Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 1: JEE Advanced Paper 1 - 2017

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.

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.

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.)

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.

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)

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)

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 $x$.