List of top Mineral Processing and Extractive Metallurgy Questions

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).

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 \[ \sigma = 10 (\dot{\varepsilon})^{0.3} \, {MPa}. \] 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 \, {J m}^{-3} \) (rounded off to one decimal place).

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).

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

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} $.

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 $\frac{{Lattice parameter of metal A}}{{Lattice parameter of metal B}} = \ldots\ldots\ldots { (rounded off to two decimal places)}$ .

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).

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).

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.

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).

The reaction represented by A → 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).

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 of dissolved hydrogen is .............. Torr (rounded off to two decimal places).

Match the steel plant related processes in Column I with the associated information in Column II. Column I: P. Corex
Q. Electric Arc Furnace
R. Midrex
S. Continuous Casting
Column II: 1. Melter-gasifier
2. Natural gas reformer
3. Electromagnetic stirrer
4. Hot heel

Which of the following conditions is/are favorable for producing low-silicon hot metal in blast furnace ironmaking?

Match the following elements in Column I with their respective ores in Column II. \begin{center} \begin{tabular}{|l|l|} \hline Column I & Column II
\hline P. Al & 1. Rutile
\hline Q. Fe & 2. Hematite
\hline R. Ti & 3. Chalcopyrite
\hline S. Cu & 4. Bauxite
\hline \end{tabular} \end{center}

Which one of the following slag components is responsible for the oxidizing power of steelmaking slags?

Hot metal from a blast furnace is treated with mill scale prior to oxygen steelmaking for _____.

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.

In the Fe-C system, the invariant reaction Liquid + $\delta$ $\rightleftharpoons$ $\gamma$ takes place at 1493 °C. This type of reaction is called ______.

Consider the following gas-phase reaction: \[ 2 {SO}_2 + {O}_2 \rightleftharpoons 2 {SO}_3 \] If the enthalpy of reaction is negative, which one of the following conditions promotes a higher equilibrium concentration of SO$_3$?

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).