JEE Advanced Paper 1 - 2014

One mole of an ideal gas at $900 \mathrm{K}$, undergoes two reversible processes, $\mathrm{I}$ followed by $\mathrm{II}$, as shown below. If the work done by the gas in the two processes are same, the value of $\ln \frac{{\mathrm{V}}_3}{{\mathrm{V}}_2}$ is

($\mathrm{U}$ : internal energy, $\mathrm{S}:$ entropy, $\mathrm{p}:$ pressure, $\mathrm{V}:$ volume, $\mathrm{R}$ : gas constant) 

(Given: molar heat capacity at constant volume, ${\mathrm{C}}_{\mathrm{V},\mathrm{m}}$ of the gas is $\frac{5}{2}\mathrm{R}$)

Give your answer as the nearest integer.

For a reaction, $A\rightleftharpoons P$ , the plots of $\left[A\right]\mathrm{a}\mathrm{n}\mathrm{d} \left[P\right]$ with time at temperatures $T_1 \mathrm{a}\mathrm{n}\mathrm{d} T_2$ are given below.



If $T_2>T_1$ , the correct statement(s) is (are)

(Assume $∆H^{⊝} \mathrm{a}\mathrm{n}\mathrm{d} ∆S^{⊝}$ are independent of temperature and ratio of $\ln K \mathrm{a}\mathrm{t} T_1 \mathrm{t}\mathrm{o} \ln K \mathrm{a}\mathrm{t} T_2$ is greater than $T_2/T_1$ . Here H, S , G and K are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

An ideal gas undergoes a reversible isothermal expansion from state $\mathrm{I}$ to state $\mathrm{II}$ followed by a reversible adiabatic expansion from state $\mathrm{II}$ to state $\mathrm{III}.$ The correct plot $\left(\mathrm{s}\right)$ representing the changes from state $\mathrm{I}$ to state $\mathrm{III}$ is(are)

($\mathrm{p}$: pressure, $\mathrm{V}$: volume, $\mathrm{T}$: temperature, $\mathrm{H}$: enthalpy, $\mathrm{S}$: entropy)

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure$1$). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure $2$), the volume (in ${\mathrm{m}}^3$) of the compartment A after the system attains equilibrium is $\frac{20}{x} {\mathrm{m}}^3$. Write the value of $x$.

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in $\mathrm{K}$) at which the reduction of cassiterite by coke would take place.

$298 \mathrm{K}: {\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{SnO}}_2\left(\mathrm{s}\right)\right)=-581.0 \mathrm{kJ} {\mathrm{mol}}^{-1}, {\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{CO}}_2\left(\mathrm{g}\right)\right)=-394.0 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{S}}^0\left({SnO}_2\left(\mathrm{s}\right)\right)=56.0 {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}, {\mathrm{S}}^0\left(\mathrm{Sn}\right(\mathrm{s}\left)\right)=52.0 {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$

${\mathrm{S}}^0\left(\mathrm{C}\right(\mathrm{s}\left)\right)=6.0 {\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}, {\mathrm{S}}^0\left({\mathrm{CO}}_2\left(\mathrm{g}\right)\right)=210.0 {\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$

Assume that the enthalpies and the entropies are temperature independent.

The surface of copper gets tarnished by the formation of copper oxide. ${\mathrm{N}}_2$ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the ${\mathrm{N}}_2$ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:

$2\mathrm{Cu}\left(\mathrm{s}\right)+\mathrm{ }{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\to \mathrm{ }{\mathrm{Cu}}_2\mathrm{O}\left(\mathrm{s}\right)\mathrm{ }+\mathrm{ }{\mathrm{H}}_2\left(\mathrm{g}\right)$

${\mathrm{P}}_{{\mathrm{H}}_2}$ Is the minimum partial pressure of ${\mathrm{H}}_2$ (in bar) needed to prevent the oxidation at $1250\mathrm{K}$. The magnitude of value of $\ln \left({\mathrm{P}}_{{\mathrm{H}}_2}\right)$ is ____.

(Given: total pressure = 1 bar, R (universal gas constant) $=\mathrm{ }8\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{K}}^{-1}\mathrm{ }{\mathrm{mol}}^{-1},\ln \left(10\right)\mathrm{ }=\mathrm{ }2.3.\mathrm{ }\mathrm{Cu}\left(\mathrm{s}\right)\mathrm{ }\mathrm{and}\mathrm{ }{\mathrm{Cu}}_2\mathrm{O}\left(\mathrm{s}\right)\mathrm{ }$ are mutually immiscible.

At $1250\mathrm{ }\mathrm{K}:\mathrm{ }2\mathrm{Cu}\left(\mathrm{s}\right)+\frac{1}{2}\mathrm{ }{\mathrm{O}}_2\left(\mathrm{g}\right)\to \mathrm{ }{\mathrm{Cu}}_2\mathrm{O}\left(\mathrm{s}\right);\mathrm{ }∆{\mathrm{G}}^{⊝}\mathrm{ }=\mathrm{ }-\mathrm{ }78,000\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}$

${\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to \mathrm{ }{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right); ∆{\mathrm{G}}^{⊝}\mathrm{ }=\mathrm{ }-\mathrm{ }1,78,000\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1};$) 

Round off the answer up to the nearest integer.

Choose the reaction(s) from the following options, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation.

A reversible cyclic process for an ideal gas is shown below. Here, $P, V, \mathrm{a}\mathrm{n}\mathrm{d} T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q, w, H \mathrm{a}\mathrm{n}\mathrm{d} U$ are heat, work, enthalpy and internal energy, respectively.



The correct option(s) is (are)