Name: ideal gas heat capacity differences
Uploaded: 2023-04-30T12:32:12.000Z
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K12 Standards

new-york-state-science-learning-standards

New York State Science Learning Standards

High School

Physical Science

HS. Energy

HS-PS3-3.

Heat Capacities of an Ideal Gas II

חשבו על שתי צלוחיות זהות המלאות בגז אידיאלי בטמפרטורות שונות שיכולות לעבור תהליכים תרמודינמיים שונים.
נניח, בתהליך של נפח קבוע, טמפרטורת הגז של הבקבוק הראשון עולה כדי להשוות לטמפרטורה של הבקבוק השני.
לאחר מכן, האנרגיה הפנימית שלו תהיה זהה לשינוי החום וניתן לכתוב אותה במונחים של קיבולת חום מולרית.
בתהליך לחץ קבוע, אם הטמפרטורה מוגברת באותה כמות, האנרגיה הפנימית של המערכת משתנה עם עבודה מסוימת שנעשתה.
מכיוון שהאנרגיה הפנימית היא פונקציית מצב, שינוי האנרגיה הפנימי של המערכת זהה בשני התהליכים.
באמצעות משוואת הגז האידיאלי בצורה דיפרנציאלית, ניתן לכתוב את העבודה שנעשתה במונחים של שינוי טמפרטורה.
על ידי ביטול הגורמים המשותפים לשני הצדדים, מתקבל היחס בין קיבולות החום המולרי עבור שני התהליכים.
כאן, R הוא קבוע הגז האוניברסלי, ולכן קיבולת החום המולרי של גז אידיאלי בתהליך לחץ קבוע תמיד גדולה מזו שבתהליך נפח קבוע.

<ol>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: Pearson.637-638.</li>
	<li>OpenStax. (2019). פיזיקה אוניברסיטאית כרך 2. [גרסת אינטרנט]. 126-127 מקור: <a href="https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas">https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas</a></li>
</ol>

יכולות חום של גז אידיאלי ii

<div style="direction:rtl">עבור מערכת שעוברת תהליך תרמודינמי במצב נפח קבוע, החום הנקלט משמש רק להגברת האנרגיה הפנימית של המערכת ולא לביצוע כל סוג של עבודה. בעוד שלמערכת העוברת תהליך תרמודינמי בתנאי לחץ קבוע, כמות החום הנספגת משמשת לא רק להגדלת האנרגיה הפנימית (כפונקציה של הטמפרטורה), אלא גם לביצוע עבודה מסוימת. קיבולת החום המולארית היא כמות החום הנדרשת כדי להעלות את הטמפרטורה של מול גז אחת ביחידה אחת. מכיוון שחלק מהחום שנספג משמש לביצוע עבודה, יש להוסיף יותר חום למערכת בלחץ קבוע כדי להעלות את הטמפרטורה שלה ביחידה אחת, קיבולת החום המולארית עבור תהליך לחץ קבוע היא תמיד גדולה יותר מיכולת החום המולארית עבור נפח קבוע תהליך. כתוצאה מכך, מהגזירה, שהתבססה על החוק הראשון של התרמודינמיקה, אנו מקבלים את הקשר הבא, כלומר <img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;"> לכן, ההבדל בין שתי יכולות החום המולאריות הוא קבוע ושווה לקבוע הגז האוניברסלי, R. זה נקרא גם קבוע הגז האידיאלי או קבוע הגז המולארי. ערכו הוא כ-8.314 והוא מתבטא באותה יחידת SI כמו קיבולת חום ספציפי מולארי J/mol⋅K. לדוגמה, עבור He, הערכים הנמדדים עבור Cp ו-CV הם 20.78 J/mol·K ו-12.47 J/mol·K, בהתאמה. ההבדל ביניהם הוא  8.31 J/mol·K שהוא קרוב לR.</div>

יכולות חום של גז אידיאלי II

עבור מערכת שעוברת תהליך תרמודינמי בתנאי נפח קבוע, החום הנבלע משמש רק להגברת הנפח הפנימי של המערכת...

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

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 constant pressure than at constant volume.

From the first law of thermodynamics, the two molar heat capacities are related by a simple equation. The difference between the constant-pressure heat capacity, Cp, and the constant-volume heat capacity, Cv, is a constant. That constant is the universal gas constant, R, also called the ideal gas constant or molar gas constant.

The value of R is about 8.314 and it uses the same SI unit as molar specific heat capacity, J/mol·K. A helium example shows this relationship clearly. For He, Cp is 20.78 J/mol·K and Cv is 12.47 J/mol·K. Their difference is 8.31 J/mol·K, which is close to R.

Ideal Gas Heat Capacity Differences

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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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Learn why ideal gases need more heat at constant pressure than at constant volume, and how Cp, Cv, and the gas constant R are related.

Ideal Gas Heat Capacity Differences | JoVE K12

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Ideal Gas Heat Capacity Differences

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