Heat has randomising influence on a system and temperature is the measure of average chaotic motion of particl

NCERT Exemplar · Q28

Q. Heat has randomising influence on a system and temperature is the measure of average chaotic motion of particles in the system. Write the mathematical relation which relates these three parameters.

Punjab PsebShort· 2mImportance★★★★★est

65% · 64/98 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

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. …

Start your 14-day free trial to unlock the full solution →

The randomising influence of heat is quantified by entropy, and its change ( $\Delta S$ ) is directly proportional to the heat transferred ( $Q_{rev}$ ) and inversely proportional to the absolute temperature ( $T$ ) at which the transfer occurs, given by the relation $\Delta S = \frac{Q_{rev}}{T}$ .

The statement "Heat has randomising influence on a system" directly refers to the concept of entropy. Entropy is a fundamental thermodynamic property that quantifies the degree of disorder or randomness within a system. When heat is added to a system, the particles gain kinetic energy, move more vigorously and chaotically, and can occupy a wider range of positions and energy states, leading to an increase in the system's disorder.

The statement "temperature is the measure of average chaotic motion of particles in the system" provides an intuitive understanding of temperature. At a microscopic level, temperature is indeed a measure of the average kinetic energy of the particles, which manifests as their chaotic, random motion.

The mathematical relation we are looking for connects the change in this randomising influence (entropy change) with the heat transferred and the temperature at which this transfer takes place.

Here's how these parameters are related:

Understanding Entropy Change ( $\Delta S$ ):

Entropy ( $S$ ) is a state function, meaning its value depends only on the current state of the system, not on how that state was reached. A change in entropy ( $\Delta S$ ) represents the change in the system's disorder. When a system absorbs heat, its disorder generally increases, so $\Delta S$ is positive. When it releases heat, its disorder decreases, and $\Delta S$ is negative.
The Role of Heat ( $Q$ ):

When heat ( $Q$ ) is transferred to a system, it increases the internal energy and kinetic energy of the particles. This increased energy allows particles to move more freely and randomly, thus increasing the system's disorder. Therefore, the change in entropy ( $\Delta S$ ) is directly proportional to the amount of heat transferred. More heat means more randomisation.
The Role of Temperature ( $T$ ):

The impact of a given amount of heat on the system's disorder depends critically on the temperature ( $T$ ) at which the heat transfer occurs.
- At low temperatures: A system at a low temperature is relatively ordered. Adding a small amount of heat will cause a significant relative increase in the disorder, as the particles gain a substantial fraction of their initial energy.
- At high temperatures: A system at a high temperature is already quite disordered. Adding the same small amount of heat will have a much less significant relative impact on the overall disorder, as the particles already possess high kinetic energy and are moving chaotically. Therefore, the change in entropy is inversely proportional to the absolute temperature $T$ (measured in Kelvin) at which the heat transfer occurs.
Combining the Relations: …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ27 — Given that ΔH = 0 for mixing of two gases. Explain whether the diffusi…→Next questionQ29 — Increase in enthalpy of the surroundings is equal to decrease in entha…

Q.Heat has randomising influence on a system and temperature is the measure of average chaotic motion of particles in the system. Write the mathematical relation which relates these three parameters.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days