Assuming that Dulong-Petit law is valid for a monoatomic solid, the ratio of heat

 Cp/Cv capacities  at 500 K is  _____. (round off to 3 decimals).

Given:  molar volume = 7×10⁶  m3 mol^-1, isothermal compressibility = 8×10¹² Pa¹, isobaric expansivity = 6×10⁵K¹ andR = 8.314 JK^-1mol^-1.

The concentration 𝐶 of a solute (in units of atomsmm3) in a solid along 𝑥 direction (for 𝑥 > 0) follows the expression 𝐶 = 𝑎1𝑥² + 𝑎2𝑥 where 𝑥 is in mm, 𝑎1 and 𝑎2 are in units of atomsmm⁵ and atoms mm4, respectively. Assuming 𝑎1= 𝑎2= 1, the magnitude of flux at 𝑥 = 2 mm is _____ × 10^–3 atomsmm2 s1 (answer rounded off to the nearest integer). Given: diffusion coefficient of the solute in the solid is 3 × 10^–3 mm2⋅s1.

During solidification of a pure metal, the radius of critical nucleus at an undercooling of 10 K is   ______ × 10^–9 m (answer rounded off to 1 decimal place).

Given: solid/liquid interface energy = 0.177 Jm^-2, melting point of the metal = 1356 K and latent heat of fusion = 1.88 × 109  Jm^-3

A rectangular block made of Material I and Material II of identical cross sections (as shown in the figure) has a temperature (T) of 435 K and 400 K at the bottom and top surfaces, respectively. Assuming purely steady state conductive heat transfer, the temperature at the interface  is _    K (round off to nearest integer).

(Given: The two parts of the block made of Material I and Material II have equal thickness of 25 mm each. The thermal conductivities of Material I and Material II are 50 Wm¹K¹ and 200 WM¹K¹, respectively.)

The partial molar enthalpy of Au in Ag-Au melt containing 25 mol% Au at 1400 K is 8300 Jmol1. Assuming regular solution behavior, the activity of Au in the melt is      (round off to 3 decimal places). Given: R = 8.314 JK1mol1

What is the equilibrium^pC0 / pC02 ratio for the given reaction at 1873 K? (round off to 2 decimal places)

Mo(s) + O2(g)  MoO2(s)

Given: Δf𝐺₁₈₇₃^∘   = 262300 J; 𝑎MoO  ₂  (s) = 0.5 and Δr𝐺  ₁₈₇₃^∘    = 120860 J for the

 reaction CO(g) + 0.5O2(g)  CO2(g); R = 8.314 JK^1mol^1.

A spherical gas bubble of radius 0.01 mm is entrapped in molten steel held at  1773 K. If the pressure outside the bubble is 1.5 bar, the pressure inside the bubble is _____ bar (round off to 1 decimal place). Given: 1 bar = 10⁵ Pa and the surface tension of the steel at 1773 K is 1.4 N⋅ m^–1.

A Newtonian incompressible liquid is contained between two parallel metal plates separated by 10^–3 m (see figure). A stress of 5 Pa is required to maintain the upper plate in motion with a constant speed of 2 ms^-1 in the horizontal direction relative to the bottom plate.

The viscosity of liquid contained between the plates is  ____ × 10^–3 Pas (answer rounded off to 1 decimal place).

According to Sieverts’ law, the equilibrium solubility of N₂ (gas) in molten steel  is  proportional to _________ .

Given: Equilibrium partial pressure of N₂ (gas) is pN₂