g) \quad ΔG° = −492900 + 109T
Assuming Fe and FeO to be pure and no solubility of gases in solids, the value of $\tfrac{p_{H2O}}{p_{H2}}$ required to reduce FeO to Fe at 1000 K is ................. (rounded off to two decimal places).
Radiative heat flux $\dot{q$ at a hot surface at a temperature $T_s$ can be expressed as} \[ \dot{q} = A \, f(T_s, T_\infty) \, (T_s - T_\infty) \] where $A$ is a constant and $T_\infty$ is the temperature of the surroundings (all temperatures in K). The function $f(T_s, T_\infty)$ is given by ____.
Consider the phase diagram of a one component system. Va, Vb and Vliquid are the molar volumes of alpha, beta and liquid phases respectively. Which one of the following statements is true?
\begin{center} \includegraphics[width=0.7\textwidth]{05.jpeg} \end{center} Given: The change in molar enthalpies, DeltaH alpha to beta and DeltaH beta to liquid, are positive.
Standard Gibbs free energies of formation of oxides per mole of O2 at 1000 K are given below. SiO2: -728 kJ, TiO2: -737 kJ, VO: -712 kJ, MnO: -624 kJ. Regarding thermodynamic feasibility of oxide reduction, which of the following statements is or are CORRECT under standard conditions at 1000 K?
Consider the following gas-phase reaction: \[ 2SO_2 + O_2 \;\rightleftharpoons\; 2SO_3 \] If the enthalpy of reaction is negative, which condition promotes a higher equilibrium concentration of \(SO_3\)?
Which one of the following is an intensive property?
For an isobaric process, the heat transferred is equal to the change in ________ of the system.
Standard Gibbs free energies of formation of some solid oxides per mole of O\(_2\) at 1000 K are given below. \[ {SiO}_2: -728 \, {kJ}, \, {TiO}_2: -737 \, {kJ}, \, {VO}: -712 \, {kJ}, \, {MnO}: -624 \, {kJ} \] Regarding thermodynamic feasibility of oxide reduction, which of the following statements is/are CORRECT under standard conditions at 1000 K?
For an isobaric process, the heat transferred is equal to the change in .............. of the system.

The excess molar Gibbs free energy of a solution of element A and B at 1000 K is given by \( G^{XS} = -3000 X_A X_B \) 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 mol% of B at 1000 K is ......... (rounded off to two decimal places). Given: Ideal gas constant \( R = 8.314 \, {J mol}^{-1} {K}^{-1} \) 
 

Consider the following cell reaction: \[ {Mg} + {Cd}^{2+} \rightleftharpoons {Mg}^{2+} + {Cd} \] The standard Gibbs free energy change for the reaction is _________ kJ (rounded off to an integer). Given: Standard oxidation potentials for the reactions with respect to the standard hydrogen electrode are:
Mg \( \rightleftharpoons \) Mg\(^{2+}\) + 2e\(^-\) \( E^\circ = 2.37 \, {V} \) Cd \( \rightleftharpoons \) Cd\(^{2+}\) + 2e\(^-\) \( E^\circ = 0.403 \, {V} \) Faraday’s constant = 96500 C mol\(^{-1}\)

Copper is being electrodeposited from a CuSO\(_4\) bath onto a stainless steel cathode of total surface area of 2 m\(^2\) in an electrolytic cell operated at a current density of 200 A m\(^{-2}\) with a current efficiency of 90%. The mass of copper deposited in 24 h is _________ kg (rounded off to two decimal places). Given: Faraday's constant = 96500 C mol\(^{-1}\), Atomic mass of copper = 63.5 g mol\(^{-1}\).

A chimney as shown in the figure requires to have a natural draft (pressure difference between the furnace and the bottom of chimney, \( P_o - P_1 \)) of \( 1.0133 \times 10^3 \) Pa. 
Given: acceleration due to gravity, g = 9.81 m s\(^{-2}\) 
Assume densities of air and flue do not change along the chimney height. Neglect frictional energy loss and kinetic energy difference at the bottom and top of the chimney. 
If the density difference between the air and flue is 0.5 kg m\(^{-3}\), the minimum height (h) of the chimney in meters is ................... (round off to nearest integer). 

A thin plate is loaded in plane stress condition with \( \sigma_{xx} = 110 \) MPa, \( \sigma_{yy} = -50 \) MPa, \( \tau_{xy} = -70 \) MPa. The maximum principal stress in MPa is ................... (round off to nearest integer).
Two circular surfaces A and B with the values of emissivity \(\epsilon\), temperature T, and respective view factors are shown in the figure. Consider heat radiation only between surfaces A and B.
Given: Stefan-Boltzmann constant, \( \sigma = 5.67 \times 10^{-8} \) Wm\(^{-2}\)K\(^{-4}\)
Net heat flow rate by radiation from surface A in kW is ................... (round off to 1 decimal place).
Enthalpy of formation of an A-B regular solution containing 80 atomic percent A is 3.36 kJ mol\(^{-1}\). The activity coefficient of A at 500 K for the solution containing 40 atomic percent A is ................... (round off to 1 decimal place).
Given: Universal gas constant, R = 8.314 J mol\(^{-1}\)K\(^{-1}\)
Concerning the chemical potentials of components in a binary system at constant pressure, the correct statement(s) is/are
Taking S as entropy, T as temperature, P as pressure, and V as volume, match Column I with Column II.
Column I
(A) Gibbs Free Energy
(B) Helmholtz Free Energy
(C) Enthalpy
(D) Internal Energy
Column 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
Maximum number of phases that can be in equilibrium for a 5-component system at constant temperature and pressure is ................... (in integer).