List of top Metallurgical Thermodynamics Questions asked in GATE Metallurgical Engineering

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\(^{-1}\).