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

Рассмотрим две одинаковые колбы, наполненные идеальным газом при разных температурах, которые могут подвергаться разным термодинамическим процессам.
Предположим, что в процессе постоянного объема температура газа в первой колбе увеличивается до уровня температуры второй колбы.
Тогда его внутренняя энергия будет такой же, как и тепловое изменение, и может быть записана в терминах молярной теплоемкости.
В процессе постоянного давления, если температура увеличивается на ту же величину, то внутренняя энергия системы изменяется, и выполняется определенная работа.
Так как внутренняя энергия является функцией состояния, то изменение внутренней энергии системы происходит одинаково при обоих процессах.
Используя уравнение идеального газа в дифференциальной форме, проделанную работу можно записать в терминах изменения температуры.
Путем отмены общих факторов с обеих сторон получается соотношение между молярными теплоемкостями для обоих процессов.
Здесь R является универсальной газовой постоянной, и, следовательно, молярная теплоемкость идеального газа при постоянном давлении всегда больше, чем при постоянном объеме.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон.637-638.</li>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. 126-127 Извлечено из <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>

Теплоёмкость индеального газа ii

Для системы, которая проходит термодинамический процесс при постоянном объёме, поглощённое тепло используется только для увеличения внутренней энергии системы, а не для выполнения какой-либо работы. В то время как для системы, проходящей термодинамический процесс при постоянном давлении, количество поглощённого тепла используется не только для увеличения внутренней энергии (как функции температуры), но и для выполнения некоторой работы. Молярная теплоёмкость - это количество тепла, необходимое для увеличения температуры 1 моля газа на 1 единицу. Поскольку некоторое поглощённое тепло используется для выполнения работы, для увеличения температуры на 1 единицу, больше тепла должно быть добавлено в систему при постоянном давлении, поэтому молярная теплоёмкость при постоянном давлении всегда больше, чем молярная теплоёмкость при постоянном объёме. Следовательно, из полученного соглашением, основанном на первом законе термодинамики, у нас есть следующее соотношение:

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

Таким образом, разница между двумя молярными теплоёмкостями является постоянной и равна универсальной газовой постоянной, R. Она также называется идеальной газовой постоянной или молярной газовой постоянной. Её значение приблизительно 8.314 и выражается в той же единице СИ, что и молярная удельная теплоёмкость J/моль·K. Например, для He измеренные значения для Cp и CV составляют 20.78 Дж/моль·К и 12.47 Дж/моль·К соответственно. Их разница составляет 8.31 Дж/моль·К, что близко к R.

Теплоёмкость индеального газа II

Для системы, которая претерпевает термодинамический процесс при постоянном объемном состоянии, поглощенное тепло используется только для увеличения внутренней ...

Education

JoVE Core

Physics

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Unit 1

Раздел 1

The First Law of Thermodynamics

Первый закон термодинамики

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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