Name: gas work in a piston cylinder
Uploaded: 2023-04-30T12:31:11.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

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

New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-4

Work Done During Volume Change

부피가 V인 팽창된 축구공을 생각해 보십시오. 공에 작용하는 압력은 대기압입니다.
공이 절벽에서 떨어져 구멍이 뚫렸다고 가정하면, 공 안의 공기가 방출됩니다. 균일한 디플레이션을 가정하고 반경을 dr의 거리만큼 줄입니다.
공에 작용하는 힘의 크기는 대기압과 공의 표면적에 따라 다릅니다.
따라서 공에 대해 주변 환경이 수행하는 작업은 대기압, 공의 표면적 및 반경 변화의 음의 곱과 같습니다.
그러나 표면적과 dr의 곱은 볼의 부피 변화입니다.
따라서 V1에서 V2로 부피가 유한하게 변하는 동안 수행된 작업은 압력과 부피 변화의 곱의 적분으로 표현될 수 있습니다.
여기서 음수 기호는 주변 환경에 의해 시스템에서 작업이 수행되었음을 나타냅니다. 반대로, 시스템에서 수행한 작업은 긍정적인 것으로 간주됩니다.

<ol>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 1. [웹 버전]. 원본 주소 <a href="https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy"> 112 https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy</a></li>
</ol>

볼륨 변경 중 수행된 작업

역학에서는 물체에 작용하는 힘이 물체를 변위시킬 때 물체에 대한 작업이 수행됩니다. 열역학에서는 열역학 과정 중에 시스템의 부피가 변할 때 시스템에 수행된 작업을 추정할 수 있습니다.

한쪽 끝에 이동식 피스톤이 장착된 실린더에 갇혀 있는 가스를 생각해 보세요. 가스가 V1 부피에서 V2 부피로 팽창하면 피스톤에 다음과 같은 힘이 가해집니다. 피스톤이 dr만큼 이동한다는 것입니다.

피스톤의 가스가 한 일은 다음과 같이 표현할 수 있습니다.

<img alt="Equation1" src="/files/ftp_upload/13675/13675_Equation_PT_1.svg" style="text-align: center; height: 10px;" />

p가 A 영역의 피스톤 면에 작용하는 압력이면 피스톤에 작용하는 힘은 다음과 같습니다.

<img alt="Equation2" src="/files/ftp_upload/13675/13675_Equation_PT_2.svg" style="text-align: center; height: 12px;" />

결과적으로 수행된 작업은 다음과 같이 표현될 수 있습니다.

<img alt="Equation3" src="/files/ftp_upload/13675/13675_Equation_PT_3.svg" style="text-align: center; height: 12px;" />

가스 부피의 변화 dV 는 Adr과 같습니다. 따라서 피스톤의 가스가 부피 V1에서 V2 로 팽창할 때 가스가 한 일은 는 다음과 같이 표현됩니다.

<img alt="Equation4" src="/files/ftp_upload/13675/13675_Equation_PT_4.svg" style="text-align: center; height: 45px;" />

여기서 적분은 시스템을 열 평형 상태로 유지하면서 극히 작은 단계에서 발생하는 과정을 의미하는 준정적 과정에만 의미가 있습니다.

피스톤이 가스를 압축하면 가스에 대한 작업이 수행되므로 일반적으로 부정적인 것으로 간주됩니다.

역학에서 물체에 작용하는 힘이 물체를 변위시킬 때 물체에 대한 작업이 수행됩니다. 열역학에서 시스템에서 수행된 작업은 다음과 같은 경우에 추정될 수 있습니다.

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

The First Law of Thermodynamics

열역학 제1법칙

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 piston area is A, the force on the piston is based on that pressure.

The work done by the gas can then be written in terms of pressure, area, and piston motion. Because the change in volume dV equals A dr, the work can also be expressed as an integral from V1 to V2. This form is meaningful only for a quasi-static process, which means the change happens in very small steps while the system stays in thermal equilibrium.

If the piston compresses the gas, the direction of work reverses. In that case, work is done on the gas, and it is conventionally treated as negative.

Gas Work in a Piston Cylinder

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 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

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.

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

Learn how gas pressure and piston motion create work during expansion or compression, and why quasi-static volume change matters in thermodynamics.

Gas Work in a Piston Cylinder | JoVE K12

physics

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HS-PS3-5

Gas Work in a Piston Cylinder

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