Work done by isothermic process | Thermodynamics | Physics | Khan Academy

Khan Academy
16 Sept 200919:03
EducationalLearning
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TLDRThis educational video script explores the concept of isothermal processes in thermodynamics, using a container with a movable piston to illustrate the behavior of a gas under varying conditions. It explains how temperature, pressure, and volume are interrelated, and the role of a heat reservoir in maintaining constant temperature during expansion. The script delves into the mathematical representation of these processes, demonstrating how work done on the system and heat transfer are related, culminating in the formula for calculating work in an isothermal expansion.

Takeaways
  • πŸ“š The classic system used for instruction involves a container with a movable piston and molecules creating pressure.
  • βš™οΈ The system starts with an initial pressure (P1), volume (V1), and temperature (T1), all in equilibrium.
  • πŸͺ¨ Adding or removing rocks (pebbles) from the top of the piston helps approximate a quasi-static process, allowing the system to stay close to equilibrium.
  • 🌑️ An isothermic process keeps the temperature constant throughout the process.
  • πŸ› οΈ Removing pebbles without external heat exchange (adiabatic process) would decrease the temperature as work is done by the system.
  • ♻️ Placing the system on a reservoir maintains a constant temperature, creating an isothermic condition.
  • πŸ“ˆ On a PV (pressure-volume) diagram, an isothermic process traces a rectangular hyperbola, showing the relationship between pressure and volume at constant temperature.
  • πŸ”’ The ideal gas law (PV = nRT) explains that at constant temperature, the product of pressure and volume is constant (PV = constant).
  • πŸ“‰ Work done in an isothermic process is calculated as nRT times the natural log of the ratio of final to initial volume (W = nRT ln(V2/V1)).
  • πŸ”₯ In an isothermic process, the heat added to the system (Q) is equal to the work done by the system (Q = W), ensuring no change in internal energy.
Q & A
  • What is the significance of the movable piston in the container system described in the script?

    -The movable piston represents a boundary that can change, allowing for variations in volume. It is crucial for demonstrating how changes in pressure, volume, and temperature affect the system during thermodynamic processes.

  • Why is the system described as being in equilibrium?

    -The system is in equilibrium because all its properties, such as volume, pressure, and temperature, are uniform and consistent throughout. This uniformity is necessary to define macroscopic properties of the system.

  • What is an isothermic process, and how does it relate to the script's content?

    -An isothermic process is a thermodynamic process in which the temperature of the system remains constant. The script discusses this process to explain how the system behaves when the temperature is maintained, even as other properties like volume change.

  • What does the term 'adiabatic' mean in the context of the script?

    -Adiabatic refers to a process where there is no exchange of heat with the surroundings. The script uses this term to contrast with the isothermic process and to illustrate what happens when no external heat is added or removed from the system.

  • How does removing pebbles from the system affect its pressure and volume in an adiabatic process?

    -In an adiabatic process, removing pebbles (which allows the volume to increase) results in a decrease in pressure, as the same number of molecules now have more space to move, colliding with the walls less frequently.

  • What happens to the temperature of an adiabatic system when work is done on it?

    -In an adiabatic system, when work is done (such as expanding the volume by removing pebbles), the temperature decreases because the system loses kinetic energy, which is converted into work, and temperature is a measure of average kinetic energy.

  • Why does the internal energy of an adiabatic system decrease when work is done on it?

    -The internal energy decreases because work is done by the system, which requires energy. Since no heat is added in an adiabatic process, the loss of kinetic energy results in a decrease in internal energy.

  • What role does a reservoir play in maintaining the temperature of a system during an isothermic process?

    -A reservoir acts as an infinitely large heat source or sink that maintains the system's temperature constant. It ensures that any heat lost or gained by the system during expansion or compression is compensated for, keeping the temperature unchanged.

  • How is the relationship between pressure and volume described during an isothermic process?

    -During an isothermic process, the relationship between pressure and volume is described by an inverse proportionality, where the product of pressure and volume (PV) remains constant, following the equation PV = nRT, where n, R, and T are constants.

  • What is the mathematical formula used to calculate the work done during an isothermic process, as described in the script?

    -The work done (W) during an isothermic process is calculated using the formula W = nRT * ln(V2/V1), where n is the number of moles, R is the ideal gas constant, T is the constant temperature, and V1 and V2 are the initial and final volumes, respectively.

  • How is the heat (Q) added to the system during an isothermic process related to the work done (W)?

    -In an isothermic process, the heat added to the system (Q) is equal to the work done by the system (W). This is because the internal energy remains constant, as indicated by the unchanged temperature, and the change in internal energy is the heat added minus the work done (Ξ”U = Q - W).

Outlines
00:00
πŸ”¬ Basic Concepts of Isothermal Processes

The paragraph introduces a classic system used for instructional purposes, emphasizing its utility in classrooms. It describes a container with a movable piston and molecules or atoms inside, creating pressure (P1) and occupying a volume (V1) at a certain temperature. The system is in equilibrium, and the macro states (pressure, volume, temperature) can only be defined when the system is uniform. The speaker discusses the concept of an isothermal process, where the temperature remains constant, and explores how removing the weight (pebbles) on the piston would affect the system in an adiabatic scenario, where no heat is exchanged with the environment. The key takeaway is that in an adiabatic process, the removal of weight would lead to an increase in volume and a decrease in pressure, but the temperature would also decrease due to the work done by the system.

05:02
🌑️ Isothermal Process with a Reservoir

This paragraph delves into the concept of an isothermal process, explaining how it can be achieved by placing the system in contact with a reservoir, which is an infinitely large body at the same initial temperature (T1). The reservoir ensures that the system's temperature remains constant. The speaker uses the analogy of a small particle (A) and a massive structure (B) to illustrate how the temperature of A would adjust to B's temperature if B is significantly larger. The paragraph also discusses the PV diagram for an isothermal process, showing that as the system's volume increases due to the removal of pebbles, the pressure decreases, but the temperature remains constant. The relationship between pressure and volume in an isothermal process is described as a rectangular hyperbola, with PV being a constant value.

10:05
πŸ“ˆ Calculating Work in an Isothermal Process

The speaker explains how to calculate the work done during an isothermal process using the ideal gas law (PV = nRT). By assuming the temperature is constant, the relationship simplifies to P = K/V, where K is a constant. The work done is then the area under the curve on the PV diagram, which can be calculated by integrating P with respect to V from the initial volume (V1) to the final volume (V2). The integral results in nRT times the natural log of V2/V1, indicating that the work done is proportional to the change in volume. This calculation is crucial for understanding the energy changes in thermal systems during isothermal processes.

15:09
πŸ”₯ Heat Transfer in Isothermal Processes

The final paragraph addresses the question of heat transfer during an isothermal process. The speaker clarifies that since the temperature remains constant, the internal energy does not change. Using the principle that the change in internal energy is equal to the heat added to the system minus the work done by the system, it is concluded that the heat added (Q) is equal to the work done (W). This means that the heat added to the system is exactly what is needed to compensate for the work done, maintaining the constant temperature. The speaker also discusses the convention in thermodynamics for representing this heat transfer, using a downward arrow and the letter Q to denote heat added to the system during the isothermal process.

Mindmap
Keywords
πŸ’‘Isothermic process
An isothermic process is a thermodynamic process in which the temperature of the system remains constant. In the context of the video, the instructor discusses maintaining a constant temperature by placing the system next to a 'reservoir' that acts as an infinite heat source or sink to keep the system's temperature stable. This concept is crucial for understanding how the system behaves under the influence of external heat exchange, as opposed to an adiabatic process where no heat is exchanged.
πŸ’‘Piston
A piston is a movable part that separates the system from its surroundings in the video's described setup. It is used to control the volume of the system by being pushed up or down, which in turn affects the pressure and temperature of the gas inside. The script uses the piston to illustrate changes in volume during an isothermic process, showing how the system's volume increases when the pressure is reduced by removing the weight (pebbles) above it.
πŸ’‘Movable ceiling
The term 'movable ceiling' is used synonymously with 'piston' in the script, referring to the barrier that separates the gas inside the container from the external environment. The movement of this 'ceiling' or piston is essential in demonstrating how changes in volume affect the state of the gas, particularly during the isothermic process discussed in the video.
πŸ’‘Quasi-static process
A quasi-static process is one that occurs so slowly that the system is always in equilibrium. The script mentions this concept when the instructor plans to remove the pebbles slowly to approximate such a process. This is important for defining macroscopic properties like pressure, volume, and temperature, which require the system to be in equilibrium for accurate measurement.
πŸ’‘Macro states
Macro states refer to the large-scale, observable properties of a system, such as volume, pressure, and temperature. The video script emphasizes that these properties can only be defined when the system is in equilibrium, which is a condition for the system to have uniform properties throughout, as opposed to the microscopic states of individual molecules.
πŸ’‘Reservoir
In the script, a reservoir is described as an infinitely large body of substance that maintains a constant temperature. It is used to illustrate how the system's temperature can be kept constant during an isothermic process. The reservoir provides or absorbs heat as needed to ensure the system's temperature remains unchanged, despite work being done on or by the system.
πŸ’‘Adiabatic process
An adiabatic process is one in which the system is completely isolated from its surroundings, meaning no heat is exchanged with the environment. The instructor uses this concept to contrast with the isothermic process, explaining that without the influence of a reservoir, the temperature of the system would decrease when work is done on it, as there is no heat to compensate for the energy lost as work.
πŸ’‘Ideal gas law
The ideal gas law is a fundamental principle in thermodynamics, expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. The script uses this law to explain the relationship between pressure and volume during an isothermic process, stating that if the temperature (T) and the number of moles (n) are constant, then the product of pressure and volume (PV) is also constant.
πŸ’‘Internal energy
Internal energy is the total energy contained within a system, which includes the kinetic and potential energies of its molecules. In the context of the video, the instructor explains that the internal energy does not change during an isothermic process because the temperature, which is a measure of the average kinetic energy, remains constant. This is important for understanding the conservation of energy in thermodynamic processes.
πŸ’‘PV diagram
A PV diagram, or pressure-volume diagram, is a graphical representation used in thermodynamics to visualize the state changes of a system. The script describes how an isothermic process would appear on a PV diagram as a path along a rectangular hyperbola, indicating that for a given temperature, the product of pressure and volume remains constant. This visualization helps in understanding the relationship between pressure, volume, and temperature during different types of processes.
πŸ’‘Work done
In thermodynamics, work done refers to the energy transferred by a system as it undergoes a change in volume, typically when a gas expands or is compressed. The script explains how the work done by the system during an isothermic expansion can be calculated as the area under the curve on a PV diagram, which is equivalent to the heat added to the system to keep the temperature constant, as the internal energy remains unchanged.
Highlights

Introduction to a classic system with a movable piston and molecules creating pressure.

Explaining the importance of equilibrium for defining macro states like volume, pressure, and temperature.

Demonstration of a quasi-static process by slowly removing pebbles to approximate a system close to equilibrium.

Introduction of the isothermic process, where temperature remains constant throughout the process.

Explanation of how removing pebbles would affect volume and pressure in an adiabatic process.

Discussion on the relationship between work done, kinetic energy, and temperature in an adiabatic process.

Clarification that in an adiabatic process, the internal energy decreases as work is done without heat exchange.

Introduction of a reservoir to maintain a constant temperature during the process.

Description of how a reservoir acts as an infinitely large object to maintain the system's temperature.

Explanation of the PV diagram and how it changes during an isothermic process.

Derivation of the relationship between pressure and volume during an isothermic process using the ideal gas law.

Illustration of the rectangular hyperbola representing the isotherm in a PV diagram.

Calculation of work done during an isothermic process using the integral of pressure over volume.

Derivation of the formula for work done as nRT times the natural log of V2 over V1.

Discussion on the heat added to the system during an isothermic process to maintain constant temperature.

Conclusion that the heat added to the system is equal to the work done, as the internal energy remains constant.

Summary of the practical implications of understanding isotherms and adiabatic processes in thermodynamics.

Transcripts
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