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

Consider two identical flasks filled with an ideal gas at different temperatures that can undergo different thermodynamic processes.
Suppose, in a constant-volume process, the first flask&#39;s gas temperature is increased to equate to the temperature of the second flask.
Then, its internal energy will be the same as the heat change and can be written in terms of molar heat capacity.
In a constant-pressure process, if the temperature is increased by the same amount, then the system&#39;s internal energy changes with some work being done.
As the internal energy is a state function, the internal energy change of the system is the same under both processes.
Using the ideal gas equation in differential form, the work done can be written in terms of temperature change.
By canceling the common factors on both sides, the relation between the molar heat capacities for both processes is obtained.
Here, R is the universal gas constant, and hence, the molar heat capacity of an ideal gas under a constant-pressure process is always greater than that under a constant-volume process.

warmtecapaciteiten van een ideaal gas ii

Voor een systeem dat een thermodynamisch proces ondergaat bij een constant volume, wordt de geabsorbeerde warmte alleen gebruikt om de interne energie van het systeem te verhogen en niet om enige vorm van werk te doen. Terwijl voor een systeem dat een thermodynamisch proces ondergaat onder constante druk, de hoeveelheid geabsorbeerde warmte niet alleen wordt gebruikt om de interne energie te verhogen (als functie van de temperatuur), maar ook om wat werk te doen. De molaire warmtecapaciteit is de hoeveelheid warmte die nodig is om de temperatuur van 1 mol gas met 1 eenheid te verhogen. Omdat een deel van de geabsorbeerde warmte wordt gebruikt om arbeid te verrichten, moet er meer warmte aan een systeem onder constante druk worden toegevoegd om de temperatuur met 1 eenheid te verhogen. De molaire warmtecapaciteit voor een proces met constante druk is altijd groter dan de molaire warmtecapaciteit voor een constant volume proces. Bijgevolg krijgen we uit de afleiding, die gebaseerd was op de eerste wet van de thermodynamica, de volgende relatie, namelijk

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;">

Het verschil tussen de twee molaire warmtecapaciteiten is dus een constante en is gelijk aan de universele gasconstante, R. Het wordt ook wel de ideale gasconstante of molaire gasconstante genoemd. De waarde ervan is ongeveer 8,314 en wordt uitgedrukt in dezelfde SI-eenheid als de molaire soortelijke warmtecapaciteit J/mol'K. Voor He zijn de gemeten waarden voor Cp en CV bijvoorbeeld 20,78 J/mol·K en 12,47 J/mol-K respectievelijk. Hun verschil is  8,31 J/mol·K, wat dichtbij R.

Warmtecapaciteiten van een ideaal gas II

For a system that undergoes a thermodynamic process at a constant volume condition, the heat absorbed is used only to increase the system&#39;s internal ...

Education

JoVE Core

Physics

Natuurkunde

Unit 1

Onderdeel 1

The First Law of Thermodynamics

De eerste wet van de thermodynamica

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

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...

heat capacities of an ideal gas iii

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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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