Standard entropy of X₂, Y₂ and XY₃ are 60, 40 and 50 JK⁻¹ mol⁻¹ , respectively. For the reaction,
$${1 \over 2} X_2$$ + $${3 \over 2} Y_2 \to$$ XY₃, $$\Delta H$$ = -30 kJ, to be at equilibrium, the temperature will be :

Assuming that water vapour is an ideal gas, the internal energy change $$\left( {\Delta U} \right)$$ when $$1$$ mol of water is vapourised at $$1$$ bar pressure and $${100^ \circ }C$$ (Given : molar enthalpy of vapourisation of water at $$1$$ bar and $$373$$ $$K$$ $$ = 41\,kJ\,mo{l^{ - 1}}\,$$
and $$R = 8.3\,J\,mo{l^{ - 1}}\,{K^{ - 1}}$$ )

Identify the correct statement regarding a spontaneous process :

In conversion of lime-stone to lime,
CaCO₃(s) $$\to$$ CaO(s) + CO₂ (g) the vales of ∆H° and ∆S° are +179.1 kJ mol−1 and 160.2 J/K respectively at 298 K and 1 bar. Assuming that ∆H° do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is :