5.3 Entropy changes in various processes
5 min read•july 30, 2024
changes in various processes are crucial to understanding the . From phase transitions to chemical reactions, entropy helps explain why some processes occur spontaneously while others don't.
By examining entropy changes in isothermal, adiabatic, reversible, and irreversible processes, we gain insight into the fundamental principles governing energy transformations and the direction of natural processes.
Entropy Changes in Processes
Entropy as a State Function
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- Entropy is a state function that measures the degree of disorder or randomness in a
- It is represented by the symbol S and has units of
- Entropy is an extensive property, meaning it depends on the amount of substance present
Isothermal and Adiabatic Processes
- Isothermal processes occur at constant temperature, while adiabatic processes occur without heat transfer between the system and its
- For an isothermal process, the change in entropy (ΔS) is equal to the heat transferred (q) divided by the absolute temperature (T):
- In an isothermal expansion (gas expanding in a piston), entropy increases as the system becomes more disordered due to the increased volume and decreased pressure
- In an isothermal compression (gas being compressed in a piston), entropy decreases as the system becomes more ordered due to the decreased volume and increased pressure
- For an adiabatic process, the change in entropy is zero because there is no heat transfer (q = 0):
- In an adiabatic expansion (rapid expansion of a gas without heat transfer), the temperature of the system decreases, but the entropy remains constant
- In an adiabatic compression (rapid compression of a gas without heat transfer), the temperature of the system increases, but the entropy remains constant
Entropy Changes: Reversible vs Irreversible
Reversible and Irreversible Processes
- Reversible processes are those that can be reversed without any net change in the system or its surroundings, while irreversible processes cannot be reversed without a net change in the system or its surroundings
- For a , the change in entropy of the system (ΔS_sys) is equal to the heat transferred (q_rev) divided by the absolute temperature (T):
- For an , the change in entropy of the system (ΔS_sys) is greater than the heat transferred (q_irrev) divided by the absolute temperature (T):
Second Law of Thermodynamics and Entropy
- The Second Law of Thermodynamics states that the total entropy of the universe (system + surroundings) always increases for an irreversible process and remains constant for a reversible process
- In an irreversible process (heat transfer from a hot object to a cold object), the entropy of the universe increases because the entropy generated by the process is always positive
- In a reversible process (isothermal expansion of an ideal gas), the entropy of the universe remains constant because the entropy generated by the process is zero
Entropy Changes in Reactions and Transitions
Entropy Changes in Phase Transitions
- Phase transitions, such as melting, vaporization, and sublimation, involve changes in entropy due to the rearrangement of particles in the system
- Entropy increases during melting (solid to liquid) and vaporization (liquid to gas) because the particles become more disordered as they gain translational and rotational freedom
- Entropy decreases during freezing (liquid to solid) and condensation (gas to liquid) because the particles become more ordered as they lose translational and rotational freedom
- The change in entropy for a phase transition can be calculated using the enthalpy of the transition (ΔH_trans) and the transition temperature (T_trans):
Entropy Changes in Chemical Reactions
- Chemical reactions involve changes in entropy due to the rearrangement of atoms and molecules in the system
- Entropy increases during reactions that produce more moles of gas than consumed (decomposition reactions), as the particles become more disordered
- Entropy decreases during reactions that consume more moles of gas than produced (synthesis reactions), as the particles become more ordered
- The change in entropy for a chemical reaction can be calculated using the standard molar entropies (S°) of the products and reactants:
- Standard molar entropies are tabulated values that represent the entropy of a substance at standard conditions (1 atm, 298 K)
Entropy and Spontaneity
Gibbs Free Energy and Spontaneity
- The spontaneity of a process is determined by the change in (ΔG), which is a function of the change in enthalpy (ΔH), temperature (T), and change in entropy (ΔS):
- A process is spontaneous when ΔG < 0, non-spontaneous when ΔG > 0, and at equilibrium when ΔG = 0
- The change in entropy (ΔS) contributes to the spontaneity of a process through the -TΔS term in the Gibbs free energy equation
- A positive change in entropy (ΔS > 0) favors spontaneity, as it makes the -TΔS term more negative and ΔG more negative
- A negative change in entropy (ΔS < 0) opposes spontaneity, as it makes the -TΔS term more positive and ΔG more positive
Temperature Dependence of Spontaneity
- The effect of entropy change on spontaneity depends on the temperature of the system
- At high temperatures, the -TΔS term becomes more significant, and entropy changes have a greater impact on spontaneity
- At low temperatures, the ΔH term becomes more significant, and enthalpy changes have a greater impact on spontaneity
- The Second Law of Thermodynamics states that the entropy of the universe always increases for a spontaneous process and remains constant for a process at equilibrium
- In a spontaneous process (ice melting at room temperature), the entropy of the system and surroundings increases, leading to an overall increase in the entropy of the universe
- In a process at equilibrium (liquid water in a sealed container at room temperature), the entropy of the system and surroundings remains constant, and there is no net change in the entropy of the universe
Key Terms to Review (18)
Calories per kelvin: Calories per kelvin is a unit of measurement that quantifies the amount of energy, expressed in calories, that is associated with a change in temperature of one kelvin. This concept is closely linked to the idea of entropy, as it helps to describe how energy disperses or spreads out at a given temperature. Understanding this relationship is essential for analyzing various processes involving heat transfer and changes in the state of matter.
Clausius Inequality: The Clausius Inequality is a fundamental principle in thermodynamics stating that the change in entropy of an isolated system is always greater than or equal to the heat transfer divided by the temperature at which it occurs. This concept helps to establish the second law of thermodynamics, emphasizing that processes involving entropy changes cannot be reversible without energy loss to the surroundings.
Dissolution of solids: Dissolution of solids refers to the process where solid solutes disperse and become incorporated into a solvent, resulting in a homogeneous solution. This process is closely linked to changes in entropy, as the arrangement of particles becomes more disordered when a solid dissolves, leading to an increase in entropy, which is a measure of disorder in a system.
Entropy: Entropy is a measure of the disorder or randomness in a system and reflects the number of ways a system can be arranged. It helps predict the direction of spontaneous processes and the energy available for work. Understanding entropy is crucial for comprehending how energy disperses in different situations and how it relates to equilibrium and spontaneity.
Entropy change for an ideal gas: Entropy change for an ideal gas refers to the measure of disorder or randomness in a system, specifically during processes involving temperature and volume changes of an ideal gas. This concept is key in understanding how energy is distributed in a system and the direction of spontaneous processes. The change in entropy can be calculated using specific equations that relate to the conditions of the gas and the processes it undergoes.
Entropy change in phase transitions: Entropy change in phase transitions refers to the measure of disorder or randomness that occurs when a substance undergoes a change from one phase to another, such as solid to liquid or liquid to gas. This change in entropy is critical in understanding how energy is distributed in a system during these transitions and plays a vital role in determining the feasibility of physical processes.
Gibbs Free Energy: Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. This concept is vital for predicting the spontaneity of processes, as it combines the system's enthalpy and entropy to determine whether a reaction or process can occur naturally without external input.
Irreversible Process: An irreversible process is a type of thermodynamic process that cannot be reversed to restore the system and its surroundings to their original states without leaving changes in both. This means that once an irreversible process occurs, the energy transformations and entropy changes result in a new equilibrium that cannot be undone. Understanding irreversible processes is crucial for analyzing state functions and path functions, as well as for evaluating entropy changes in various processes.
J/k: In thermodynamics, 'j/k' represents joules per kelvin, which is the unit of measurement for entropy. This measure indicates how much energy is dispersed in a system at a specific temperature, highlighting the relationship between energy and disorder within that system. Understanding 'j/k' helps in analyzing the changes in entropy during various physical and chemical processes, allowing for insights into the spontaneity and feasibility of reactions.
Mixing of gases: Mixing of gases refers to the process where two or more gaseous substances combine to form a homogeneous mixture. This process is crucial for understanding how gases behave in different situations, especially in terms of entropy changes and thermodynamic properties, as the distribution and interaction of gas molecules can significantly affect the overall energy states and disorder of the system.
Non-spontaneous process: A non-spontaneous process is a reaction or change that does not occur naturally under a given set of conditions and requires an input of energy to proceed. These processes are characterized by an increase in free energy, meaning that they will not happen without external work or energy supply, distinguishing them from spontaneous processes, which occur without additional energy. Understanding these processes involves exploring how entropy and free energy influence the likelihood of reactions occurring.
Reversible Process: A reversible process is a thermodynamic process that can be reversed without leaving any changes in the system or surroundings. This means that both the forward and reverse processes can occur infinitely slowly, allowing the system to remain in equilibrium throughout. Understanding reversible processes is crucial as they help establish maximum efficiency and serve as idealized benchmarks for real processes in energy transformations and chemical reactions.
Second Law of Thermodynamics: The Second Law of Thermodynamics states that in any energy transfer or transformation, the total entropy of an isolated system can never decrease over time, and is often expressed in terms of the irreversibility of natural processes. This law highlights the tendency of systems to evolve towards a state of maximum entropy, which has important implications for energy, heat, work, and spontaneity in various processes.
Spontaneous reaction: A spontaneous reaction is a process that occurs without external intervention, typically characterized by a decrease in free energy and an increase in the overall entropy of the universe. This term is closely related to the natural tendency of systems to move toward equilibrium and achieve a state of higher disorder over time, leading to a greater distribution of energy among particles.
Surroundings: In thermodynamics, the surroundings refer to everything outside a system that can exchange energy or matter with that system. Understanding the surroundings is essential because changes in a system’s energy, including heat and work, are often influenced by interactions with the surroundings, which play a key role in processes involving entropy changes.
System: In physical chemistry, a system is a specific portion of matter or a region in space that is being studied, separated by its surroundings by a boundary. This boundary can be real or imaginary, and it defines what is included in the analysis. Understanding the concept of a system is crucial as it helps to analyze energy exchanges and transformations, particularly when discussing entropy changes in various processes.
δs = q_rev/t: The equation δs = q_rev/t defines the change in entropy (δs) as the reversible heat transfer (q_rev) divided by the temperature (t) at which this transfer occurs. This relationship emphasizes that entropy is a measure of energy dispersal in a system, connecting it to spontaneous processes where energy naturally spreads out. The significance of this equation lies in its ability to quantify the irreversible nature of real processes and how they impact the overall direction of thermodynamic systems.
δs_universe = δs_system + δs_surroundings: This equation represents the principle of entropy conservation in a closed system, stating that the change in entropy of the universe ($$δs_{universe}$$) is equal to the sum of the change in entropy of the system ($$δs_{system}$$) and the change in entropy of the surroundings ($$δs_{surroundings}$$). It emphasizes that in any thermodynamic process, the total entropy can either increase or remain constant, but it cannot decrease, reflecting the second law of thermodynamics.