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

Rozważmy dwie identyczne kolby wypełnione gazem doskonałym w różnych temperaturach, które mogą ulegać różnym procesom termodynamicznym.
Załóżmy, że w procesie o stałej objętości temperatura gazu w pierwszej kolbie wzrasta tak, aby zrównała się z temperaturą drugiej kolby.
Wtedy jego energia wewnętrzna będzie taka sama jak zmiana ciepła i można ją zapisać w kategoriach molowej pojemności cieplnej.
W procesie stałego ciśnienia, jeśli temperatura wzrasta o tę samą wartość, wówczas wewnętrzna energia systemu zmienia się wraz z wykonaną pracą.
Ponieważ energia wewnętrzna jest funkcją stanu, wewnętrzna zmiana energii układu jest taka sama w obu procesach.
Korzystając z równania gazu doskonałego w postaci różniczkowej, wykonaną pracę można zapisać w kategoriach zmiany temperatury.
Poprzez znoszenie czynników wspólnych po obu stronach uzyskuje się zależność między molowymi pojemnościami cieplnymi dla obu procesów.
Tutaj R jest uniwersalną stałą gazową, a zatem molowa pojemność cieplna gazu doskonałego w procesie stałego ciśnienia jest zawsze większa niż w procesie o stałej objętości.

<ol>
	<li>Young, H.D i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson.637-638.</li>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 2. [Wersja internetowa]. 126-127 Pobrane z <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>

pojemność cieplna gazu doskonałego ii

W przypadku układu, który przechodzi proces termodynamiczny przy stałej objętości, pochłonięte ciepło jest wykorzystywane jedynie do zwiększenia energii wewnętrznej układu, a nie do wykonania jakiejkolwiek pracy. Natomiast w przypadku układu przechodzącego proces termodynamiczny w warunkach stałego ciśnienia ilość pochłoniętego ciepła wykorzystywana jest nie tylko na zwiększenie energii wewnętrznej (w funkcji temperatury), ale także na wykonanie pewnej pracy. Ciepło molowe to ilość ciepła potrzebna do podniesienia temperatury 1 mola gazu o 1 jednostkę. Ponieważ część pochłoniętego ciepła jest wykorzystywana do wykonania pracy, należy dodać więcej ciepła do układu pod stałym ciśnieniem, aby zwiększyć jego temperaturę o 1 jednostkę. Ciepło molowe dla procesu przy stałym ciśnieniu jest zawsze większe niż ciepło molowe dla stałej objętości proces. W konsekwencji z wyprowadzenia, które oparliśmy na pierwszej zasadzie termodynamiki, otrzymujemy następującą zależność, czyli

<img alt="Równanie1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

Zatem różnica między dwiema molowymi pojemnościami cieplnymi jest stała i równa uniwersalnej stałej gazowej R. Nazywa się ją również stałą gazu doskonałego lub stałą molową gazu. Jego wartość wynosi w przybliżeniu 8,314 i jest wyrażana w tej samej jednostce SI, co molowe ciepło właściwe J/mol·K. Na przykład dla He zmierzone wartości Cp i CVwynoszą 20,78 J/mol² ;K i 12,47 J/mol·K, odpowiednio. Różnica polega na tym, że... 8,31 J/mol⋅K, czyli blisko R.

Pojemność cieplna gazu doskonałego II

W przypadku systemu, który jest poddawany procesowi termodynamicznemu w warunkach stałej objętości, pochłonięte ciepło jest wykorzystywane tylko do zwiększenia wewnętrznej ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

The First Law of Thermodynamics

Pierwsza zasada termodynamiki

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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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