Second Law of Thermodynamics PDF

The direction of spontaneous change The first law of thermodynamics focuses on the conservation of energy within a system, particularly looking at the change in enthalpy (ΔH) during a process. This law helps us understand how much energy is transferred as heat or work, but it does not tell us about...

The direction of spontaneous change The first law of thermodynamics focuses on the conservation of energy within a system, particularly looking at the change in enthalpy (ΔH) during a process. This law helps us understand how much energy is transferred as heat or work, but it does not tell us about the direction of a reaction or whether a reaction will occur spontaneously. To predict the direction of spontaneous change, we need more than just ΔH because spontaneity depends not only on energy but also on entropy, the measure of disorder or randomness in a system. Key Points: 1. Enthalpy (ΔH): o Provides information on whether a process absorbs or releases energy. o Exothermic processes (negative HΔH) release energy and are often spontaneous, but not always. 2. Entropy (ΔS): o Reflects the tendency of systems to move toward greater disorder. o A positive ΔS suggests increased randomness, often associated with spontaneity. 3. Gibbs Free Energy (ΔG): o The key criterion for spontaneity is the Gibbs free energy change, ΔG, which combines enthalpy and entropy: o At constant temperature and pressure, a negative ΔG indicates a spontaneous process. Predicting Equilibrium and Spontaneity Spontaneous processes Spontaneous processes are naturally occurring changes that proceed in a specific direction without external intervention. Through observation, we see that many processes have a preferred direction, often due to the natural tendency for systems to move toward higher entropy (greater disorder) or to release energy. Examples of Spontaneous Processes: 1. Heat Transfer: o Heat naturally flows from a hot object to a cold one. This increases the overall entropy of the system, as energy disperses from a concentrated source to a more spread-out distribution. The reverse—heat flowing from cold to hot—does not happen spontaneously and requires external energy input (e.g., a refrigerator or heat pump). 2. Gas Mixing: o When two different gases are placed in separate containers and then allowed to mix, the molecules will spread out to occupy the available space evenly. This process is driven by an increase in entropy, as the gas molecules distribute randomly across the available volume. The reverse process, where mixed gases separate back into their original states, does not happen spontaneously and would require intervention (e.g., selective membranes or cooling). Key Points About Spontaneity: Irreversibility of Spontaneous Processes: o Once a spontaneous process has occurred, reversing it without external intervention is highly unlikely or impossible in practice. o While theoretically possible to reverse, this would require an input of energy or highly controlled conditions. Entropy and Spontaneity: o Spontaneous processes often lead to an increase in entropy (ΔS>0) in the system and surroundings combined. o For example, when heat flows from hot to cold or gases mix, entropy increases as the system moves towards a more probable, disordered state. Gibbs Free Energy: o In thermodynamic terms, a process is spontaneous if the Gibbs free energy change (ΔG) is negative, combining both the enthalpy (ΔH) and entropy ΔS) factors:  o Negative ΔG indicates a spontaneous process, while positive ΔG indicates that energy input is required for the process to proceed in the reverse direction. In summary, spontaneous processes are those that naturally move toward states of lower energy or higher entropy, and reversing these processes typically requires external intervention to impose order or concentrate energy. Entropy Entropy (S) is a measure of the disorder or randomness within a system. It’s a crucial concept in thermodynamics because it helps determine the natural direction of processes. Key Points about Entropy: 1. Degree of Disorder: o A system with higher entropy (S) has a greater degree of disorder or randomness. o For example, gases have higher entropy than liquids, and liquids have higher entropy than solids due to the increasing freedom of particle movement. 2. Order vs. Disorder: o Systems with lower entropy are more ordered and structured. o When a process leads to a more disordered state (such as the melting of ice or the mixing of two gases), the entropy increases. 3. State Function: o Entropy is a thermodynamic state function, meaning its value depends only on the current state of the system, not on the path taken to reach that state. o This makes it similar to other state functions like enthalpy (H) and internal energy (U). 4. Change in Entropy (ΔS): o The change in entropy, ΔS, for a process provides essential information about the direction of the process. o In spontaneous processes, the total entropy of the system and its surroundings generally increases (ΔStotal>0). 5. Entropy and Spontaneous Change:  o Entropy is a key factor in determining whether a process will occur spontaneously. o For a process to be spontaneous, the overall entropy change (ΔSuniverse) must be positive, meaning the entropy of the universe (system + surroundings) increases. Entropy in Spontaneity and Equilibrium: While the first law of thermodynamics (energy conservation) tells us that energy cannot be created or destroyed, it doesn’t explain the direction of processes. The second law of thermodynamics states that in any spontaneous process, the entropy of the universe tends to increase. At equilibrium, entropy is maximized, meaning there is no net change, as the system has reached a stable state with no preferred direction of change. In summary, entropy is a central concept for understanding the natural progression of systems, with ΔS as a key indicator of the direction and spontaneity of chemical and physical processes. Entropy (S) vs. temperature for a single component The relationship between entropy (S) and temperature for a single component is foundational in thermodynamics, illustrating how entropy changes with temperature and across different phases. Key Concepts: Entropy vs. Temperature 1. Third Law of Thermodynamics: o At absolute zero (0 K), the entropy of a perfectly ordered crystal is zero (S=0) for pure substances. This is because, at 0 K, the system is in its most ordered state with minimal molecular movement. o As temperature increases from 0 K, entropy also increases because particles gain energy and their motion becomes less ordered. 2. Entropy Decreases as Temperature Decreases: o As the temperature lowers, entropy decreases since particles slow down, reducing randomness and increasing order. o This trend continues until reaching 0 K, where entropy theoretically becomes zero for a perfectly ordered substance. 3. Phase Transitions and Entropy: o Phase transitions (solid to liquid, liquid to gas) involve significant changes in entropy. ▪ When a substance melts or vaporizes, its entropy rises sharply due  to the increased freedom of movement in the new phase. ▪ For example, when ice melts into water, the solid structure breaks down, allowing molecules to move more freely, which increases entropy. o Large drops in entropy occur when going from a less ordered phase to a more ordered one, such as gas condensing into a liquid or liquid freezing into a solid. 4. Entropy Within a Phase: o Within a single phase (solid, liquid, or gas), entropy increases as temperature rises, although not as dramatically as at phase transitions. o At lower temperatures within a phase, entropy decreases gradually as molecular motion becomes more restricted, increasing order. 5. Entropy as a Thermodynamic State Function: o Entropy is a state function, meaning the change in entropy (ΔS) for any process depends only on the initial and final states of the system, not on the path taken to reach those states. o This property allows us to calculate ΔS for complex processes by considering only the net changes between states, making it path- independent. Summary: The entropy of a system generally increases with temperature due to increased molecular motion and disorder. Entropy jumps significantly at phase transitions, reflecting the change in molecular freedom. At absolute zero, entropy is zero for a perfect crystal, illustrating the extreme order in that state. As a state function, entropy changes are path-independent, relying solely on the beginning and end states of a process. Energy; relating temperature, heat and entropy In thermodynamics, energy can be understood through the concepts of an intensity factor and a capacity factor. This framework helps describe how energy in various forms is transferred and measured, with the intensity factor representing the driving force and the capacity factor representing the extent or capacity over which that force acts. Key Examples: 1. Mechanical Energy: o For mechanical systems, energy is represented as the product of force and distance:  ▪ Intensity factor: Force – the driving force that causes an object to move. ▪ Capacity factor: Distance – the extent of movement over which the force acts. o Energy (mechanical work) = force × distance. 2. Pressure and Volume: o In thermodynamic systems, energy can also be represented by the relationship between pressure and volume. ▪ Intensity factor: Pressure – the driving force exerted by gas molecules on the walls of a container. ▪ Capacity factor: Volume – the space in which the gas molecules can move. o Energy (pressure-volume work) = pressure × volume. 3. Electrical Energy: o For electrical systems, energy is a product of electrical potential and the quantity of charge. ▪ Intensity factor: Electrical Potential (voltage) – the driving force pushing electric charges through a conductor. ▪ Capacity factor: Quantity of Charge – the total amount of electric charge moved. o Energy (electrical work) = potential × charge. Temperature, Heat, and Entropy: In thermodynamics, heat and entropy relate to temperature in a similar intensity- capacity framework: Temperature serves as the intensity factor because it represents the driving force for heat transfer. Heat flows spontaneously from a higher temperature to a lower temperature. Entropy (S) acts as the capacity factor because it represents the extent or "amount" of heat energy in a system at a given temperature. Thus, the energy transfer due to heat (q) can be expressed as: where: T (temperature) is the driving force or intensity of heat transfer,  ΔS (change in entropy) is the capacity factor, reflecting the extent of heat absorbed or released in the system. Summary: Using intensity and capacity factors allows us to generalize energy in different forms. Temperature, heat, and entropy in thermodynamics follow this structure, where temperature is the driving force for heat transfer, and entropy represents the extent to which heat is transferred, much like other energy forms such as mechanical, pressure- volume, and electrical systems. Heat (q) as a form of energy Heat (q) is a form of energy that can be described similarly to other forms of energy, in terms of an intensity factor and a capacity factor. Heat as Energy: Intensity Factor: The temperature (T) of the system is the driving force for heat transfer. Heat naturally flows from a body at a higher temperature to one at a lower temperature. Capacity Factor: The entropy (S) of the system represents the capacity or extent to which heat is absorbed or released by the system. Entropy quantifies the degree of disorder or randomness associated with the transfer of heat. Thus, the energy transferred as heat can be expressed as: Relation Between Heat and Entropy: Key Points: Reversible and irreversible processes In thermodynamics, reversible and irreversible processes describe the way a system transitions between states, and how equilibrium is achieved. 1. Spontaneous Processes: A spontaneous process occurs naturally without the need for external intervention. It results in a change in the system that moves it towards a state of greater disorder or entropy. In spontaneous processes, the system and its surroundings are generally not at equilibrium at the start of the process. The system undergoes a change, and the process continues until it reaches equilibrium, which is a state where the system's properties no longer change over time. 2. Irreversible Processes: An irreversible process is one where the system and its surroundings are not at equilibrium, and the process continues spontaneously in one direction until it reaches equilibrium. Irreversibility often arises due to factors such as friction, heat dissipation, or other dissipative forces. These processes cannot be undone without leaving some energy behind, often as heat. For example, the expansion of a gas into a vacuum is irreversible; once the gas has expanded, the process cannot be reversed without external work. 3. Reversible Processes: A reversible process is one in which the system is in equilibrium with its surroundings at every point in the process. o Dynamic equilibrium: In a reversible process, both the system and surroundings are at equilibrium after each infinitesimal change. That means for each tiny change, the system remains balanced, and the process can, in theory, be reversed by an infinitesimally small change in conditions. Reversible processes are idealized and are not commonly found in nature because they require infinitely slow changes, which prevent dissipative effects like friction and heat loss.  o For example, the compression and expansion of an ideal gas in a frictionless piston can be considered reversible if it occurs at such a slow pace that the system is in equilibrium at every step. 4. Key Differences: Irreversible Process: o The system is not in equilibrium with its surroundings at any point. o The process happens spontaneously in one direction until equilibrium is reached. o Energy dissipation (e.g., heat loss, friction) is typically involved. Reversible Process: o The system and surroundings are in equilibrium after each infinitesimal change. o The process can be reversed without any net change in the system or surroundings. Summary: Spontaneous processes occur naturally but tend to be irreversible, leading the system to equilibrium. Reversible processes maintain equilibrium at every step and are theoretical constructs, idealized as occurring infinitely slowly. Irreversible processes are more common in nature, as they involve changes that cannot be easily reversed without external intervention. Reversible transfer of heat The reversible transfer of heat refers to the process in which heat is transferred in such a way that both the system and surroundings are in equilibrium at every step, and the process can be reversed without a net change in the total energy of the system and surroundings. Example: Ice and Water in Equilibrium at 0°C Key Formula: Calculating Entropy Change: Heat Transfer Between Ice and Water: In this reversible process, the heat gained by the ice during melting is exactly equal to the heat lost by the surrounding water during freezing. The entropy change for the system (ice) is balanced by the entropy change for the surroundings (water). Therefore, the total change in entropy of the universe (system + surroundings) is zero, indicating that there is no overall increase in entropy during this reversible process. Key Points: Irreversible transfer of heat Total Entropy Change for the Universe: This positive change in entropy signifies the irreversibility of the process. In an irreversible heat transfer, energy is dispersed and cannot be fully recovered, leading to an increase in the total entropy of the universe. Key Points: Second law of thermodynamics The Second Law of Thermodynamics states that in any spontaneous process, the entropy of the universe always increases. This law introduces the concept that natural processes tend to move towards states of higher disorder or randomness. Reversible and Irreversible Processes: This reflects that in an irreversible process, entropy increases, and the total entropy of the universe rises. In other words, the system undergoes changes that result in a greater increase in disorder, and some energy is irreversibly dispersed, typically as heat. The Second Law of Thermodynamics: The second law of thermodynamics can be expressed as: In words, this means that: In a spontaneous process, the entropy of the universe increases. Reversible processes occur in such a way that the entropy of the system and surroundings change equally but do not cause a net increase in the entropy of the universe. Irreversible processes, on the other hand, result in a positive increase in the total entropy of the universe. Conclusion: Spontaneous processes are always associated with a net increase in entropy of the universe. The second law also tells us that no process can be perfectly reversible in nature; there will always be some entropy increase when heat is transferred or work is done in any real system.