Second Law of Thermodynamics in Chemistry

The Second Law of Thermodynamics states that the entropy of the universe increases in the course of every spontaneous process. Entropy, often referred to as a measure of disorder, is a state function that is directly defined by the second law.

1.0What is Second Law of Thermodynamics

Have you ever noticed that once you mix milk into coffee, it never separates back on its own? Or that once you scramble an egg, it can’t be unscrambled? Why does your phone's battery always seem to drain, but never charge itself? These everyday occurrences all illustrate the concept of the "arrow of time." This principle dictates that certain processes only happen in one direction—forward. In physics, this is closely tied to the thermodynamic arrow of time, or entropy, which measures the level of disorder within a system. Represented by ΔS, changes in entropy highlight that over time, isolated systems naturally evolve towards greater disorder and randomness, making the progression of time asymmetrical and irreversible.

In any spontaneous (irreversible) process, the entropy of the universe always increases. The change in entropy (ΔS) of a system can be determined by the formula:

where dq_rev is the heat exchanged in a small reversible step and T is the absolute temperature at which the heat is absorbed.

2.0Types of Entropy Changes

1. ΔS_system​: Entropy change of the system.
2. ΔS_surrounding​: Entropy change of the surroundings.
3. ΔS_total: Entropy change of the universe, which is the sum of the entropy changes of the system and surroundings.

For a spontaneous process:

ΔS_universe = ΔS_system+ΔS_surrounding > 0

For a reversible process: ΔS_universe = 0

This implies that during an irreversible process, the entropy of the universe increases, while during a reversible process, it remains constant.

3.0Physical Significance of Entropy (ΔS)

Entropy (ΔS) is a measure of disorder or randomness in a system. To understand this, imagine heating a substance. If you supply the same amount of heat at two different temperatures, say T₁​ (low) and T₂​ (high), the increase in disorder will be more significant at the lower temperature (T₁​). This is because, at lower temperatures, the system is already in a relatively ordered state, so adding heat increases the kinetic energy and disorder more compared to adding the same heat at a higher temperature, where the particles are already moving faster and are more disordered.

4.0Determining Entropy Change of the Surroundings

For irreversible processes, calculating the entropy change (ΔS) directly is difficult due to their fast and unpredictable nature. To address this, we use a hypothetical reversible path where temperature and heat exchange are known.

The change in entropy is given by - $\frac{Heatabsorbedbyanentity}{Exacttemperatureatwhichheatisabsorbed}$

1. Reversible Process: In reversible processes, changes occur in a controlled way. Entropy change (ΔS) for the system and surroundings is calculated as:

where dq_rev​ is the heat exchanged reversibly and T is the absolute temperature.

2. Irreversible Process: In irreversible processes, the surroundings, being large and stable, absorb heat predictably. The entropy change of the surroundings is given by:

where q_irr​ is the actual heat exchanged. This method helps estimate the overall entropy change even without knowing the system's exact temperature.

5.0Second law (in terms of Engine)

• No Perfect Heat Engine: It is impossible for a cyclic engine to convert all the absorbed heat into work without affecting the surroundings. There will always be some heat loss.
• Heat Flow: Heat cannot spontaneously flow from a colder body to a hotter body without external work or intervention.
• Heat and Work Conversion: Complete conversion of heat into work in a cyclic process is not possible, although the reverse (work into heat) can be achieved. This indicates that heat (disordered energy) and work (ordered energy) are not equivalent in thermodynamics.

6.0Heat Engine

A heat engine is a device that converts heat into work while operating in a cyclic manner. It absorbs heat from a high-temperature source, performs work, and rejects some heat to a low-temperature sink. 

Q_H = Heat gained by engine per cycle

Q_C = Heat rejected by engine per cycle

The efficiency (η) of a heat engine is given by:

7.0Solved Questions on the second law of thermodynamics

Q. A heat pump uses 300 J of work to extract 400 J of heat from a low-temperature reservoir. How much heat is delivered to the high-temperature reservoir?

Solution:

The heat pump transfers energy by doing work to move heat from a cooler area (low-temperature reservoir) to a warmer area (high-temperature reservoir). The total heat delivered to the high-temperature reservoir is the sum of the heat extracted from the low-temperature reservoir and the work done by the pump.

Given:

• Work done (W) = 300 J
• Heat extracted from the low-temperature reservoir (Q_low​) = 400 J

The heat delivered to the high-temperature reservoir (Q_high​) is calculated as:

Q_high=Q_low+W

Substitute the given values:

Q_high = 400 J + 300 J = 700 J

Q.2 Three moles of an ideal gas are expanded isothermally from 2 L to 10 L at 27°C. Calculate the changes in entropy for the system (ΔS_sys​), surroundings (ΔS_surr​), and the universe (ΔS_univ​) for the following cases:

1. Reversible Expansion
2. Irreversible Expansion against a constant external pressure of 1 atm.
3. Free Expansion

Given Data:

• Number of moles (n) = 3 mol
• Initial volume (V_i​) = 2 L
• Final volume (V_f​) = 10 L
• Temperature (T) = 27°C = 300 K
• External pressure (P_ext​) = 1 atm (for irreversible case)

Sol.

1. Reversible Isothermal Expansion:

(i) Entropy Change of the System (ΔS_sys​):

The change in entropy for the system is given by:

Where: R = 8.314 J/mol·K (Universal Gas Constant)

Substitute the values:

(ii) Entropy Change of the Surroundings (ΔS_surr​):

For a reversible process, the change in entropy of the surroundings is equal in magnitude but opposite in sign to the heat absorbed by the system. Since the process is isothermal:

The heat absorbed by the system, q_rev​, is given by:

(iii) Entropy Change of the Universe (ΔSuniv\Delta S_{univ}ΔSuniv​):

ΔS_uni = ΔS_sys + ΔS_surr

ΔS_uni​ = ΔS_sys​ + ΔS_surr​ 

ΔSuniv = 40.18 − 40.18= 0 J/K

2. Irreversible Expansion Against a Constant External Pressure:

(i) Entropy Change of the System (ΔS_sys):

The entropy change of the system remains the same as in the reversible case because entropy is a state function:

         ΔS_sys​  = 40.18 J/K

(ii) Entropy Change of the Surroundings (ΔS_surr​):

For irreversible processes, the work done is P_ext× ΔV. The heat exchange with the surroundings is:

                             q_irr = P_ext × ΔV

Where:

• ΔV = V_f−V_i = 10−2 =8 L= 8×10⁻³ m³
• P_ext = 1 atm =101.3 kPa =101.3 J/L

(iii) Entropy Change of the Universe (ΔSuniv):

ΔS_uni = ΔS_sys​ + ΔS_surr​ 

ΔS_uni = 40.18−2.70 = 37.48 J/K

3. Free Expansion:

(i) Entropy Change of the System (ΔS_sys​):

The entropy change of the system remains the same:

ΔS_sys = 40.18 J/K

(ii) Entropy Change of the Surroundings (ΔS_surr):

In a free expansion, no heat is exchanged with the surroundings:

ΔS_surr = 0 J/K

(iii) Entropy Change of the Universe (ΔS_uni​):

ΔS_uni = ΔS_sys+ΔS_surr

 ΔS_uni =40.18 + 0 =40.18 J/K