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

Consider an inflated soccer ball having a volume of V. The pressure acting on the ball is the atmospheric pressure.
Suppose the ball falls off the cliff and gets punctured; the air inside the ball releases. Assuming uniform deflation, let its radius be reduced by a distance of dr.
The magnitude of the force acting on the ball depends on the atmospheric pressure and the surface area of the ball.
Therefore, the work done by the surroundings on the ball equals the negative product of the atmospheric pressure, the ball&#39;s surface area, and the change in its radius.
However, the product of surface area and dr is the change in the volume of the ball.
Therefore, during a finite change in volume from V1 to V2, work done can be expressed as the integral of the product of pressure and change in volume.
Here the negative sign indicates that the work is done on the system by the surroundings. Conversely, the work done by the system is considered positive.

work done during volume change

In mechanics, work is done on an object when the force acting on it displaces the object. In thermodynamics, work done on a system can be estimated when the system's volume changes during any thermodynamic process.
Consider a gas confined to a cylinder fitted with a movable piston at one end. If the gas expands from volume V1 to volume V2, it exerts a force on the piston, such that the piston moves by a distance dr.
The work done by the gas on the piston can be expressed as
<img alt="Work formula, \(dW = F dr\), representing differential work in physics equations." src="/files/ftp_upload/13675/13675_Equation_PT_1.svg" style="text-align: center; height: 10px;" data-altupdatedat="1761830439000" data-alt="Equation1" />
If p is the pressure acting on the face of the piston of area A, then the force acting on the piston is
<img alt="Fluid mechanics formula F=pA for pressure-area force relationship." src="/files/ftp_upload/13675/13675_Equation_PT_2.svg" style="text-align: center; height: 12px;" data-altupdatedat="1761830439000" data-alt="Equation2" />
Consequently, the work done can be expressed as
<img alt="thermodynamic work formula dW=pAdr equation for pressure-volume analysis" src="/files/ftp_upload/13675/13675_Equation_PT_3.svg" style="text-align: center; height: 12px;" data-altupdatedat="1761830439000" data-alt="Equation3" />
The change in the volume of the gas dV equals Adr. Therefore, the work done by the gas on the piston when it expands from volume V1 to V2 is expressed as
<img alt="Thermodynamics work formula \( W = \int_{V1}^{V2} pdV \), equation, educational use." src="/files/ftp_upload/13675/13675_Equation_PT_4.svg" style="text-align: center; height: 45px;" data-altupdatedat="1761830439000" data-alt="Equation4" />
Here, the integral is only meaningful for a quasi-static process, which means a process that takes place in infinitesimally small steps, keeping the system at thermal equilibrium.
If the piston compresses the gas, the work is done on the gas, and hence conventionally, is considered negative.

In mechanics, work is done on an object when the force acting on it displaces the object. In thermodynamics, work done on a system can be estimated when ...

Education

JoVE Core

Physics

Unit 1

The First Law of Thermodynamics

KEY TERMS AND CONCEPTS

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

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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,...

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...

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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...

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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...

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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...

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Free Expansion: Pressure, Volume, and Temperature

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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...

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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

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Florida Department of Education

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SC.912.P.10.2

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HS-PS3-5

Gas Work in a Piston Cylinder

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