The spontaneity means, having the potential to proceed without the assistance of external agency. The processe

NCERT Exemplar · Q17

Q. The spontaneity means, having the potential to proceed without the assistance of external agency. The processes which occur spontaneously are (Note: more than one of the given options may be correct.)

(i) flow of heat from colder to warmer body.

(ii) gas in a container contracting into one corner.

(iii) gas expanding to fill the available volume.

(iv) burning carbon in oxygen to give carbon dioxide.

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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 increase the total entropy of the universe and proceed without external work. Gas expansion into available volume and exothermic combustion are spontaneous; heat flowing uphill and gas spontaneously contracting violate the second law.

Spontaneity is governed by the second law of thermodynamics: a process occurs spontaneously if it increases the total entropy of the universe (system plus surroundings), or equivalently, if the Gibbs free energy of the system decreases under constant temperature and pressure. The key insight is that nature favors dispersal—of energy and of matter—unless constrained.

When we say a process is spontaneous, we mean it has an intrinsic thermodynamic drive. It will happen on its own once initiated, without continuous external intervention. This does not mean it happens instantly (diamond turning to graphite is spontaneous but glacially slow), only that the thermodynamic arrow points in that direction.

Let's examine each option through the lens of entropy and natural tendency:

1. Flow of heat from colder to warmer body (option (i))

Heat spontaneously flows from hot to cold, never the reverse, because that direction increases total entropy. When heat $q$ moves from a hot reservoir at temperature $T_h$ to a cold one at $T_c$ , the cold body gains entropy $\frac{q}{T_c}$ while the hot body loses $\frac{q}{T_h}$ . Since $T_c < T_h$ , the gain exceeds the loss:

\Delta S_{\text{total}} = \frac{q}{T_c} - \frac{q}{T_h} > 0

Reversing this—pumping heat from cold to hot—requires external work (a refrigerator or heat pump). The process described in (i) violates the Clausius statement of the second law and is non-spontaneous.

2. Gas in a container contracting into one corner (option (ii))

A gas naturally expands to fill all available space because there are vastly more microstates (arrangements of molecules) when the gas occupies the full volume than when confined to a corner. Entropy is $S = k \ln \Omega$ , where $\Omega$ is the number of accessible microstates. Spontaneous contraction would decrease entropy without compensating increase elsewhere, violating the second law.

To compress a gas into one corner requires external work—a piston, a pump, something to fight the gas's natural tendency to spread. This process is non-spontaneous.

3. Gas expanding to fill the available volume (option (iii))

This is the textbook example of spontaneous entropy increase. When a gas expands into a vacuum (free expansion) or even against a small pressure, the molecules access more spatial configurations. The entropy change for an ideal gas expanding isothermally from $V_1$ to $V_2$ is:

\Delta S = nR \ln \frac{V_2}{V_1} > 0 \quad \text{when } V_2 > V_1

No external agency is needed; remove a partition and the gas spreads on its own. This is spontaneous.

Tip

Whenever you see "gas expanding into available space" or "mixing of gases," think spontaneous. Whenever you see "gas contracting" or "unmixing," think non-spontaneous.

4. Burning carbon in oxygen to give carbon dioxide (option (iv)) …

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Q.The spontaneity means, having the potential to proceed without the assistance of external agency. The processes which occur spontaneously are (Note: more than one of the given options may be correct.)

1. Flow of heat from colder to warmer body (option (i))

2. Gas in a container contracting into one corner (option (ii))

3. Gas expanding to fill the available volume (option (iii))

4. Burning carbon in oxygen to give carbon dioxide (option (iv)) …

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