ΔS = Q/T

Definition

ΔS = Q/T is a fundamental equation in thermodynamics that describes the relationship between the change in entropy (ΔS) of a system, the heat transfer (Q) to or from the system, and the absolute temperature (T) of the system. This equation is a key concept in understanding the second law of thermodynamics and the spontaneous nature of various physical and chemical processes.

5 Must Know Facts For Your Next Test

1. The equation ΔS = Q/T is used to calculate the change in entropy (ΔS) of a system when heat (Q) is transferred to or from the system at a constant absolute temperature (T).
2. Entropy is a measure of the disorder or randomness of a system, and the second law of thermodynamics states that the entropy of an isolated system not in equilibrium will tend to increase over time.
3. Spontaneous processes, such as the flow of heat from a hot object to a cold object, are characterized by an increase in the entropy of the universe.
4. The change in entropy (ΔS) is positive for spontaneous processes, indicating an increase in disorder or randomness, and negative for non-spontaneous processes, indicating a decrease in disorder or randomness.
5. The equation ΔS = Q/T is a powerful tool for understanding the direction and feasibility of various physical and chemical processes, as well as the efficiency of energy conversion devices.

Review Questions

• Explain the relationship between the change in entropy (ΔS), heat transfer (Q), and absolute temperature (T) as described by the equation ΔS = Q/T.
  • The equation ΔS = Q/T describes the relationship between the change in entropy (ΔS) of a system, the heat transfer (Q) to or from the system, and the absolute temperature (T) of the system. Specifically, the change in entropy is directly proportional to the amount of heat transferred and inversely proportional to the absolute temperature. This means that for a positive heat transfer (Q > 0), the change in entropy will be positive, indicating an increase in the disorder or randomness of the system. Conversely, for a negative heat transfer (Q < 0), the change in entropy will be negative, indicating a decrease in the disorder or randomness of the system. The magnitude of the change in entropy is also influenced by the absolute temperature, with larger changes occurring at lower temperatures.
• Discuss how the equation ΔS = Q/T relates to the second law of thermodynamics and the spontaneous nature of various processes.
  • The equation ΔS = Q/T is closely linked to the second law of thermodynamics, which states that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. Spontaneous processes, such as the flow of heat from a hot object to a cold object, are characterized by an increase in the entropy of the universe, as described by the equation ΔS = Q/T. For a spontaneous process, the change in entropy (ΔS) is positive, indicating an increase in disorder or randomness. This is because the heat transfer (Q) is positive, and the absolute temperature (T) is always positive. In contrast, non-spontaneous processes, such as the flow of heat from a cold object to a hot object, have a negative change in entropy (ΔS), which is not favored by the second law of thermodynamics. The equation ΔS = Q/T provides a quantitative way to assess the spontaneity and feasibility of various physical and chemical processes.
• Analyze how the equation ΔS = Q/T can be used to understand the efficiency of energy conversion devices, such as heat engines and refrigerators.
  • The equation ΔS = Q/T can be used to understand the efficiency of energy conversion devices, such as heat engines and refrigerators. In a heat engine, heat (Q) is transferred from a high-temperature source to a low-temperature sink, and some of this heat is converted into useful work. The change in entropy (ΔS) of the heat engine is related to the heat transfer (Q) and the temperatures of the high-temperature source (Th) and the low-temperature sink (Tc) through the equation ΔS = Q/Th - Q/Tc. The efficiency of the heat engine is then determined by the ratio of the work output to the heat input, which is limited by the second law of thermodynamics and the change in entropy. Similarly, in a refrigerator, work is input to transfer heat (Q) from a low-temperature source to a high-temperature sink, and the change in entropy (ΔS) is given by ΔS = Q/Tc - Q/Th. The efficiency of the refrigerator is then limited by the second law of thermodynamics and the change in entropy, as described by the equation ΔS = Q/T.

Related terms

Entropy: Entropy is a measure of the disorder or randomness of a system. It quantifies the amount of energy in a system that is not available to do useful work.

Second Law of Thermodynamics: The second law of thermodynamics states that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

Spontaneous Process: A spontaneous process is a process that occurs naturally without the input of external work. Spontaneous processes are characterized by an increase in the entropy of the universe.