Name: free expansion: pressure, volume, and temperature
Uploaded: 2023-04-30T12:32:36.000Z
Duration: 1 min 27 s
Channel: JoVE

K12 Standards

new-york-state-science-learning-standards

New York State Science Learning Standards

High School

Physical Science

HS. Energy

HS-PS3-3.

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

Pressure and Volume in an Adiabatic Process

חשבו על נפח של מולקולות אוויר העולות באטמוספירה. ככל שהלחץ יורד עם הגובה, מולקולות האוויר מנסות לשמור על אותו לחץ על ידי הגדלת נפחן בתהליך אדיאבטי.
שינוי האנרגיה הפנימי כתוב במונחים של קיבולת חום מולרית ומסודר מחדש.
שימוש בחוק הגז האידיאלי, בידול וסידור מחדש של המונחים נותנים ביטוי לשינוי טמפרטורה.
השוואת משוואות שינוי הטמפרטורה המתקבלות מהחוק הראשון של התרמודינמיקה וחוק הגז האידיאלי וסידור מחדש נותנת משוואה במונחים של קיבול החום המולרי.
חלק לאורך כל הדרך על ידי pV והשתמש ביחס בין קיבולות חום מולארי. ניתן לפשט עוד יותר את המשוואה באמצעות היחס ביניהם.
עם אינטגרציה ושימוש בביטוי מתמטי כללי עבור לוגריתמים, מתקבל התנאי לכך שגז אידיאלי יעבור תהליך אדיאבטי במונחים של לחץ ונפח.
באופן דומה, ניתן לכתוב את התנאים לתהליכים אדיאבטיים במונחים של טמפרטורה-נפח ולחץ-טמפרטורה.
לכן, כאשר האוויר מתפשט, הטמפרטורה יורדת כפי שניתן על ידי תנאי נפח הטמפרטורה, מתעבה ליצירת עננים.

<ol>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: פירסון. עמ' 640, 641</li>
	<li>ווקר, ג'ארל (2007). האלידיי ורזניק יסודות הפיזיקה. ויילי. עמ' 573-574</li>
</ol>

לחץ ונפח בתהליך אדיבטי

<div style="direction:rtl">התפשטות חופשית של גז היא תהליך אדיאבטי. עם זאת, ישנם מעט הבדלים בין התרחבות חופשית להתרחבות אדיאבטית. במהלך התרחבות חופשית, לא מתבצעת עבודה, ואין שינוי באנרגיה הפנימית. אבל, עבור התרחבות אדיאבטית, העבודה נעשית, ויש שינוי באנרגיה הפנימית. במהלך תהליך אדיאבטי, היחס בין הלחץ לנפח מתקבל מהתנאי לתהליך האדיאבטי, כלומר,  <img alt="Equation1" src="/files/ftp_upload/13688/13688_PT Equation_1.svg" style="text-align: center; height: 13px;"> עם זאת, עבור תהליך התרחבות חופשי, תנאי זה אינו מתקיים גם אם ההרחבה היא אדיאבטית. כמו כן, בתהליך התפשטות חופשי, הגז נמצא במצב שיווי משקל רק בנקודות הראשוניות והאחרונות. לפיכך, על דיאגרמת pV, ניתן לשרטט רק את הנקודות הראשוניות והסופיות הללו, לא את ההרחבה עצמה. בנוסף לכך, הטמפרטורה הראשונית והסופית לתהליך אדיאבטי קשורות בביטוי, <img alt="Equation2" src="/files/ftp_upload/13688/13688_PT Equation_2.svg" style="text-align: center; height: 18px;"> אבל עבור ההתרחבות החופשית, אין שינוי באנרגיה הפנימית; לפיכך, הטמפרטורות הראשוניות והסופיות שוות. לפיכך, במקום המשוואה לעיל, יש לנו <img alt="Equation3" src="/files/ftp_upload/13688/13688_PT Equation_3.svg" style="text-align: center; height: 13px;"> מהביטוי לטמפרטורה, המצב ההתחלתי והסופי של התפשטות חופשית נמצאים על אותו איזותרמי בתרשים pV . כעת, אם מניחים שהגז הוא אידיאלי, אז, מכיוון שאין שינוי בטמפרטורה, לא יכול להיות שינוי במכפלת הלחץ והנפח. מכאן שעבור ההתפשטות החופשית, ניתן לבטא את הלחץ והנפח כ, <img alt="Equation4" src="/files/ftp_upload/13688/13688_PT Equation_4.svg" style="text-align: center; height: 13px;"></div>

התפשטות חופשית של גז היא תהליך אדיאבטי. עם זאת, ישנם הבדלים מעטים בין התפשטות חופשית לבין התפשטות אדיאבטית . במהלך התרחבות חופשית, ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

The First Law of Thermodynamics

החוק הראשון של התרמודינמיקה

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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 adiabatic. The gas is in equilibrium only at the start and the end of free expansion. Because of that, only the initial and final points can be shown on a pV diagram, not the path of the expansion.

The temperature behavior is also different. For adiabatic expansion, the initial and final temperatures are linked by an equation. For free expansion, the internal energy stays the same, so the initial and final temperatures are equal. This means the two states lie on the same isotherm, or constant-temperature line, on a pV diagram.

If the gas is ideal, a constant temperature means the product of pressure and volume does not change. So for free expansion, pressure and volume can be written with the same value of pV at the initial and final states. This makes free expansion a useful case for comparing adiabatic behavior with a process that changes volume without changing internal energy.

Free Expansion: Pressure, Volume, and Temperature

free-expansion-pressure-volume-temperature

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,...

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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...

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Path Dependence in Gas Work

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Two Gas Paths to the Same Volume

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Heat, Work, and Internal Energy

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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...

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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...

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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...

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

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...

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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...

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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.

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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...

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Explore how free expansion differs from adiabatic expansion, including no work done, unchanged internal energy, equal temperatures, and pV diagram behavior.

Free Expansion: Pressure, Volume, and Temperature | JoVE K12

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Free Expansion: Pressure, Volume, and Temperature

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