Consider the following statements:
$(A)$ Entropy of a perfect crystalline solid at absolute zero approaches zero.
$(B)$ For spontaneity of a reaction at constant temperature and pressure, $T\Delta S > \Delta H$ (where $\Delta H$ is positive).
Identify the correct answer from the options given below.

  • A
    Both ‘$A$’ and ‘$B$’ are true
  • B
    ‘$A$’ is true but ‘$B$’ is false
  • C
    Both ‘$A$’ and ‘$B$’ are false
  • D
    ‘$A$’ is false but ‘$B$’ is true

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The ratio of heats liberated at $298 \ K$ from the combustion of one $kg$ of coke and by burning water gas obtained from $1 \ kg$ of coke is. (Assume coke to be $100 \%$ carbon.) (Given enthalpies of combustion of $CO_{2}, CO$ and $H_{2}$ as $393.5 \ kJ/mol, 283.5 \ kJ/mol, 285.5 \ kJ/mol$ respectively all at $298 \ K$.) (in $: 1$)

Standard entropies of $X_2$,$Y_2$ and $XY_3$ are $60$,$40$ and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2} X_2 + \frac{3}{2} Y_2 \rightarrow XY_3$,the enthalpy change is $\Delta H = -30 \ kJ \ mol^{-1}$. At what temperature will the reaction be at equilibrium (in $K$)?

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Match the following terms in Column-$I$ with their corresponding descriptions in Column-$II$:
Column-$I$Column-$II$
$(a)$ Adiabatic process$(1)$ Heat
$(b)$ Isolated system$(2)$ At constant volume
$(c)$ Isothermal change$(3)$ First law of thermodynamics
$(d)$ Path function$(4)$ No exchange of matter and energy
$(e)$ State function$(5)$ No heat exchange
$(f)$ $\Delta U = q$$(6)$ Constant temperature
$(g)$ Law of conservation of energy$(7)$ Internal energy
$(h)$ Reversible process$(8)$ $p_{ext} = 0$
$(i)$ Free expansion$(9)$ At constant pressure
$(j)$ $\Delta H = q$$(10)$ Infinitely slow process involving multiple equilibrium states
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