Thermodynamic entropy definition clarification | Physics | Khan Academy
TLDRThis video delves into the concept of entropy, explaining its definition as the heat added to a system divided by temperature. It clarifies that entropy is a state variable and demonstrates its validity through the reversible Carnot cycle. The importance of reversibility in defining entropy is highlighted, contrasting reversible and irreversible systems and emphasizing that entropy calculations must be based on reversible processes.
Takeaways
- 🔄 The concept of entropy was introduced with a definition that relates it to the heat added to a system and the temperature at which it was added.
- 🔍 The script tests the validity of entropy as a state variable using the Carnot cycle, which is a reversible process.
- 📈 The Carnot cycle was reviewed, highlighting its isothermal and adiabatic processes, and the importance of pebbles (or weights) to represent pressure changes.
- ♨️ Heat transfer (Q1 and Q2) during the Carnot cycle occurs at different temperatures (T1 and T2), and the total entropy change for a complete cycle is zero, indicating a state variable.
- 🔧 The script emphasizes that the entropy definition used was only valid for reversible processes, not just any process.
- 🔄 Revisiting the concept of reversibility, the script explains that a process must be quasistatic and frictionless to be considered reversible.
- 🔧 Friction in a system generates heat, which affects the reversibility and the ability to return to the original state after a cycle.
- 🚫 The Carnot cycle is theoretically reversible and represents the most efficient engine, which is unachievable in practice due to the frictionless requirement.
- 🔄 The script demonstrates that the entropy definition does not hold for irreversible systems, as shown by a thought experiment involving friction.
- 🔄 Entropy can still be discussed for irreversible reactions, but it is calculated based on a reversible process that would achieve the same state change.
- 📝 The script concludes by reinforcing the importance of using reversible heat and temperature to calculate entropy changes, even for irreversible processes.
Q & A
What is the initial definition of change in entropy given in the video?
-The change in entropy is defined as the heat added to a system divided by the temperature at which it was added to the system.
What thermodynamic cycle does the speaker use to test the validity of this entropy definition?
-The speaker uses the Carnot cycle to test the validity of the entropy definition.
Why is it important for entropy to be a state variable?
-For entropy to be a state variable, its value should not depend on the path taken to reach a particular state but only on the state variables.
What key property of the Carnot cycle is emphasized to validate the entropy definition?
-The reversibility of the Carnot cycle is emphasized to validate the entropy definition.
What does the term 'quasistatic' mean in the context of thermodynamic processes?
-In thermodynamic processes, 'quasistatic' refers to a process that happens so slowly that the system remains in near equilibrium at all times.
Why is friction an important factor in discussing reversibility?
-Friction is important because it generates heat and resists movement, making it impossible to return to the exact same state, thus breaking reversibility.
How does the presence of friction affect the movement of the piston in the system?
-The presence of friction means that the piston will not move as much as expected when pebbles are removed or added, because some energy is lost to heat.
What does the speaker mean by 'heat generated from friction'?
-Heat generated from friction refers to the heat produced due to the resistance between the moving parts of the system, such as the piston and the walls of the cylinder.
How does friction impact the total change in internal energy during expansion and contraction?
-Friction causes additional heat to be generated during both expansion and contraction, altering the expected changes in internal energy.
What distinction does the speaker make between reversible and irreversible systems when calculating entropy?
-For reversible systems, entropy can be calculated directly using heat added divided by temperature. For irreversible systems, the calculation must consider the heat that would be added by an equivalent reversible system to determine the change in entropy.
Why is the Carnot cycle considered the most efficient potential engine?
-The Carnot cycle is considered the most efficient because it is a frictionless, reversible process, meaning it loses no energy to friction.
What conclusion does the speaker reach about the entropy definition after considering irreversible systems?
-The speaker concludes that the thermodynamic definition of entropy must be based on a reversible system, as it fails to be a valid state variable for irreversible systems.
What key point does the speaker emphasize about the definition of entropy in the context of the Carnot cycle?
-The speaker emphasizes that the entropy definition worked in the initial example because the Carnot cycle is reversible, and this reversibility is crucial for the definition to hold.
How does the concept of 'quasi-equilibrium' relate to reversibility in thermodynamic processes?
-'Quasi-equilibrium' means that the system is nearly in equilibrium at all times, which is necessary but not sufficient for reversibility. The process must also be frictionless.
What would be the effect of performing the Carnot cycle in a real-world scenario with friction?
-In a real-world scenario with friction, the system would generate heat during the process, making it irreversible and less efficient, and preventing it from returning to the exact same state.
Outlines
🔄 Entropy and the Carnot Cycle
The speaker revisits the concept of entropy, initially defining it as the heat added to a system divided by the temperature at which it was added. They test this definition using the Carnot cycle, a thermodynamic cycle that is theoretically reversible. The Carnot cycle involves isothermal and adiabatic processes, where the system moves from one state to another by adding or removing heat at constant temperatures. The speaker emphasizes that the total change in entropy for a complete Carnot cycle equals zero, which supports the idea that entropy is a state variable. However, they clarify that this definition of entropy only holds true for reversible processes, such as the Carnot cycle.
🔧 Reversible Processes and Friction
The speaker delves into the concept of reversibility, explaining that for a process to be reversible, it must be quasistatic and frictionless. They illustrate this with a thought experiment involving a piston system, where friction generates heat. The speaker shows that in a reversible process, removing and then adding back the same amount of pebbles (representing work) would return the system to its original state. However, with friction, the system would not return to the exact same state due to the heat generated by friction. The Carnot cycle is highlighted as an example of a reversible process, which is why it is considered the most efficient theoretical engine.
🚫 Entropy in Irreversible Systems
The speaker explores the implications of defining entropy in irreversible systems, using a simple thought experiment with a frictional piston system. They show that if the definition of entropy (Q/T) is applied to an irreversible process, the total change in entropy would not be zero, contradicting the state variable property. The speaker demonstrates that the heat added to the system, minus the heat released, plus the heat generated by friction, must equal zero for the internal energy change to be zero. This highlights that the definition of entropy as Q/T is only valid for reversible processes, not for irreversible ones.
🔄 Entropy Calculation for Irreversible Reactions
The speaker concludes by discussing how to calculate entropy changes for irreversible reactions. They explain that while the direct application of the entropy definition (Q/T) is not valid for irreversible processes, one can still determine the entropy change by considering what would have happened in a reversible process. The speaker suggests that the change in entropy for an irreversible reaction can be found by calculating the heat that would have been added in a reversible process and dividing it by the temperature at which it would have been added. This approach ensures that the thermodynamic definition of entropy remains consistent and applicable.
Mindmap
Keywords
💡Entropy
💡Carnot Cycle
💡State Variable
💡Reversibility
💡Quasistatic Process
💡Friction
💡Isothermal Process
💡Adiabatic Process
💡Heat Engine
💡Internal Energy
💡Perpetual Motion Machine
Highlights
Introduction of the concept of entropy and its definition as the heat added to a system divided by the temperature.
Testing the validity of entropy as a state variable using the Carnot cycle.
Explanation of the Carnot cycle's PV diagram and its stages.
Heat transfer in the Carnot cycle at high and low temperatures.
Demonstration that the total change in entropy in a Carnot cycle equals zero, indicating entropy as a state variable.
Clarification that the entropy definition's validity is contingent on the process being reversible.
Review of the concept of reversibility in thermodynamic processes.
Definition of quasistatic processes and their relation to reversibility.
Explanation of frictionless conditions as a requirement for reversibility.
Illustration of how friction affects the reversibility of a system.
The Carnot cycle's inherent reversibility and its implications for engine efficiency.
Demonstration that the entropy definition only works for reversible systems, not irreversible ones.
Thought experiment showing the impact of friction on the entropy calculation in an irreversible system.
Explanation of how to calculate entropy changes for irreversible processes by considering a reversible path.
Emphasis on the importance of using reversible heat and temperature for entropy calculations.
Clarification that entropy can be discussed for any process, but calculations must be based on reversible conditions.
Final emphasis on the thermodynamic definition of entropy requiring heat added to a reversible system divided by temperature.
Transcripts
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