Name: two gas paths to the same volume
Uploaded: 2023-09-18T17:11:15.000Z
Duration: 1 min 24 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

Energy

PHYS.PS3.7

Heat and Free Expansion

热力学系统所做的功在所有条件下都依赖于路径。
考虑一个由压力阀连接的两个圆柱体系统。初始时，圆柱体 A 中充满理想气体，而圆柱体 B 为空
加热气缸 A 时，气体吸收热量，导致气缸 A 内的压力暂时升高，从而打开压力阀。气体等温膨胀进入气缸 B，使气缸 A 内的压力下降。
考虑到连接管中的气体粒子可忽略不计，最终气体体积等于两个气缸中气体体积之和。
此处，由于气体受热，压力阀承受了做功。
在另一个过程中，考虑同一系统处于其初始状态，且与周围环境隔热，因此不发生热量交换。
如果移除阀门，气体将迅速自由膨胀进入气缸 B，最终达到与第一个过程相同的终态体积。
在此膨胀过程中，边界不发生移动，表明气体在自由膨胀过程中对外做功为零。

<ol>
	<li>Young， HD 和 Freedman， RA （2012）。大学物理与现代物理。加利福尼亚州旧金山:皮尔逊。第 628 页。</li>
	<li>OpenStax 的。（2019）. 大学物理学第 2 卷。[网络版] 第 112-115 页。取自 <a href="https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy>https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy</a></li>
</ol>

热和自由膨胀

热力学系统所做的功不仅取决于初始状态和最终状态，还取决于中间状态，即路径。 就像做功一样，当热量被添加到热力学系统中时，它会经历状态的变化，而达到的状态取决于从初始状态到最终状态的路径。 例如一个装有活塞的理想气缸。 当气缸被恒温加热时，气体分子吸收能量并以受控等温方式缓慢膨胀。 这将活塞向上推动，气体最终达到最终体积。 在这里，气体由于活塞上的热膨胀完成了功。 气体也可以通过不同的过程达到相同的最终体积。 例如一个由绝缘壁包围并由薄的可移动隔板分隔的圆柱体。 其下隔层在相同温度下充满相同量的气体，因此初始状态与上述相同。 当隔板被移除时，气体经历快速、不受控制的膨胀，没有热量穿过隔热壁，并达到与上述情况相同的最终体积。 在这里，气体在膨胀过程中不做功，因为它不会推动任何移动的物体。 气体不受控制地膨胀到真空中的现象称为自由膨胀。 实验上，理想气体自由膨胀下，温度没有变化。 这意味着气体的最终状态保持不变。 在两种情况下，从初始状态到最终状态过渡期间的中间状态（压力和体积）完全不同。 因此，它代表连接相同初始状态和最终状态的两条不同路径。

热力学系统所做的功不仅取决于初态和末态，还取决于中间状态，即取决于过程路径。

Education

教育

JoVE Core

物理学

Unit 1

第一单元

The First Law of Thermodynamics

热力学第一定律

KEY TERMS AND CONCEPTS

关键术语与概念

two gas paths to the same volume

Heat added to a thermodynamic system can lead to the same final state through different paths. The path matters because work and heat depend not only on the initial and final states, but also on the steps in between. In this topic, an ideal gas is used to show two different ways to reach the same volume.

In the first case, the gas is in a cylinder with a piston and is heated at a constant temperature. As the gas molecules absorb energy, the gas expands slowly in a controlled isothermal process. This pushes the piston upward, and the gas reaches the final volume. During this expansion, the gas does work on the piston.

The second case uses a cylinder with insulating walls and a thin removable partition. The lower part contains the same amount of gas at the same temperature, so the initial state matches the first example. When the partition is removed, the gas expands quickly and without control. No heat passes through the insulating walls, and the gas does not push against anything that moves, so no work is done.

This sudden expansion into a vacuum is called free expansion. For an ideal gas, experiments show no change in temperature during free expansion. That means the final state stays the same in both cases. Even so, the pressure and volume during the change are very different, so the two processes follow different paths between the same starting and ending states.

Two Gas Paths to the Same Volume

thermodynamic systems

Open, Closed, and Isolated Systems

A thermodynamic system is the part of the world that scientists study for its heat and energy behavior. It sits inside a surrounding environment, or surroundings. The system and the surroundings can exchange heat and do work across the boundary that separates them. The immediate surroundings affect the system most strongly because they interact with it directly. A kettle of boiling tea shows how this works in everyday life. The tea and the kettle together form the system. If the lid is open,...

work done during volume change

Gas Work in a Piston Cylinder

Gas work in a piston cylinder describes how pressure and volume change are related in thermodynamics. In mechanics, work happens when a force moves an object. In thermodynamics, work done on a system can be estimated when the system changes volume during a process. A gas can be trapped in a cylinder with a movable piston at one end. When the gas expands from volume V1 to volume V2, it pushes on the piston and moves it by a small distance dr. If the pressure on the piston face is p and the...

path between thermodynamics states

Path Dependence in Gas Work

Work done by an ideal gas can depend on the path it takes between two thermodynamic states. The transcript compares two routes from state A to state C for the same gas. In both cases, the gas expands from volume V1 to volume V2, but the work is not the same. Along path AC, the gas stays at constant temperature T. It expands from V1 to V2. The work done by the gas is found from the pressure-volume relation for an ideal gas. After substituting pressure as nRT/V and integrating, the work for this...

heat and free expansion

Heat added to a thermodynamic system can lead to the same final state through different paths. The path matters because work and heat depend not only on the initial and final states, but also on the steps in between. In this topic, an ideal gas is used to show two different ways to reach the same volume. In the first case, the gas is in a cylinder with a piston and is heated at a constant temperature. As the gas molecules absorb energy, the gas expands slowly in a controlled isothermal process.

internal energy

How Internal Energy Changes in Gas Systems

Internal energy is the energy stored inside a thermodynamic system. It is the sum of the kinetic and potential energies of the molecules or other particles in the system. Molecular kinetic energy includes translational motion, rotation, and vibration. Molecular potential energy comes from interactions between molecules. A system’s location and overall motion do not affect its internal energy. For an ideal monatomic gas, each particle is a single atom. That means there is no rotational or...

first law of thermodynamics

Heat, Work, and Internal Energy

Heat, work, and internal energy are linked by the first law of thermodynamics. This law is a generalized form of energy conservation. It explains how energy changes when heat is added to or removed from a system, and when the system does work or has work done on it. The change in internal energy equals the heat transferred into the system minus the work done by the system. Added heat increases internal energy. For that reason, heat is taken as positive when it enters the system and negative...

first law of thermodynamics: problem-solving

first-law-of-thermodynamics-problem-solving

First Law of Thermodynamics: Solving Problems

The first law of thermodynamics links internal energy, heat, and work. It states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system. This is a general form of energy conservation, and it can be used for any thermodynamic process. To solve a first-law problem, start by identifying the thermodynamic system. Then list the initial and final states of the process. Next, identify the known and unknown quantities. It is...

cyclic processes and isolated systems

Net Work in a Cyclic Thermodynamic Process

A cyclic thermodynamic process returns a system to its initial state. In a cycle, the change in internal energy is zero. An isolated system is different because it has zero heat exchange and zero work, so its internal energy stays constant. For a non-isolated system, the internal energy change is zero only when the process is cyclic. The first law of thermodynamics relates internal energy, heat transfer, and work. It states that the change in internal energy is the difference between the net...

isothermal processes

Isothermal Expansion and Heat Transfer

An isothermal process is a thermodynamic process that happens at constant temperature. During the process, heat slowly flows into the system or out of the system so thermal equilibrium is maintained. Phase changes are common examples of isothermal processes. Water can evaporate into steam at a constant temperature, and water can also freeze into ice at a constant temperature. An ideal gas can also undergo isothermal expansion or compression. Here, an ideal gas in an isolated cylinder expands...

isochoric and isobaric processes

Constant Volume and Pressure in Thermodynamics

Thermodynamic processes can happen at constant volume or at constant pressure. An isochoric process is a constant-volume process. In this case, the volume does not change, so the work done by the system is zero. The first law of thermodynamics still applies, so any heat added or removed changes the internal energy of the system only. A simple example is heating 1000 g of water from 40 degrees celsius to 70 degrees celsius at constant volume. Because the process is isochoric, no work is done by...

heat capacities of an ideal gas i

Ideal Gas Heat Capacity at Constant Pressure

Heat capacity describes how much heat a substance absorbs for a given change in temperature. It is also called thermal capacity, and its SI unit is J/K. Specific heat capacity is the heat needed to raise the temperature of 1 kg of a substance by 1 K, and its SI unit is J/kg·K. The video also explains molar heat capacity. This is the amount of heat added or removed to change the temperature of 1 mole of a substance by 1 K. It can be measured at constant volume or constant pressure, and it is...

heat capacities of an ideal gas ii

Ideal Gas Heat Capacity Differences

Ideal gas heat capacities depend on whether the gas is heated at constant volume or constant pressure. At constant volume, the heat absorbed only raises the internal energy of the system. No work is done in this case. At constant pressure, the situation is different. The heat absorbed increases the internal energy and also does work. Molar heat capacity is the heat needed to raise the temperature of 1 mole of gas by 1 unit. Because some of the added heat goes into work, more heat is needed at...

heat capacities of an ideal gas iii

Ideal Gas Heat Capacity and Degrees of Freedom

Ideal gas heat capacity depends on degrees of freedom, which are the independent ways a gas molecule can move, rotate, and vibrate. If d is the number of degrees of freedom, the molar heat capacity at constant volume can be written in terms of d. The molar heat capacity at constant pressure can also be written using the relationship between the two heat capacities. The ratio of molar heat capacity at constant pressure to molar heat capacity at constant volume is called the ratio of heat...

adiabatic processes for an ideal gas

Gas Temperature Changes in Adiabatic Processes

Adiabatic processes change the temperature of an ideal gas without heat transfer. In an adiabatic compression, no heat is added, but work is done on the gas. That work raises the gas temperature. In an adiabatic expansion, the gas does work and its temperature drops. A common example is the compression of a gas-air mixture inside a car engine cylinder. The compression happens so quickly that there is no time for heat to move between the mixture and its surroundings. Even so, the work done on...

pressure and volume in an adiabatic process

pressure-and-volume-in-an-adiabatic-process

Free Expansion: Pressure, Volume, and Temperature

Free expansion shows how pressure, volume, and temperature behave when a gas expands without doing work. It is an adiabatic process, but it is not the same as adiabatic expansion. In free expansion, no work is done and the internal energy does not change. In adiabatic expansion, work is done and the internal energy changes. For an adiabatic process, the pressure-volume relation comes from the adiabatic condition. That relation does not apply to free expansion, even though the expansion is...

work done in an adiabatic process

Adiabatic Compression in an Engine Cylinder

Adiabatic compression in an engine cylinder changes the pressure, temperature, and volume of a gas-air mixture. In this setup, gasoline vapor is injected into the cylinder when the piston is in its expanded position. The mixture starts at 20 °C, 1.00 x 10^5 N/m^2, and 240 cm^3. The mixture is then compressed adiabatically to 40 cm^3. Adiabatic means no heat is exchanged with the surroundings during the process. For this calculation, the compression is treated as quasi-static, even though real...

thermodynamic potentials

Energy Forms in Thermodynamics

Thermodynamic potentials are energy-based state functions used to analyze a thermodynamic system. They help describe how a system changes under different conditions. The four main thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These potentials can be written using two of the variables pressure, volume, temperature, and entropy. In each case, the rate of change of the potential with respect to the other two variables gives useful...

maxwell's thermodynamic relations

Using Maxwell's Relations in Thermodynamics

Maxwell's thermodynamic relations help solve problems in thermodynamics. They connect partial differentials for quantities that are hard to measure in the lab with quantities that are easier to measure. This makes them useful for working with temperature, pressure, volume, and entropy. These relations come from thermodynamic potentials and the symmetry of second derivatives. Thermodynamic potentials are exact differentials, so the order of second differentiation does not change the result.

joule-thomson effect

Gas Cooling and Heating in Throttling

Gas cooling and heating in throttling is explained by the Joule-Thomson effect, also called the Joule-Kelvin effect. It describes how a fluid changes temperature when it passes through a valve or porous plug in a thermally insulated system. This type of flow is called a throttling process. In the experiment, a high-pressure gas is forced through a throttle valve or porous plug into a lower-pressure region. The gas expands as it moves into the larger volume. Work is done on the gas as it is...

key terms and concepts

Compare isothermal expansion and free expansion in an ideal gas. See how heat, work, and path affect the same final volume in thermodynamics.

Two Gas Paths to the Same Volume | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

Physical Science

HS-PS3-4

Arizona Science Standards

HS.P4

HS.P4U1.8

Florida Department of Education

SC.912.P.10

SC.912.P.10.2

The universe is composed of matter in different forms, and all forms of matter contain energy.&#160; The different forms of energy on Earth originate from ...

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Kinetic Energy - I

It&#8217;s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the ...

Kinetic Energy - II

The kinetic energy of a particle is one-half of the product of the particle&#8217;s mass and the square of its speed. Note that just as Newton&#8217;s ...

Gravitational Potential Energy

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of ...

Elastic Potential Energy

Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is ...

Conservation of Mechanical Energy

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Mechanisms of Heat Transfer I

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Mechanisms of Heat Transfer II

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Identify and calculate different types of energy and their transformations (thermal, kinetic, potential, including magnetic and electrical potential energies) from one form to another in a system. Identify and calculate different types of energy and their transformations (thermal, kinetic, potential, including magnetic and electrical potential energies) from one form to another in a system. EXPLANATION:  In 6.PS3 students were introduced to the various types of energy and mechanisms for their transformations. Students should now be able to quantify the total energy of a system as well as quantify each different type of energy in a system. Energy is an abstract concept that does not have a physical form. It is a substance-like quantity that is recognized to be conserved as a system changes. Calculations present an opportunity to observe that potential energies are due to the positions of objects within a field, while kinetic energy is based on an object’s mass and motion. Students can evaluate the total energy of a system by imagining that there are different types of energy storage accounts, just as money can be stored in different accounts. Energy can transferred into or out of any of these accounts. Three different processes can account for all energy changes: working, heating, and radiating. In energy storage due to field effects, such as gravitational or electrostatic fields, the field itself stores the potential energy and not the object in the field.

PHYS.PS3.1

What is Energy?

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Heat Flow and Specific Heat

Heat is a type of energy transfer that is caused by a temperature difference, and it can change the temperature of an object. Since heat is a form of ...

Investigate conduction, convection, and radiation as a mechanism for the transfer of thermal energy.Investigate conduction, convection, and radiation as a mechanism for the transfer of thermal energy. EXPLANATION: Thermal energy is the energy of a system due to the motion of the particles in that system. One object can transfer its thermal energy to another object through the processes of heating or radiating. Convection and conduction are processes which require a physical medium to transfer the thermal energy. In the case of conduction, two objects are in direct contact, while convection transfers thermal energy through a liquid or gaseous medium. Radiation is a unique form of energy transfer which can transfer without a medium. One packet of this energy is called a photon. The energy of the photon determines the effect that it will have when it interacts with matter. Low energy photons such a microwaves add to the motion of matter and result in an increase of the thermal energy. Photons carry energy from the sun to Earth.

PHYS.PS3.2

Quantifying Heat

Thermal Energy&#160;

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force-and-potential-energy-in-one-dimension

Force and Potential Energy in One Dimension

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force-and-potential-energy-in-three-dimensions

Force and Potential Energy in Three Dimensions

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Energy Diagrams - I

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Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the ...

Use the principle of energy conservation and mathematical representations to quantify the change in energy of one component of a system when the energy that flows in and out of the system and the change in energy of the other components is known.         Use the principle of energy conservation and mathematical representations to quantify the change in energy of one component of a system when the energy that flows in and out of the system and the change in energy of the other components is known.         EXPLANATION:  In PHYS.PS3.1 students quantify the various types of energy and consider methods for energy transfer. If a student is able to evaluate the total energy of a system, such evaluations before and after a change to a system provide a mechanism to show that energy of a system has been conserved. For example, students might use pie charts to show the distribution of the total energy. For an object about to freefall, the pie chart might be 100% gravitational potential energy. Mid-descent, the energy might be half gravitational potential energy and half kinetic energy. After colliding with the ground, the total energy may have decreased, which can be represented as heat energy lost from the pie chart.

PHYS.PS3.3

Linear Momentum

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Force and Momentum

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Impulse

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Impulse-Momentum Theorem

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Conservation of Momentum: Introduction

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PHYS.PS3.4

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Construct an argument based on qualitative and quantitative evidence that relates the change in temperature of a substance to its mass and heat energy added or removed from a system. Construct an argument based on qualitative and quantitative evidence that relates the change in temperature of a substance to its mass and heat energy added or removed from a system.  EXPLANATION: Two different materials will undergo different degrees of temperature change even with the same amount of energy added to each. Heat capacity is a ratio (the slope of a temperature vs. heat added) that describes the change in temperature of a sample dependent on the amount of heating. Empirical determination of the heat capacity of a substance requires that both phase and mass of the substance are constants. Students can utilize proportional reasoning in the design of a second portion of this experiment to determine the effect of mass on temperature change.

PHYS.PS3.5

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work-energy-theorem-for-motion-along-a-curve

Work-Energy Theorem for Motion Along a Curve

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Work Done Over an Inclined Plane

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Define power and solve problems involving the rate of energy production or consumption (P=∆E/∆t). Explain and predict changes in power consumption based on changes in energy demand or elapsed time. Investigate power consumption and power production systems in common use.  Define power and solve problems involving the rate of energy production or consumption (P=∆E/∆t). Explain and predict changes in power consumption based on changes in energy demand or elapsed time. Investigate power consumption and power production systems in common use. EXPLANATION:  This standard pairs well with PHYS.PS3.6. Students should understand that a given task will require a certain minimum amount of energy. In accordance with the work-energy theorem, this would be described as work done on the system. Power incorporates a rate element into this discussion. An object can be lifted to an identical height by two different mechanisms. The total energy input into the system (the object and Earth’s gravitational field) will be the same in either case. However, if one mechanism for lifting the object does this in a smaller amount of time, it is said to be more powerful. Students may compare two different devices that accomplish the same task, but have different power ratings and explain the impact of the different power ratings on how the devices are used. For example, two microwaves might both pop a bag of popcorn, but a more powerful microwave might do it faster or be more likely to burn the popcorn at recommended time settings.

PHYS.PS3.6

Two Gas Paths to the Same Volume

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