Textbook Question
The normal freezing point of n-octane (C8H18) is -57 °C. (d) Is there any temperature at which liquid n-octane and solid n-octane are in equilibrium? Explain.
Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 22
Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (d) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.
Verified step by step guidance1
Step 1: Understand the concept of entropy and the second law of thermodynamics. The second law states that the total entropy of an isolated system can never decrease over time. It is often stated as the entropy of the universe increases for any spontaneous process.
Step 2: Analyze statement (a). According to the second law of thermodynamics, the entropy of the universe (system plus surroundings) increases for any spontaneous process. Therefore, evaluate whether this statement aligns with the second law.
Step 3: Evaluate statement (b). For irreversible processes, the total entropy change of the universe is positive, but the entropy change of the system is not necessarily equal and opposite to that of the surroundings. Consider the nature of irreversible processes and how they affect system and surroundings.
Step 4: Consider statement (c). The entropy of the system itself does not have to increase in a spontaneous process; it is the total entropy of the system and surroundings that must increase. Reflect on examples where the system's entropy decreases but the process is still spontaneous.
Step 5: Examine statement (d). For an isothermal process, the entropy change \( \Delta S \) is given by \( \Delta S = \frac{q_{rev}}{T} \), where \( q_{rev} \) is the heat transferred reversibly and \( T \) is the absolute temperature. This indicates that the entropy change depends on both temperature and heat transfer.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy and the Second Law of Thermodynamics
Entropy is a measure of the disorder or randomness in a system. The Second Law of Thermodynamics states that in any spontaneous process, the total entropy of the universe (system plus surroundings) must increase. This principle helps to determine the direction of spontaneous processes and is fundamental in understanding thermodynamic behavior.
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00:48
Second Law of Thermodynamics Example
Entropy Change in Irreversible Processes
In irreversible processes, the total entropy change of the universe is greater than zero, but the entropy change of the system is not necessarily equal and opposite to that of the surroundings. This concept highlights the distinction between reversible and irreversible processes, where the latter often leads to an overall increase in entropy due to dissipative effects.
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01:17Irreversible Changes in Matter
Isothermal Processes and Heat Transfer
An isothermal process occurs at a constant temperature, and the entropy change during such a process is calculated using the formula ΔS = Q_rev/T, where Q_rev is the heat transferred reversibly and T is the absolute temperature. This relationship indicates that both the amount of heat transferred and the temperature play crucial roles in determining the entropy change during isothermal conditions.
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Related Practice
Textbook Question
A system goes from state 1 to state 2 and back to state 1 following a reversible path in both directions. Which of the following statements about this process is or are true?
c. The value of w on going from state 1 to state 2 is equal in magnitude and opposite in sign to the value of w on going from state 2 back to state 1.
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Textbook Question
Indicate whether each statement is true or false. (a) ΔS is a state function. (b) If a system undergoes a reversible change, the entropy of the universe increases. (c) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) If a system undergoes a reversible process, the entropy change of the system must be zero.
Textbook Question
The normal boiling point of Br2(l) is 58.8 °C, and its molar enthalpy of vaporization is ΔHvap = 29.6 kJ/mol. (a) When Br2(l) boils at its normal boiling point, does its entropy increase or decrease?
Textbook Question
The normal boiling point of Br2(𝑙) is 58.8 °C, and its molar enthalpy of vaporization is Δ𝐻vap=29.6kJ/mol. (b) Calculate the value of Δ𝑆 when 1.00 mol of Br2(𝑙) is vaporized at 58.8 °C.
Textbook Question
The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (a) When molten gallium solidifies to Ga(s) at its normal melting point, is ΔS positive or negative?