Second Law of Thermodynamics: Definition, Formula and Examples

Second Law of Thermodynamics

Edited By Shivani Poonia | Updated on Jul 02, 2025 06:31 PM IST

One of the basic principles ruling physical processes, the Second Law of Thermodynamics deals with the spontaneous direction of energy transfer and the new concept of entropy. It says that the sum of the entropies of an isolated system will always grow larger or remain constant over time, never decreasing, for any natural thermodynamic process. It is the first law to introduce irreversibility in natural processes, while those described by the First Law of Thermodynamics are reversible. The Second Law has many statements, one of which is the Kelvin-Planck statement: "No heat engine can convert all of the heat supplied to it by a single thermal reservoir into work with no other effect."

This Story also Contains

Second Law of Thermodynamics
Some Solved Examples
Summary

Second Law of Thermodynamics

It is not possible to convert heat into work without compensation.

Work can always be converted into heat but the conversion of heat into work does not take place under all conditions.
It is impossible to construct a machine that is able to convey heat by a cyclic process from a colder to a hotter body unless work is done on the machine by some outside agency (Clausius statement).
The heat of the coldest body among those participating In a cyclic process cannot serve as a source of work (Thomson statement).
It is Impossible by means of the inanimate material agency to derive mechanical work or effort from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects (Kelvin-Planck statement)
Nature tends to pass from a less probable to a more probable state (Ludwig Boltzmann statement).
Whenever a spontaneous process takes place it is accompanied by an increase in the total entropy of the universe.

Some Solved Examples

Example 1: Which of the following processes is iso-entropic?

1)Isobaric process

2) Adiabatic process

3)Isothermal process

4)Isochoric process

Solution

As we have learned,

According to the definition of entropy,

Change in entropy,

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

As the heat change in the adiabatic process is equal to zero. Hence the change in entropy will be zero, which means the entropy will change in the process.

So the adiabatic reversible process will iso-entropic process as well.

Example 2: The entropy (S^o) in (JK^-1mol^-1) of the following substances are :

$\begin{aligned} & \mathrm{CH}_4(\mathrm{~g}): 186.2 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ & \mathrm{O}_2(\mathrm{~g}): 205.0 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ & \mathrm{CO}_2(\mathrm{~g}): 213.6 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ & \mathrm{H}_2 \mathrm{O}(\mathrm{l}): 69.9 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\end{aligned}$

The entropy change $\Delta S^0$ for the reaction $\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{l})$ is :

1) -312.7

2)-242.8

3)-108.1

4)-37.6

Solution

In the given reaction:

$\begin{aligned} & \mathrm{CH}_{4(\mathrm{~g})}+2 \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_{2(\mathrm{~g})}+\mathrm{H}_2 \mathrm{O}_{(\mathrm{l})} \\ & \Delta \mathrm{S}=\sum \mathrm{S}^{\circ}(\text { products })-\sum \mathrm{S}^{\circ}(\text { reactants }) \\ & \Delta \mathrm{S}=(213.6+69.9)-\{186.2+2(205)\} \\ & \therefore \Delta \mathrm{S}=-312.7 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\end{aligned}$

Hence, the answer is the option

Example 3: A sample of 18 g of H₂O is slowly heated from 300 K to 400 K. Calculate the change in entropy (in J/K) during heating. (Given: specific heat of water is $4200 \frac{\mathrm{J}}{\mathrm{kg} \cdot \mathrm{K}_{\mathrm{f}}}$)

1)7.81

2) 21.75

3)-7.81

4)36.25

Solution

As we learned,

$\Delta \mathrm{S}=\mathrm{m} \times \mathrm{C}_{\mathrm{P}} \times \operatorname{In} \frac{\mathrm{T}_2}{\mathrm{~T}_1}$

$\Rightarrow \Delta \mathrm{S}=\frac{18}{1000} \times 4200 \times \operatorname{In} \frac{400}{300}$

$\Rightarrow \Delta \mathrm{S}=21.75 \mathrm{~J} / \mathrm{K}$

Hence, the answer is ($\Delta S=21.75 \mathrm{~J} / K)$)

Summary

The Second Law of Thermodynamics states that the total entropy of an isolated system cannot diminish but either increases or remains constant over time; thus, it forms the spontaneity of energy transfer and the irreversibility in processes. It refers to an intrinsic tendency to disorder and equilibrial states; hence, it is not possible to transform heat into work without any other effects, totally. This law is expressed by means of the Kelvin-Planck statement, which forbids the perfect conversion of heat into work, and the Clausius statement, which rejects the spontaneous flow of heat from cold to hot bodies.

Frequently Asked Questions (FAQs)

1. What is the Second Law of Thermodynamics in simple terms?

The Second Law of Thermodynamics states that the entropy (disorder) of an isolated system always increases over time. In simpler terms, it means that energy tends to spread out and become less useful if left alone. This law explains why hot things cool down, why we can't create perpetual motion machines, and why some processes are irreversible.

2. How does the Second Law of Thermodynamics relate to energy efficiency?

The Second Law of Thermodynamics is crucial for understanding energy efficiency. It tells us that no energy transfer or conversion can be 100% efficient. Some energy will always be lost as heat or other forms of less useful energy. This is why even the best engines, refrigerators, or power plants can never achieve perfect efficiency.

3. What is entropy, and why is it important in the Second Law?

Entropy is a measure of the disorder or randomness in a system. The Second Law states that the total entropy of an isolated system always increases over time. This concept is important because it helps explain the direction of spontaneous processes, the limitations of heat engines, and why some reactions occur while others don't.

4. Can entropy ever decrease in a system?

While the entropy of an isolated system always increases, the entropy of a non-isolated system can decrease. However, this decrease must be accompanied by an even greater increase in entropy elsewhere, ensuring that the total entropy of the universe still increases. For example, the formation of an ice crystal decreases local entropy, but the heat released to the surroundings increases overall entropy.

5. How does the Second Law explain why heat flows from hot to cold objects?

The Second Law of Thermodynamics explains this phenomenon through entropy. When heat flows from a hot object to a cold one, it increases the overall entropy of the system. The cold object gains more entropy than the hot object loses, resulting in a net increase in entropy. This spontaneous process continues until thermal equilibrium is reached, maximizing entropy.

6. What is a heat engine, and how does the Second Law limit its efficiency?

A heat engine is a device that converts thermal energy into mechanical work. The Second Law limits the efficiency of heat engines because some energy must always be lost as heat to a cold reservoir. The maximum theoretical efficiency (Carnot efficiency) depends on the temperature difference between the hot and cold reservoirs. In practice, real heat engines are even less efficient due to additional energy losses.

7. How does the Second Law relate to the concept of free energy?

The Second Law of Thermodynamics is closely related to free energy, particularly Gibbs free energy in chemistry. Free energy combines the effects of enthalpy and entropy to predict the spontaneity of reactions. The Second Law dictates that spontaneous processes decrease the system's free energy while increasing the universe's overall entropy.

8. Why are some processes irreversible according to the Second Law?

The Second Law states that the entropy of an isolated system always increases. Some processes, like mixing gases or breaking an egg, increase entropy so much that reversing them would require a decrease in the universe's total entropy, which is impossible. These processes are called irreversible because they can't be undone without external input of energy and organization.

9. How does the Second Law explain the impossibility of a perpetual motion machine?

A perpetual motion machine would violate the Second Law of Thermodynamics. Such a machine would need to operate without any energy input and with 100% efficiency, which is impossible according to the Second Law. In any real machine, some energy is always lost as heat due to friction and other inefficiencies, eventually causing the machine to stop.

10. What is the heat death of the universe, and how is it related to the Second Law?

The heat death of the universe is a hypothetical end state where the universe reaches maximum entropy. According to the Second Law, the total entropy of the universe is constantly increasing. Eventually, this could lead to a state where all energy is evenly distributed, and no more useful work can be extracted. This concept is directly derived from the Second Law's prediction of ever-increasing entropy.

11. How does the Second Law affect chemical reactions?

The Second Law of Thermodynamics influences chemical reactions by favoring processes that increase the overall entropy of the system and surroundings. Reactions that increase disorder (like dissolving a solid in a liquid) are often spontaneous. The law also explains why some endothermic reactions can occur spontaneously if they result in a large enough increase in entropy.

12. What is the relationship between the Second Law and the spontaneity of reactions?

The Second Law helps determine the spontaneity of reactions through the concept of Gibbs free energy. A reaction is spontaneous if it decreases the system's free energy and increases the universe's total entropy. This relationship is captured in the equation ΔG = ΔH - TΔS, where a negative ΔG indicates a spontaneous process.

13. How does the Second Law explain the unidirectional flow of time?

The Second Law of Thermodynamics provides a possible explanation for the "arrow of time." As entropy always increases in isolated systems, it creates a distinction between past and future. We can tell the difference between a video played forward or backward based on whether entropy is increasing or decreasing, aligning with our perception of time's direction.

14. What is the Clausius statement of the Second Law?

The Clausius statement of the Second Law of Thermodynamics states that heat cannot spontaneously flow from a colder body to a hotter body. This means that to transfer heat from a cold object to a hot one, we must input work (like in a refrigerator). This statement is equivalent to saying that the entropy of an isolated system always increases.

15. How does the Second Law relate to the efficiency of refrigerators and air conditioners?

The Second Law of Thermodynamics sets limits on the efficiency of refrigerators and air conditioners. These devices move heat from a cold space to a warmer one, which doesn't happen spontaneously. They require energy input, and their efficiency is limited by the temperature difference between the cold and hot reservoirs. The law explains why it's impossible to create a perfect refrigerator that doesn't consume any energy.

16. What is the significance of the Second Law in living systems?

Living systems seem to defy the Second Law by maintaining order, but they actually conform to it. Organisms decrease their internal entropy by increasing the entropy of their surroundings (e.g., by consuming food and releasing heat). The Second Law explains why living things need a constant energy input and why perpetual life is impossible without such input.

17. How does the Second Law relate to information theory?

The Second Law of Thermodynamics has interesting connections to information theory. Information can be viewed as a form of negative entropy or "negentropy." Creating or storing information requires energy and increases the entropy of the surroundings. This connection helps explain phenomena like the energy cost of computation and the idea of "Maxwell's demon."

18. What is the Kelvin-Planck statement of the Second Law?

The Kelvin-Planck statement of the Second Law of Thermodynamics states that it is impossible to construct a device that operates in a cycle and produces no effect other than the extraction of heat from a single reservoir and the performance of an equivalent amount of work. This statement emphasizes the impossibility of converting heat completely into work.

19. How does the Second Law explain why we can't un-scramble an egg?

Un-scrambling an egg is a classic example of an irreversible process explained by the Second Law. When an egg is scrambled, its entropy increases significantly. Reversing this process would require a decrease in entropy, which is highly improbable in an isolated system. While theoretically possible, the energy and precise control required make it practically impossible.

20. What is the connection between the Second Law and the quality of energy?

The Second Law of Thermodynamics introduces the concept of energy quality. While the First Law states that energy is conserved, the Second Law tells us that the quality of energy degrades over time. High-quality energy (like electrical energy) can be fully converted to low-quality energy (like heat), but the reverse is not completely possible, explaining why some forms of energy are more useful than others.

21. How does the Second Law impact the efficiency of solar cells?

The Second Law of Thermodynamics sets theoretical limits on the efficiency of solar cells. Solar radiation has high entropy due to its high temperature source (the sun). When converting this energy to lower-temperature, lower-entropy electrical energy, some energy must be lost as heat. This fundamental limit, known as the Shockley-Queisser limit, explains why even ideal solar cells can't be 100% efficient.

22. What is the relationship between the Second Law and chemical equilibrium?

The Second Law of Thermodynamics is crucial in understanding chemical equilibrium. At equilibrium, the system has reached a state of maximum entropy (considering both the system and surroundings). The law explains why reactions proceed to equilibrium and don't continue to completion - the point of maximum entropy represents the most probable state for the system.

23. How does the Second Law explain the cooling of a cup of hot coffee?

The cooling of a cup of hot coffee is a classic example of the Second Law in action. Heat spontaneously flows from the hot coffee to the cooler surroundings because this process increases the overall entropy. The energy spreads out, becoming less concentrated and less useful, aligning with the law's prediction of increasing disorder over time.

24. What is the significance of the Second Law in the formation of chemical bonds?

The Second Law of Thermodynamics plays a crucial role in chemical bonding. While bond formation often decreases entropy (by reducing molecular freedom), it can still be favorable if it leads to a greater increase in entropy of the surroundings (usually through heat release). This balance between system entropy and surroundings entropy determines whether bonds will form spontaneously.

25. How does the Second Law relate to the concept of free energy in biochemical systems?

In biochemical systems, the Second Law is often applied through the concept of Gibbs free energy. Processes that decrease free energy (negative ΔG) are spontaneous. This helps explain why some reactions in living organisms can proceed "uphill" against concentration gradients - they are coupled with other reactions that release more free energy, ensuring the overall process increases entropy and follows the Second Law.

26. What is the connection between the Second Law and the impossibility of reaching absolute zero temperature?

The Second Law of Thermodynamics implies that it's impossible to reach absolute zero temperature. As a system approaches absolute zero, its entropy approaches a minimum value. However, to remove the last bit of heat and reach absolute zero would require an infinite number of steps, each with diminishing returns. This is known as the Third Law of Thermodynamics and is a consequence of the Second Law.

27. How does the Second Law explain the direction of diffusion?

The Second Law of Thermodynamics explains why diffusion occurs from areas of high concentration to low concentration. This process increases the overall entropy of the system by spreading out particles and increasing disorder. The spontaneous nature of diffusion is a direct result of the system moving towards a state of maximum entropy, as predicted by the Second Law.

28. What is the relationship between the Second Law and the spontaneous mixing of gases?

The spontaneous mixing of gases is a clear demonstration of the Second Law. When two different gases are allowed to mix, they will spontaneously diffuse into each other, increasing the system's entropy. This process is irreversible without external work, as separating the gases would decrease entropy, violating the Second Law for an isolated system.

29. How does the Second Law impact the efficiency of fuel cells?

The Second Law of Thermodynamics limits the efficiency of fuel cells, just as it does for heat engines. While fuel cells can be more efficient than traditional combustion engines, they still can't achieve 100% efficiency. Some energy is always lost as heat due to irreversible processes within the cell, aligning with the Second Law's prediction of entropy increase.

30. What is the significance of the Second Law in understanding phase changes?

The Second Law of Thermodynamics is crucial in understanding phase changes. For instance, the spontaneous melting of ice at room temperature is driven by an increase in entropy. While the entropy of the water increases as it melts, there's a decrease in entropy of the surroundings as heat is absorbed. The process occurs because the total entropy increase of the universe is positive, as predicted by the Second Law.

31. How does the Second Law explain why chemical reactions often produce heat?

Many chemical reactions produce heat (are exothermic) because of the Second Law. These reactions often increase the entropy of the surroundings by releasing heat, which spreads energy and increases disorder. Even if the reaction decreases the entropy of the system (like in the formation of a solid), the heat released often leads to a net increase in the universe's entropy, making the process spontaneous.

32. What is the connection between the Second Law and the concept of reversibility in thermodynamics?

The Second Law of Thermodynamics is closely tied to the concept of reversibility. A reversible process is an idealized process where the system and surroundings can be returned to their initial states without any net change in entropy. In reality, all processes involve some irreversibility and increase in entropy, as predicted by the Second Law. The degree of irreversibility is a measure of the entropy produced.

33. How does the Second Law relate to the efficiency of heat pumps?

The Second Law of Thermodynamics sets limits on the efficiency of heat pumps, which move heat from a cold reservoir to a hot one. The law dictates that this process requires work input. The coefficient of performance (COP) of a heat pump, which measures its efficiency, is limited by the temperatures of the hot and cold reservoirs. This limitation is a direct consequence of the Second Law.

34. What is the significance of the Second Law in understanding the Gibbs phase rule?

The Second Law of Thermodynamics is fundamental to the Gibbs phase rule, which describes the number of degrees of freedom in a thermodynamic system at equilibrium. The rule is derived from the condition of maximum entropy at equilibrium, a direct consequence of the Second Law. It helps predict the number of phases that can coexist at equilibrium under given conditions.

35. How does the Second Law explain the spontaneity of exothermic reactions?

The Second Law of Thermodynamics helps explain why many exothermic reactions are spontaneous. These reactions release heat to the surroundings, increasing the entropy of the surroundings. Even if the reaction decreases the entropy of the system (like forming a more ordered product), the large increase in the surroundings' entropy often leads to an overall increase in the universe's entropy, making the process spontaneous.

36. What is the relationship between the Second Law and the concept of chemical potential?

Chemical potential, a key concept in chemical thermodynamics, is closely related to the Second Law. It represents the change in Gibbs free energy when the amount of a substance in a system changes. The Second Law dictates that in a system at equilibrium, the chemical potential of a substance must be the same in all phases where it is present. This principle helps predict the direction of mass transfer in chemical and physical processes.

37. How does the Second Law impact our understanding of osmosis?

The Second Law of Thermodynamics is crucial in explaining osmosis. Water moves from an area of low solute concentration to high solute concentration across a semipermeable membrane because this process increases the overall entropy of the system. The movement of water molecules increases their disorder, outweighing the increased order from diluting the concentrated solution, thus aligning with the Second Law's prediction of entropy increase.

38. What is the significance of the Second Law in understanding the Joule-Thomson effect?

The Joule-Thomson effect, where a real gas cools upon expansion, is a consequence of the Second Law of Thermodynamics. As a gas expands, it does work against intermolecular attractive forces, which requires energy. This energy comes from the gas's internal energy, leading to cooling. The process increases the entropy of the gas, aligning with the Second Law, even though the temperature decreases.

39. How does the Second Law relate to the concept of maximum work in thermodynamics?

The Second Law of Thermodynamics is fundamental to the concept of maximum work in thermodynamics. It states that the maximum work that can be extracted from a system is obtained through a reversible process. In reality, due to irreversibilities and entropy production, the actual work obtained is always less than this theoretical maximum, illustrating the limitations imposed by the Second Law.

40. What is the connection between the Second Law and the spontaneity of endothermic reactions?

The Second Law of Thermodynamics helps explain why some endothermic reactions can be spontaneous. While these reactions absorb heat and often decrease the entropy of the surroundings, they can still occur spontaneously if they significantly increase the entropy of the system. If the TΔS term in the Gibbs free energy equation (ΔG = ΔH - TΔS) is larger than ΔH, the reaction will be spontaneous despite being endothermic.

41. How does the Second Law explain the impossibility of a perfect heat engine?

The Second Law of Thermodynamics precludes the existence of a perfect heat engine. Such an engine would convert all input heat into work, which would violate the law's statement that some heat must always be exhausted to a cold reservoir. The Carnot cycle represents the most efficient possible heat engine, but even it cannot achieve 100% efficiency due to the