List of top Mineral Processing and Extractive Metallurgy Questions asked in GATE Metallurgical Engineering

Match the phenomena in Column I with the typical observations in Column II. 

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

Match each crystal defect in Column I with the corresponding type in Column II. 

The following are the activation energies for diffusion of carbon and iron at 773 K in polycrystalline BCC iron: P = Activation energy for diffusion of carbon in BCC iron through the lattice Q = Activation energy for diffusion of iron in BCC iron through the lattice R = Activation energy for diffusion of iron in BCC iron along the grain boundary Which one of the following statements is CORRECT?

For a two-dimensional field described by \( T(x, y) = \frac{1}{3} xy(x + y) \), the magnitude of its gradient at the point \( (1, 1) \) is .......... (rounded off to two decimal places).

X-ray diffraction using a monochromatic radiation of wavelength 0.154 nm is performed on powder samples of metal A (with FCC crystal structure) and metal B (with BCC crystal structure). If the first peak in both the cases occurs at a Bragg angle \( \theta = 20^\circ \), then the value of \(\frac{{Lattice parameter of metal A}}{{Lattice parameter of metal B}} = \ldots\ldots\ldots { (rounded off to two decimal places)}\) .

Molten steel at 1900 K having dissolved hydrogen needs to be vacuum degassed. The equilibrium partial pressure of hydrogen to be maintained to achieve 1 ppm (mass basis) of dissolved hydrogen is ......... Torr (rounded off to two decimal places). Given: For the hydrogen dissolution reaction in molten steel \( \left( \frac{1}{2} {H}_2(g) = [{H}] \right) \), the equilibrium constant (expressed in terms of ppm of dissolved H) is: \[ \log_{10} K_{eq} = \frac{1900}{T} + 2.4 \] 1 atm = 760 Torr. 
 

Consider the following reactions and their standard Gibbs free energies (in J): \[ {Fe(s)} + \frac{1}{2} {O}_2(g) \rightleftharpoons {FeO(s)} \quad \Delta G^\circ = -264900 + 65T \] \[ 2 {H}_2(g) + {O}_2(g) \rightleftharpoons 2 {H}_2{O(g)} \quad \Delta G^\circ = -492900 + 109T \] Assuming Fe and FeO to be pure and no solubility of gases in the solids, the value of \( \frac{p_{H_2O}}{p_{H_2}} \) required to reduce solid FeO to solid Fe at 1000 K is _________ (rounded off to two decimal places). Given: Ideal gas constant \( R = 8.314 \, {J mol}^{-1} {K}^{-1} \).

For a component fabricated from an alloy A with plane strain fracture toughness, \( K_{IC} = 50 \, {MPa m}^{1/2} \), fracture was observed to take place at a crack length of 0.4 mm at a tensile service stress of \( \sigma \). If the same component is instead fabricated from alloy B with \( K_{IC} = 75 \, {MPa m}^{1/2} \), the crack length at which a similar crack geometry will result in fracture (under identical tensile service stress of \( \sigma \)) is _________ mm (rounded off to one decimal place).

A single crystal BCC metal with a lattice parameter \( a = 0.4 \, \text{nm} \) is subjected to deformation at a shear strain rate of \( 0.001 \, \text{s}^{-1} \).
If the average mobile dislocation density in the single crystal is \( 10^{10} \, \text{m}^{-2} \), the average dislocation velocity is _________ (\( \times 10^{-3} \, \text{m s}^{-1} \)) (rounded off to two decimal places).
Given: Burgers vector \( b = \frac{a}{2} \langle 111 \rangle \).

A cylindrical specimen is subjected to plastic deformation in tension up to a uniform elongation of 10%. The final cross-sectional area of the gage section is found to be 20 mm\(^2\). The initial cross-sectional area of the gage section is _________ mm\(^2\) (rounded off to an integer).

The reaction represented by \( A \rightarrow B \) follows first-order kinetics. At a given temperature, 20% of the reaction is completed in 223 s. The time taken to complete 50% of the reaction at the same temperature is _________ s (rounded off to the nearest integer).

A cylindrical Al alloy billet of 300 mm diameter is hot extruded to produce a cylindrical rod of 75 mm diameter at a constant true strain rate (\( \dot{\varepsilon} \)) of 10 s\(^{-1}\). The flow stress (\( \sigma \)) of the alloy at the extrusion temperature is given by:
\[ \sigma = 10 (\dot{\varepsilon})^{0.3} \, \text{MPa}. \] Assume the alloy is perfectly plastic and there is no temperature rise during the extrusion process.
The ideal plastic work of deformation per unit volume is _________ (\( \times 10^6 \, \text{J m}^{-3} \)) (rounded off to one decimal place).