Problem 14 - A Complete Resource Book in Chemistry for JEE Main

Question

Considering entropy (S) as a thermodynamic parameter, the criterion for the spontaneity of any process is (a) \(\Delta \mathrm{S}_{\text {system }}+\Delta \mathrm{S}_{\text {surroundings }}>0\) (b) \(\Delta \mathrm{S}_{\text {system }}-\Delta \mathrm{S}_{\text {surroundings }}>0\) (c) \(\Delta \mathrm{S}_{\text {system }}>0\) (d) \(\Delta \mathrm{S}_{\text {surroundings }}>0\)

Step-by-Step Solution

Answer

Option (a): \( \Delta \mathrm{S}_{\text{system}} + \Delta \mathrm{S}_{\text{surroundings}} > 0 \).

Step 1: Understanding the Question

We are tasked with determining the correct criterion for the spontaneity of a thermodynamic process based on changes in entropy of the system and its surroundings. Entropy is a measure of disorder or randomness in a system.

Step 2: Thermodynamic Spontaneity

For a process to be spontaneous, the total entropy change (the sum of entropy change of the system and surroundings) must be positive. This is derived from the second law of thermodynamics which states that the total entropy - or the entropy of the universe - increases for a spontaneous process.

Step 3: Analyzing the Available Options

From the options given: (a) sums the system and surroundings entropy and suggests it must be greater than 0. (b) subtracts the surroundings entropy from the system entropy and suggests it must be greater than 0. (c) considers only the system's entropy to be positive. (d) considers only the surroundings' entropy to be positive.

Step 4: Choosing the Right Option

According to the second law of thermodynamics, the criterion for a spontaneous process is for the total entropy change to be greater than zero, i.e., the sum of the change in the system's entropy and surroundings' entropy should be greater than zero. Hence, option (a) is correct: \( \Delta \mathrm{S}_{\text{system}} + \Delta \mathrm{S}_{\text{surroundings}} > 0 \).

Key Concepts

Entropy

Entropy is a fundamental concept in thermodynamics, often described as a measure of a system's disorder or randomness. In simple terms, it helps us understand how energy is distributed within a system. When we say a system has high entropy, it means the energy is dispersed widely and the system is more disordered. On the other hand, low entropy indicates a more ordered state.

Entropy has a significant impact on spontaneity in thermodynamic processes. When studying entropy within a given system, scientists consider not just the system itself but also its surroundings. This is because the universe, as an entire system, always moves towards higher entropy according to natural laws.

• A process where overall entropy increases is more likely to be spontaneous.
• Entropy doesn't just concern heat but also probability, where a more probable state is usually more disordered.
• Measuring entropy changes involves considering both the system and its surroundings.

Second Law of Thermodynamics

The Second Law of Thermodynamics is a cornerstone of physics and chemistry, providing insight into the directionality of processes. This law states that in an isolated system, the total entropy can never decrease over time. It must either increase or, in some ideal cases, remain constant.

This law implies that natural processes tend to move towards a state of maximum entropy. Essentially, things naturally progress towards what we perceive as disorder or randomness.

• This law is the reason why perpetual motion machines are impossible, as energy will always disperse, increasing entropy, and cannot be totally converted back into useful work.
• The Second Law indicates that for any spontaneous process, the total entropy change of the universe must be positive.
• In practical terms, this law helps in predicting the feasibility and direction of chemical reactions and physical transformations.

Spontaneous Processes

Spontaneous processes are those that occur naturally without any external energy input. This concept is closely linked to entropy and the Second Law of Thermodynamics. A process will be spontaneous if it results in an increase in the overall entropy of the universe, which includes both the system and its surroundings.

The criteria for spontaneity is that the sum of the entropy changes for the system and the surroundings must be greater than zero. Hence, these processes are guided by the tendency to reach a higher state of disorder.

• Spontaneity does not necessarily mean that a process will occur quickly; it merely indicates the direction of natural change.
• A spontaneous change can still be slow, such as rusting of iron.
• Spontaneous processes are essential in understanding why certain reactions occur in nature, while others require energy input.