Metallurgical Engineering Gate 2024 Questions with Answer

Ques 53 GATE 2024

If for element A, the formation enthalpy and formation entropy per vacancy created are 0.5 eV and 3k_B, respectively, then the equilibrium vacancy concentration (in mole fraction) at 500 K is _______ × 10^-4. (Round off to two decimal places)
Given: Boltzmann constant, k_B = 8.62 × 10^-5 eV⋅atom^-1⋅K^-1

Ques 54 GATE 2024

A steel bar is subjected to fatigue loading with a tensile mean stress. Given that the ultimate tensile strength is 1000 MPa and the fatigue limit under fully reversed loading is 250 MPa, the fatigue limit for a mean stress of 100 MPa, considering Goodman relationship is _______ MPa. (Round off to the nearest integer)

Ques 55 GATE 2024

During carburization of a steel at 950 °C, carbon concentration is measured as 0.8 wt.% at a depth of 0.3 mm after one hour. The time required to get the same carbon concentration at a depth of 0.6 mm at the same carburization temperature is _______ hours. (Round off to the nearest integer).

Ques 56 GATE 2024

An ideal solution is formed by mixing 10 grams of A and 50 grams of B at 673 K. The molar free energy of mixing is _______ kJ⋅mol^-1. (Round off to one decimal place)
Given: Universal gas constant R = 8.314 J⋅mol^-1⋅K^-1
Atomic weight of A = 40𝑔𝑟𝑎𝑚𝑠. 𝑚𝑜l^-1
Atomic weight of B = 60 𝑔𝑟𝑎𝑚𝑠. 𝑚𝑜l^-1

Ques 57 GATE 2024

The cupric ion (Cu²⁺) concentration in the electrolyte (at 298 K) required to make the potential of pure copper equal to 0.17 V is _______ × 10^-6 gram-mol⋅(litre)^-1. (Round off to two decimal places).
Gas constant R = 8.314 J⋅mol^-1⋅K^-1
Faraday's constant F = 96500 C⋅mol^-1 (of electrons)
Standard reduction potential of Cu, E° = 0.34 V

Ques 58 GATE 2024

A non-porous spherical Fe₂O₃ particle of initial radius of 5 × 10^-2 m is topo-chemically reduced by H₂ where the reactant-product interface is sharp and spherical, and reaction rate is proportional to the interfacial area. The radius of the unreacted Fe₂O₃ particle after 600 s will be _______ × 10^-2 m. (Round off to the nearest integer).
Given: Rate constant k = 5 × 10^-5 m⋅s^-1

Ques 59 GATE 2024

A long metallic cylindrical rod of radius r, length L (>> r) and electrical resistivity ρ_e is kept in vacuum and is carrying an electric current of I. The only way it loses heat to the ambient is via radiation. If the ambient temperature is T₀, then the steady-state temperature of the rod is _______ K.
(Round off to the nearest integer).
Given: Stefan-Boltzmann constant = 5.667 × 10^-8 W⋅m^-2⋅K^-4
r = 0.1 mm    L = 1 m     ρ_e = 10^-8 Ω⋅m
I = 0.3 A     T₀ = 300 K
Neglect the heat loss by the two flat ends of the rod and assume emissivity = 1.

Ques 60 GATE 2024

1000 kg of sphalerite concentrate containing 60% ZnS is COMPLETELY roasted with stoichiometric amount of pure oxygen. The amount of oxygen required is _______ kg. (Round off to one decimal place).
Assume that the other components in the concentrate are not reactive.
Given: Atomic weight values (in gram⋅mol^-1) for Zn = 65, S = 32, O = 16.

Ques 61 GATE 2024

800 grams of A-B alloy containing 20 wt.% B is held at temperature T₁. The weight of B dissolved in α at that temperature is _______ grams. (Round off to the nearest integer).

Ques 62 GATE 2024

A mild steel pipeline is connected to zinc for cathodic protection at a current density of 10 mA⋅m^-2. The quantity of zinc required per square meter of the pipeline per year is _______ grams. (Round off to the nearest integer).
Given: Atomic weight of Zn is 65 gram⋅mol^-1.
Faraday's constant F = 96500 C⋅mol^-1 (of electrons)

Ques 63 GATE 2024

A large rectangular component is undergoing fully-reversed cyclic loading, and the component is known to grow the dominant fatigue crack from the outer surface. If the stress amplitude (σ_A) is 100 MPa and the critical stress intensity factor K_IC of the material is 50 MPa⋅m^1/2, then the crack length at which the component will fail catastrophically is _______ mm. (Round off to one decimal place)
Given: The geometric factor α for this loading condition is 1.12.

Ques 64 GATE 2024

In casting, for a simple vertical gating system with a gate of cross-sectional area 2 cm² and spruce height of 10 cm, the filling time for a mould of dimensions 40 cm × 20 cm × 10 cm, is _______ s. (Round off to one decimal place)
Given: Acceleration due to gravity g = 980 cm⋅s^-2

Ques 65 GATE 2024

During arc welding, the actual heat input is 200 J⋅mm^-3 and the current and voltage are 200 A and 20 V, respectively. For a weld cross-sectional area of 2 mm² and heat transfer efficiency of 0.9, the velocity of welding is _______ mm⋅s^-1. (Round off to the nearest integer).