GATE MT branch:mt PYQs & Answers — Page 19

Questions 181–190 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 19 of 65

The following data is obtained from an experiment:

| x | 1 | 2 | 3 | | y | 8 | 15 | 19 |

If the data is fit using the straight line

(where m and c are constants) using the least-squares method, then the value of m is ________. (Round off to one decimal place).

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The integral

evaluates to ________. (Round off to two decimal places)

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If for element A, the formation enthalpy and formation entropy per vacancy created are 0.5 eV and

, respectively, then the equilibrium vacancy concentration (in mole fraction) at 500 K is ________

. (Round off to two decimal places)

Given: Boltzmann constant,

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A steel bar is subjected to fatigue loading with a tensile mean stress. Given that the ultimate tensile strength is 1000

and the fatigue limit under fully reversed loading is 250

, the fatigue limit for a mean stress of 100

, considering Goodman relationship is _____

. (Round off to the nearest integer)

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During carburization of a steel at 950 °C, carbon concentration is measured as 0.8 wt.% at a depth of 0.3

after one hour. The time required to get the same carbon concentration at a depth of 0.6

at the same carburization temperature is _____

. (Round off to the nearest integer).

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An ideal solution is formed by mixing 10

of A and 50

of B at 673

. The molar free energy of mixing ______

. (Round off to one decimal place)

Given: Universal gas constant

Atomic weight of A = 40

Atomic weight of B = 60

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The cupric ion (Cu

) concentration in the electrolyte (at 298

) required to make the potential of pure copper equal to 0.17

is ______

. (Round off to two decimal places).

Gas constant

Faraday’s constant

(of electrons)

Standard reduction potential of Cu,

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A non-porous spherical Fe

particle of initial radius of

is topochemically reduced by H

, where the reactant-product interface is sharp and spherical, and reaction rate is proportional to the interfacial area. The radius of the unreacted Fe

particle after 600

will be ______

. (Round off to the nearest integer).

Given: Rate constant

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A long metallic cylindrical rod of radius

, length

(

) and electrical resistivity

is kept in vacuum and is carrying an electric current of

. The only way it loses heat to the ambient is via radiation. If the ambient temperature is

, then the steady-state temperature of the rod is ________

. (Round off to the nearest integer).

Given: Stefan-Boltzmann constant =

Neglect the heat loss by the two flat ends of the rod and assume emissivity = 1.

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100

of sphalerite concentrate containing 60% ZnS is COMPLETELY roasted with stoichiometric amount of pure oxygen. The amount of oxygen required is _____

. (Round off to one decimal place).

Assume that the other components in the concentrate are not reactive.

Given: Atomic weight values (in

) for Zn = 65, S = 32, O = 16.

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GATE MT branch:mt PYQs

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