Assertion (A): Spontaneous process is an irreversible process and may be reversed by some external agency. Rea

NCERT Exemplar · Q56

Q. Assertion (A): Spontaneous process is an irreversible process and may be reversed by some external agency. Reason (R): Decrease in enthalpy is a contributory factor for spontaneity.

(i) Both A and R are true and R is the correct explanation of A.

(ii) Both A and R are true but R is not the correct explanation of A.

(iii) A is true but R is false.

(iv) A is false but R is true.

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Concept understanding — Entropy Change Prediction

Entropy Change Prediction

Imagine you have a box of marbles — all neatly arranged, reds on one side, blues on the other. Now shake the box. What happens? The colours mix. They never spontaneously unmix. That tendency — for things to go from ordered to disordered — is what entropy measures. Entropy is a measure of disorder or randomness in a system.

When you predict an entropy change, you're asking: Will this process make the system more disordered or less disordered? And by how much?

The Core Intuition

Entropy change ( $\Delta S$ ) is positive when disorder increases, negative when disorder decreases. Three things drive this:

Volume change — More space means more positions for particles → more disorder. A gas expanding into vacuum has $\Delta S > 0$ .
Temperature change — Higher temperature means particles move faster, explore more states → more disorder. Heating something increases entropy.
Phase change — Solid → liquid → gas is a ladder of increasing disorder. Melting ice increases entropy; freezing water decreases it.

Note

Entropy always increases for spontaneous processes in an isolated system (Second Law of Thermodynamics). But for a non-isolated system, entropy can decrease locally — as long as the surroundings' entropy increases enough to compensate.

The Precise Statement

For a reversible process at constant temperature, the entropy change is:

\Delta S = \frac{Q_{\text{rev}}}{T}

where $Q_{\text{rev}}$ is the heat transferred reversibly, and $T$ is the absolute temperature (in Kelvin).

For an irreversible process (which is what actually happens), you calculate $\Delta S$ by imagining a reversible path between the same initial and final states — because entropy is a state function. It depends only on where you start and end, not how you get there.

\Delta S = \int \frac{dQ_{\text{rev}}}{T}

For common cases, you use these:

Process	Formula	Sign intuition
Isothermal expansion/compression (ideal gas)	$\Delta S = nR \ln\frac{V_2}{V_1}$	Expanding → more volume → $\Delta S > 0$
Heating/cooling (constant pressure)	$\Delta S = nC_p \ln\frac{T_2}{T_1}$	Heating → higher T → $\Delta S > 0$
Phase change (melting, boiling)	$\Delta S = \frac{\Delta H_{\text{phase}}}{T_{\text{phase}}}$	Melting/boiling → more disorder → $\Delta S > 0$

How to Predict Without Calculation

You don't always need numbers. Ask these questions in order:

Is there a phase change? Solid → liquid or liquid → gas always increases entropy. Reverse decreases it.
Is the number of gas molecules changing? In a reaction, more gas molecules means more disorder. $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ (gas → liquid) has $\Delta S < 0$ because 3 gas molecules become 2 liquid molecules.
Is temperature increasing or decreasing? Higher temperature → higher entropy.
Is volume increasing? More space → more entropy. …

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Spontaneous processes are indeed irreversible and can be reversed by external work; enthalpy decrease contributes to spontaneity but doesn't explain irreversibility. Both statements are true, but R does not explain A.

Understanding Spontaneity and Irreversibility

A spontaneous process is one that occurs naturally under given conditions without continuous external intervention. The deep connection between spontaneity and irreversibility lies in the second law of thermodynamics: every spontaneous process increases the entropy of the universe.

The key insight is that while a spontaneous process proceeds in one direction on its own, reversing it requires an external agency to do work on the system. When you reverse a spontaneous process, you're fighting against the natural tendency of the universe to maximize entropy.

Evaluating the Assertion

Let's examine whether assertion (A) is correct.

Spontaneous processes are irreversible: This is true in the thermodynamic sense. A truly reversible process is an idealization that proceeds infinitely slowly through equilibrium states. Real spontaneous processes happen at finite rates and generate entropy, making them irreversible.
Can be reversed by external agency: Absolutely true. Consider a gas spontaneously expanding into a vacuum (irreversible). You can compress it back using a piston (external work), but the universe as a whole has still experienced a net entropy increase when you account for the surroundings. The refrigerator is a perfect everyday example—heat spontaneously flows from hot to cold, but a refrigerator (external agency) pumps heat from cold to hot.

Assertion (A) is true.

Evaluating the Reason

Now let's examine whether reason (R) is correct.

Does enthalpy decrease contribute to spontaneity? Yes, it does. The Gibbs free energy criterion for spontaneity at constant temperature and pressure is:

\Delta G = \Delta H - T\Delta S < 0

A negative $\Delta H$ (exothermic process) makes a negative contribution to $\Delta G$ , favoring spontaneity. Many spontaneous processes—combustion, crystallization, acid-base neutralization—are exothermic.

Watch out

Enthalpy decrease alone does not guarantee spontaneity. Endothermic processes can be spontaneous if the entropy increase is large enough (like ice melting above 0°C or dissolution of ammonium nitrate in water).

Reason (R) is true.

Does R Explain A? …

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Q.Assertion (A): Spontaneous process is an irreversible process and may be reversed by some external agency. Reason (R): Decrease in enthalpy is a contributory factor for spontaneity.

Understanding Spontaneity and Irreversibility

Evaluating the Assertion

Evaluating the Reason

Does R Explain A? …

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Q.Assertion (A): Spontaneous process is an irreversible process and may be reversed by some external agency.
Reason (R): Decrease in enthalpy is a contributory factor for spontaneity.

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