GATE MT format:nat PYQs & Answers — Page 4

Questions 31–40 of 232. Imported answers require independent review unless marked reviewed.

Topic practice 232 questionsPage 4 of 24

For a two-dimensional field described by

, the magnitude of its gradient at the point

is _____ (rounded off to two decimal places).

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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

, then the value of

= _____ (rounded off to two decimal places).

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The excess molar Gibbs free energy of a solution of element A and B at 1000 K is given by

, where

and

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

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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 (½ H

(g) = [H]), the equilibrium constant (expressed in terms of ppm of dissolved H) is:

1 atm = 760 Torr

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The value of

is _____ (in integer).

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Consider the following reactions and their standard Gibbs free energies (in J):

Fe(s) +

(g) ⇌ FeO(s)

2 H

(g) + O

(g) ⇌ 2 H

O(g)

Assuming Fe and FeO to be pure and no solubility of gases in the solids, the value of

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

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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

, density of quartz = 2600 kg m

, density of water = 1000 kg m

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Consider the following cell reaction:

Mg + Cd

⇌ Mg

+ 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 standard hydrogen electrode are:

Mg ⇌ Mg

+ 2e

E° = 2.37 V

Cd ⇌ Cd

+ 2e

E° = 0.403 V

Faraday’s constant = 96500 C mol

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Copper is being electrodeposited from a CuSO

bath onto a stainless steel cathode of total surface area of 2 m

in an electrolytic cell operated at a current density of 200 A m

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

, atomic mass of copper = 63.5 g mol

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An intrinsic semiconductor has conductivity of 100 Ω

at 300 K and 300 Ω

at 500 K.

The band gap of the semiconductor is _____ eV (rounded off to two decimal places).

Given: Boltzmann constant

= 8.6 × 10

eV K

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GATE MT format:nat PYQs

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Question 57