Entropy

List-I contains various physical/chemical processes, and List-II contains combinations of changes in enthalpy $(\Delta H)$ and entropy $(\Delta S)$. Match each entry in List-I to the appropriate entry in List-II, and choose the correct option.

Match List - I with List - II.

Given $V_1$ and $V_2$ are initial and final volumes respectively.

Choose the correct answer from the options given below :

One mole of an ideal monoatomic gas undergoes two reversible processes ($\mathrm{A}\to\mathrm{B}$ and $\mathrm{B}\to\mathrm{C}$) as shown in the given figure:

$\mathrm{A}\to\mathrm{B}$ is an adiabatic process. If the total heat absorbed in the entire process ($\mathrm{A}\to\mathrm{B}$ and $\mathrm{B}\to\mathrm{C}$) is $RT_2\ln 10$, the value of $2\log V_3$ is _____.

[Use, molar heat capacity of the gas at constant pressure, $C_{\mathrm{p,m}} = \frac52 R$]

The value of entropy change, $S_\beta - S_\alpha$ (in $\mathrm{J\,mol^{-1}\,K^{-1}}$), at 300 K is _____.

[Use: $\ln 2 = 0.69$. Given: $S_\beta - S_\alpha = 0$ at 0 K]

The correct option(s) about entropy (S) is(are)

[R = gas constant, F = Faraday constant, T = Temperature]

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

($p$: pressure, $V$: volume, $T$: temperature, $H$: enthalpy, $S$: entropy)

One mole of an ideal gas at 900 K, undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $\ln\dfrac{V_3}{V_2}$ is ____.

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

(Given: molar heat capacity at constant volume, $C_{V,m}$ of the gas is $\frac52R$)

An ideal gas is expanded from $(\mathrm{p_1, V_1, T_1})$ to $(\mathrm{p_2, V_2, T_2})$ under different conditions. The correct statement(s) among the following is(are)

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant $K$ in terms of change in entropy is described by

An ideal gas undergoes isothermal expansion at constant pressure. During the process :

One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surroundings $(\Delta S_{surr})$ in $\mathrm{J\,K^{-1}}$ is

(1 L atm = 101.3 J)

A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following :

Match the thermodynamic processes given under Column I with the expressions given under Column II.

For the process
$$\ce{H2O(l) -> H2O(g)}$$
at $T=100\ ^\circ$C and 1 atmosphere pressure, the correct choice is

The molar heat capacity ($C_p$) of $\ce{CD2O}$ is 10 cals at 1000 K. The change in entropy associated with cooling of 32 g of $\ce{CD2O}$ vapour from 1000 K to 100 K at constant pressure will be :

(D = deuterium, at. mass = 2 u)

The entropy (S°) of the following substances are :

$\ce{CH4}$ (g) 186.2 J K$^{-1}$ mol$^{-1}$
$\ce{O2}$ (g) 205.0 J K$^{-1}$ mol$^{-1}$
$\ce{CO2}$ (g) 213.6 J K$^{-1}$ mol$^{-1}$
$\ce{H2O}$ ($l$) 69.9 J K$^{-1}$ mol$^{-1}$

The entropy change (ΔS°) for the reaction
$$\ce{CH4(g) + 2O2(g) -> CO2(g) + 2H2O(l)}$$
is :

For an ideal gas, consider only $P$-$V$ work in going from an initial state $X$ to the final state $Z$. The final state $Z$ can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct? [take $\Delta S$ as change in entropy and $w$ as work done]

Match the transformations in column I with appropriate options in column II

STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work.

and

STATEMENT-2: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

For the process $\ce{H2O}(l)$ (1 bar, 373 K) → $\ce{H2O}(g)$ (1 bar, 373 K), the correct set of thermodynamic parameters is