List of top Questions asked in GATE Metallurgical Engineering

Which one of the following matrices is orthogonal?

Match the casting defects in Column I with the characteristic features 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?

Front tension is applied during cold rolling of a thin metal sheet. Which of the following statements is/are TRUE?

Which of the following statements is/are CORRECT when Ni is added as an alloying element to a low alloy steel?

Which of the following statements is/are CORRECT with respect to fusion welding and solid-state welding of metals and alloys?

Which of the following welding processes does NOT / do NOT utilize a consumable electrode?

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

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 \( R = 8.314 \, {J mol}^{-1} {K}^{-1} \) 
 

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 value of \[ \lim_{x \to 0} \frac{6(x - \sin x)}{x^3} \] is ........ (in integer).

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 \( R = 8.314 \, {J mol}^{-1} {K}^{-1} \).

The diameter of spherical galena particles that have the same settling velocity as spherical quartz particles of diameter 25 μm (both settling in water) is _________ μm (rounded off to one decimal place). Assume Stokes law of settling to be valid. Given: Density of galena = 7400 kg m\(^{-3}\), Density of quartz = 2600 kg m\(^{-3}\), Density of water = 1000 kg m\(^{-3}\).

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\(^{-1}\).

An intrinsic semiconductor has conductivity of 100 Ω\(^{-1}\) m\(^{-1}\) at 300 K and 300 Ω\(^{-1}\) m\(^{-1}\) at 500 K. The band gap of the semiconductor is _________ eV (rounded off to two decimal places). Given: Boltzmann constant \( k_B = 8.6 \times 10^{-5} \, {eV K}^{-1} \)

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).

Temperatures at two sides of a 0.4 m thick copper plate are 1000°C 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 _________ \( \times 10^5 \, {W m}^{-2} \) (in integer). Given: Thermal conductivity of copper \( k = 400 \, {W m}^{-1} {K}^{-1} \).

In polycrystalline Ni, Nabarro-Herring diffusion creep was found to be the rate controlling creep mechanism at a certain temperature. At that temperature, if the steady state strain rate is \( 10^{-8} \, {s}^{-1} \) at a stress of 10 MPa, the steady state strain rate of \( 10^{-9} \, {s}^{-1} \) will be obtained at a stress value of _________ MPa (in integer). Assume that the same creep mechanism is rate controlling during the creep deformation.