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

Farklı termodinamik işlemlerden geçebilen farklı sıcaklıklarda ideal bir gazla doldurulmuş iki özdeş şişeyi düşünün.
Sabit hacimli bir işlemde, birinci şişenin gaz sıcaklığının, ikinci şişenin sıcaklığına eşit olacak şekilde artırıldığını varsayalım.
Daha sonra iç enerjisi ısı değişimi ile aynı olacaktır ve molar ısı kapasitesi cinsinden yazılabilir.
Sabit basınçlı bir proseste, sıcaklık aynı miktarda arttırılırsa, sistemin iç enerjisi yapılan bazı işlerle birlikte değişir.
İç enerji bir durum fonksiyonu olduğundan, sistemin iç enerji değişimi her iki süreçte de aynıdır.
Diferansiyel formda ideal gaz denklemi kullanılarak, yapılan iş sıcaklık değişimi cinsinden yazılabilir.
Her iki taraftaki ortak faktörleri iptal ederek, her iki işlem için molar ısı kapasiteleri arasındaki ilişki elde edilir.
Burada, R evrensel gaz sabitidir ve bu nedenle, sabit basınçlı bir işlem altında ideal bir gazın molar ısı kapasitesi her zaman sabit hacimli bir işlem altındakinden daha büyüktür.

<ol>
	<li>Genç, H.D ve Freedman, R.A. (2012). Modern Fizik ile Üniversite Fiziği. San Francisco, Kaliforniya: Pearson.637-638.</li>
	<li>Stax'ı açın. (2019). Üniversite Fiziği Cilt 2. [Web sürümü]. 126-127 <a href="https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas" adresinden alındı>https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas</a></li>
</ol>

İdeal bir gazın isı kapasiteleri ii

Bir termodinamik sürece tabi olan bir sistem, sabit hacim koşullarında ısının sadece sistem iç enerjisini arttırmak için kullanıldığı durumlarda meydana gelir. Sabit basınç koşullarında ise, termodinamik süreç boyunca emilen ısı hem iç enerjiyi (sıcaklık fonksiyonu olarak) artırmak hem de bir miktar iş yapmak için kullanılır. Molar ısı kapasitesi, 1 mol gazın sıcaklığını 1 birim arttırmak için gereken ısı miktarıdır. İş yapmak için emilen bir miktar ısı olduğundan, birim hacimdeki bir sistemin sıcaklığını 1 birim artırmak için sabit basınç altında daha fazla ısı eklenmelidir. Bu nedenle, bir sabit basınç süreci için molar ısı kapasitesi, sabit hacim süreci için molar ısı kapasitesinden her zaman daha büyüktür. Sonuç olarak, termodinamiğin birinci yasası dayanan türetilmiş bir ilişkiyi aşağıdaki gibi elde ederiz:

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

Bu nedenle, iki molar ısı kapasitesi arasındaki fark sabit bir değerdir ve evrensel gaz sabiti olarak adlandırılır. Değerinin yaklaşık olarak 8.314 olduğu ve aynı SI birimi olan molar özgül ısı kapasitesi J/mol⋅K olarak ifade edildiği unutulmamalıdır. Örneğin, He gazı için ölçülen değerlerinden Cp ve CV sırasıyla 20.78 J/mol·K ve 12.47 J/mol·K'dır. Aralarındaki fark 8.31J/mol·K olan bu değer, R'ye yakındır.

İdeal Bir Gazın Isı Kapasiteleri II

Sabit hacim koşulunda termodinamik bir işleme tabi tutulan bir sistem için, emilen ısı yalnızca sistemin iç hacmini artırmak için kullanılır.

Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

The First Law of Thermodynamics

Termodinamiğin Birinci Kanunu

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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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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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