Name: ideal gas heat capacity differences
Uploaded: 2023-04-30T12:32:12.000Z
Duration: 1 min 23 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.

Heat Capacities of an Ideal Gas II

ضع في اعتبارك قارورتين متطابقتين مملوءتين بغاز مثالي في درجات حرارة مختلفة يمكن أن تخضع لعمليات ديناميكية حرارية مختلفة.
لنفترض ، في عملية ذات حجم ثابت ، أن درجة حرارة غاز القارورة الأولى تزداد لتساوي درجة حرارة القارورة الثانية.
بعد ذلك ، ستكون طاقته الداخلية هي نفسها تغير الحرارة ويمكن كتابتها من حيث السعة الحرارية المولارية.
في عملية الضغط المستمر ، إذا زادت درجة الحرارة بنفس المقدار ، فإن الطاقة الداخلية للنظام تتغير مع القيام ببعض الأعمال.
نظرا لأن الطاقة الداخلية هي دالة حالة ، فإن تغيير الطاقة الداخلية للنظام هو نفسه في كلتا العمليتين.
باستخدام معادلة الغاز المثالية في شكل تفاضلي ، يمكن كتابة العمل المنجز من حيث تغير درجة الحرارة.
من خلال إلغاء العوامل المشتركة على كلا الجانبين ، يتم الحصول على العلاقة بين القدرات الحرارية المولية لكلتا العمليتين.
هنا ، R هو ثابت الغاز العالمي ، وبالتالي ، فإن السعة الحرارية المولية للغاز المثالي في ظل عملية ضغط ثابت تكون دائما أكبر من تلك الموجودة في عملية الحجم الثابت.

<ol>
	<li>يونغ ، إتش دي وفريدمان ، ر. (2012). الفيزياء الجامعية مع الفيزياء الحديثة. سان فرانسيسكو ، كاليفورنيا: بيرسون 637-638.</li>
	<li>OpenStax. (2019). جامعة الفيزياء المجلد 2. [نسخة الويب]. 126-127 تم الاسترجاع من <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>

السعة الحرارية للغاز المثالي ii

<div style="direction:rtl">بالنسبة للنظام الذي يخضع لعملية ديناميكية حرارية في حالة حجم ثابت، يتم استخدام الحرارة الممتصة فقط لزيادة الطاقة الداخلية للنظام وليس للقيام بأي نوع من العمل. بينما بالنسبة للنظام الذي يخضع لعملية ديناميكية حرارية تحت ظروف ضغط ثابت، فإن كمية الحرارة الممتصة تستخدم ليس فقط لزيادة الطاقة الداخلية (كدالة لدرجة الحرارة) ولكن أيضًا للقيام ببعض الأعمال. السعة الحرارية المولية هي كمية الحرارة اللازمة لزيادة درجة حرارة 1 مول من الغاز بمقدار 1 وحدة. نظرًا لاستخدام بعض الحرارة الممتصة لإنجاز شغل، يجب إضافة المزيد من الحرارة إلى نظام تحت ضغط ثابت لزيادة درجة حرارته بمقدار وحدة واحدة، وتكون السعة الحرارية المولية لعملية ضغط ثابت دائمًا أكبر من السعة الحرارية المولية لحجم ثابت عملية. وبالتالي فمن الاشتقاق الذي اعتمد على القانون الأول للديناميكا الحرارية نحصل على العلاقة التالية وهي <img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;"> وبالتالي فإن الفرق المتجهي بين السعتين الحراريتين الموليتين هو ثابت ويساوي ثابت الغاز العالمي R. ويسمى أيضًا ثابت الغاز المثالي أو ثابت الغاز المولي. تبلغ قيمتها حوالي 8.314 ويتم التعبير عنها بنفس وحدة النظام الدولي للوحدات مثل السعة الحرارية النوعية المولية J/mol'K. على سبيل المثال، بالنسبة لـ He، القيم المقاسة لـ Cp وCV هي 20.78 J/mol&#183؛K و12.47 J/mol·K، على التوالي. الفرق المتجهي بينهما هو  8.31 J/mol·K وهي قريبة من R.</div>

السعة الحرارية للغاز المثالي II

بالنسبة للنظام الذي يخضع لعملية ديناميكية حرارية في حالة حجم ثابت ، يتم استخدام الحرارة الممتصة فقط لزيادة ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

The First Law of Thermodynamics

القانون الأول للديناميكا الحرارية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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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heat capacities of an ideal gas ii

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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