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Thermodynamics and Entropy

Exploring the fundamental thermodynamic relation, this overview highlights the role of entropy in chemical thermodynamics, its significance in open systems, and its impact on phase transitions. It delves into entropy generation, changes in ideal gas processes, and the thermodynamics of phase changes, providing essential insights into the behavior of systems under various conditions.

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1

The equation representing this concept is written as dU = TdS - pdV, where dU signifies the ______ change in internal energy.

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differential

2

In the equation dU = TdS - pdV, T stands for the ______ temperature and dS for the differential change in ______.

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absolute entropy

3

The variable 'p' in the fundamental thermodynamic relation denotes ______, while dV represents the differential change in ______.

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pressure volume

4

This thermodynamic relation is not limited to quasistatic processes but applies to any process, even when the system is not in ______.

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equilibrium

5

The fundamental thermodynamic relation is crucial for deriving other thermodynamic equations like the ______ relations and heat capacity equations.

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Maxwell

6

Equations derived from the fundamental thermodynamic relation are valid for all systems, regardless of their ______ details.

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microscopic

7

Entropy definition in thermodynamics

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Measure of disorder/randomness in a system; increases over time in isolated systems.

8

Clausius definition of entropy change equation

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δq_rev/T = ΔS; calculates entropy change with reversible heat exchange (δq_rev) and absolute temperature (T).

9

Standard molar entropy significance

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Entropy per mole at standard temperature (298 K); useful for comparing substances' entropy.

10

In chemical engineering, ______ systems interact with their environment by exchanging mass and ______.

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open energy

11

In the entropy balance equation, Ṁ_k stands for the mass flow rate of component k, and Ŝ_k represents the ______ entropy of that component.

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specific

12

Q̇ and T in the entropy balance equation refer to the rate of ______ transfer and the absolute ______, respectively.

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heat temperature

13

Ŝ_gen, a term in the entropy balance for open systems, denotes the rate of entropy ______, which is always non-negative.

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generation

14

Entropy ______ occurs due to irreversible processes like chemical reactions and is consistent with the ______ law of thermodynamics.

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generation second

15

The second law of thermodynamics states that while energy remains ______, entropy does not and is actually ______ in all real processes.

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conserved produced

16

Isothermal process entropy change equation for ideal gas

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ΔS = nR ln(V/V_0) for volume change, ΔS = -nR ln(P/P_0) for pressure change

17

Entropy change at constant pressure for ideal gas

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ΔS = nC_P ln(T/T_0), where C_P is heat capacity at constant pressure

18

Entropy change at constant volume for ideal gas

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ΔS = nC_v ln(T/T_0), where C_v is heat capacity at constant volume

19

The entropy of fusion is found using the formula ΔS_fus = ΔH_fus/______, where T_m represents the ______.

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T_m melting point

20

To calculate the entropy of vaporization, the formula ΔS_vap = ΔH_vap/______ is used, with T_b indicating the ______.

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T_b boiling point

21

Phase transitions occur without a change in ______ and ______, and are key to understanding thermodynamic systems.

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temperature pressure

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Exploring the Fundamental Thermodynamic Relation

The fundamental thermodynamic relation is an essential equation in thermodynamics that describes the internal energy change of a system. It is expressed as dU = TdS - pdV, where dU is the differential change in internal energy, T is the absolute temperature, dS is the differential change in entropy, p is the pressure, and dV is the differential change in volume. This relation is applicable to any process, including those that are not quasistatic, meaning the system may not be in equilibrium during the transition. It forms the basis for deriving other important thermodynamic equations, such as the Maxwell relations and the equations for heat capacities, which are applicable to all systems irrespective of their microscopic details.
Industrial plant with central steam turbine, insulated pipes and operator in safety uniform carefully observes the machine.

The Significance of Entropy in Chemical Thermodynamics

Entropy is a fundamental concept in chemical thermodynamics, representing the degree of disorder or randomness in a system. According to the second law of thermodynamics, the total entropy of an isolated system can never decrease over time, and it is at a maximum at equilibrium. The Clausius definition of entropy allows for the calculation of entropy change (ΔS) through the equation δq_rev/T = ΔS, where δq_rev is the reversible heat exchange and T is the absolute temperature. Entropy is an extensive property, proportional to the size of the system, but can also be expressed as an intensive property, such as specific or molar entropy. The standard molar entropy is the entropy per mole of a substance at a standard temperature (usually 298 K). Entropy also plays a role in the mixing of substances and is a key factor in determining the spontaneity of a reaction when combined with enthalpy changes, as seen in the Gibbs free energy equation, ΔG = ΔH - TΔS.

Entropy Generation in Open Systems

Open systems, which exchange mass and energy with their surroundings, are common in chemical engineering and are analyzed using the principles of thermodynamics. The entropy balance for an open system is given by dS/dt = Σ(Ṁ_kŜ_k) + (Q̇/T) + Ŝ_gen, where dS/dt is the rate of change of entropy, Ṁ_k is the mass flow rate of component k, Ŝ_k is the specific entropy of component k, Q̇ is the rate of heat transfer, T is the absolute temperature, and Ŝ_gen is the rate of entropy generation. Entropy generation occurs due to irreversible processes such as chemical reactions, heat transfer, and friction, and is always non-negative, consistent with the second law of thermodynamics. This principle emphasizes that while energy is conserved, entropy is not—it is produced in all real processes.

Entropy Changes in Ideal Gas Processes

The entropy change in ideal gas processes can be quantified using specific equations. For an isothermal process, where the temperature remains constant, the change in entropy (ΔS) is given by ΔS = nR ln(V/V_0) for volume changes, or ΔS = -nR ln(P/P_0) for pressure changes, where n is the number of moles, R is the ideal gas constant, and V_0 and P_0 are the initial volume and pressure, respectively. For processes at constant volume or pressure, the entropy change is related to the heat capacity, with ΔS = nC_P ln(T/T_0) for constant pressure and ΔS = nC_v ln(T/T_0) for constant volume, where C_P and C_v are the heat capacities at constant pressure and volume, respectively. These equations assume no phase changes and constant heat capacities.

Entropy and Phase Transitions

Phase transitions involve significant entropy changes and occur at constant temperature and pressure. The entropy change associated with a phase transition is calculated by dividing the enthalpy change of the transition (ΔH) by the transition temperature (T). For example, the entropy of fusion (ΔS_fus) is determined by ΔS_fus = ΔH_fus/T_m, where ΔH_fus is the enthalpy of fusion and T_m is the melting point temperature. Similarly, the entropy of vaporization (ΔS_vap) is calculated using ΔS_vap = ΔH_vap/T_b, where ΔH_vap is the enthalpy of vaporization and T_b is the boiling point temperature. These calculations are essential for understanding the thermodynamics of phase changes and are fundamental to the study of thermodynamic systems.