2 nd Law of thermodynamics and Entropy Questions in English

(D) Entropy $(S)$ is a measure of the randomness or disorder of a system. $A$ positive entropy change $(\Delta S > 0)$ occurs when the system becomes more disordered,such as during a phase transition from a more ordered state (liquid) to a less ordered state (gas).
In the reaction $H_2O_{(l)} \longrightarrow H_2O_{(g)}$,liquid water is converted into water vapor. Since gas molecules have much higher randomness compared to liquid molecules,the entropy of the system increases,making $\Delta S$ positive.
In other options,the reactions involve a decrease in the number of moles of gas or a transition from a disordered state to a more ordered state (like liquid to solid or gas to solid),which results in a negative entropy change.

(D) The entropy change during a phase transition is given by the formula $\Delta S = \frac{q_{rev}}{T} = \frac{m \times L_f}{T}$.
Given:
Mass of ice $(m)$ $= 27.3 \ g$
Latent heat of fusion $(L_f)$ $= 330 \ J g^{-1}$
Temperature $(T)$ $= 0^{\circ} C = 273 \ K$
Substituting the values:
$\Delta S = \frac{27.3 \ g \times 330 \ J g^{-1}}{273 \ K}$
$\Delta S = \frac{9009 \ J}{273 \ K} = 33 \ J K^{-1}$.

(A) The given process represents the phase transition of water from liquid to gas at its boiling point $(373.15 \ K)$ and standard pressure $(1 \ bar)$.
Since the system is in equilibrium at the boiling point,the change in Gibbs free energy is $\Delta G = 0$.
During the phase change from liquid to gas,the disorder of the system increases,which means the entropy change is positive,$\Delta S > 0$ (or $\Delta S = +ve$).

(A) The entropy of vaporisation $(\Delta S_{vap})$ is given by the formula: $\Delta S_{vap} = \frac{\Delta H_{vap}}{T_b}$
Given: $\Delta H_{vap} = 24.64 \ kJ \ mol^{-1} = 24640 \ J \ mol^{-1}$
Boiling point $T_b = 35 + 273 = 308 \ K$
Substituting the values: $\Delta S_{vap} = \frac{24640 \ J \ mol^{-1}}{308 \ K} = 80 \ J \ K^{-1} \ mol^{-1}$

(C) Entropy is a state function that measures the degree of randomness or disorder in a system.
For a reversible process,the change in entropy $(dS)$ is defined as the ratio of the heat exchanged reversibly $(\delta q_{rev})$ to the absolute temperature $(T)$ at which the exchange occurs.
Thus,the mathematical expression is $dS = \frac{\delta q_{rev}}{T}$.

(A) When water evaporates,it changes from a liquid state to a gaseous state.
In the gaseous state,the molecules have more freedom of movement compared to the liquid state.
Therefore,the disorder or entropy of the system increases during evaporation.

(D) The second law of thermodynamics,specifically the Kelvin-Planck statement,asserts that it is impossible for any device that operates on a thermodynamic cycle to receive heat from a single thermal reservoir and produce a net amount of work.
In other words,heat cannot be completely converted into work in a cyclic process without leaving some effect on the surroundings.