Name: path dependence in gas work
Uploaded: 2023-04-30T12:31:19.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-4

Path Between Thermodynamics States

Si consideri un cilindro con un gas ideale di volume Vo a una pressione di po dotato di un pistone senza attrito attaccato a una massa. Il pistone rimane fermo mentre la pressione è in equilibrio.
Se la massa si riduce della metà, la pressione esterna sul pistone si riduce proporzionalmente. La maggiore pressione interna del gas spinge il pistone in avanti fino al raggiungimento di un nuovo equilibrio.
Il volume del gas aumenta. Il sistema raggiunge un nuovo stato termodinamico eseguendo un lavoro.
Supponiamo che lo stesso stato finale si raggiunga riducendo la massa in due fasi. Inizialmente, la pressione diminuisce a 0,75po e il lavoro svolto è rappresentato dall'area sotto la seconda curva.
Riducendo ulteriormente la massa nel secondo stadio, il lavoro svolto dal gas è uguale all'area sotto la terza curva. Pertanto, il lavoro totale svolto dal gas nel secondo processo è la somma delle aree sotto le due curve.
Pertanto, il lavoro svolto dal gas è diverso per i diversi processi e, quindi, è una funzione dipendente dal percorso.

<ol>
 <li>Young, H.D., Freedman, R.A. Fisica universitaria con fisica moderna. San Francisco, CA: Pearson. 628 (2012).</li>
 <li>OpenStax. Fisica universitaria Vol.2. Pg 110 [versione web]. Estratto da <a href="https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy.">https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy.</a>.</li>
</ol>

percorso tra gli stati termodinamici

Consideriamo i due processi termodinamici che coinvolgono un gas ideale rappresentati dai percorsi AC e ABC nella Figura 1:

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;" />

Nel primo processo per il percorso da A a C, il gas viene mantenuto a temperatura costante T. Subisce un'espansione dal volume V_1 al volume V_2.

Il lavoro compiuto da un gas ideale è espresso come:

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;" />

Sostituendo la pressione come nRT/V dall'equazione del gas ideale e integrando i termini, il lavoro compiuto da un gas ideale a temperatura costante è ottenuto come:

<img alt="Equation2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;" />

Nel secondo processo, per il percorso da A a B, il gas ideale viene prima espanso dal volume V_1 al volume V_2 a pressione costante p_1 applicando calore. Il gas viene poi raffreddato a volume costante V_2 lungo il percorso da B a C, in modo che la sua pressione scenda a p_2.

Per il percorso da A a B, il lavoro viene svolto a pressione costante, quindi:

<img alt="Equation3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;" />

Per il percorso da B a C, siccome il volume rimane costante, non viene compiuto alcun lavoro dal gas né sul gas da parte dell'ambiente. Perciò, il lavoro totale compiuto dal gas in questo processo è lo stesso del lavoro compiuto per il percorso da A a B.

In entrambi i processi, il gas si espande dal volume V_1 al volume V_2, in modo che la sua pressione cambi da p_1 a p_2. Ciononostante, il lavoro compiuto in entrambi i processi è diverso. Questo dimostra che il lavoro compiuto da un sistema dipende dal percorso.

Percorso tra gli stati termodinamici

Si considerino i due processi termodinamici che coinvolgono un gas ideale che sono rappresentati dai percorsi AC e ABC nella Figura 1:

Nel primo processo per il percorso A a ...

Education

Didattica

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Physics

Fisica

Unit 1

Unità 1

The First Law of Thermodynamics

Il Primo Principio della Termodinamica

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

path dependence in gas work

Work done by an ideal gas can depend on the path it takes between two thermodynamic states. The transcript compares two routes from state A to state C for the same gas. In both cases, the gas expands from volume V1 to volume V2, but the work is not the same.

Along path AC, the gas stays at constant temperature T. It expands from V1 to V2. The work done by the gas is found from the pressure-volume relation for an ideal gas. After substituting pressure as nRT/V and integrating, the work for this isothermal process is obtained.

Along path ABC, the gas follows two steps. First, it expands from V1 to V2 at constant pressure p1 by applying heat. Then it is cooled at constant volume V2, and its pressure drops to p2. During the constant-pressure step AB, work is done by the gas. During the constant-volume step BC, no work is done because the volume does not change.

The total work for path ABC is therefore the same as the work done during AB. Even though both paths connect the same start and end states and the pressure changes from p1 to p2, the work values are different. This shows that work done by a system is path-dependent.

Path Dependence in Gas Work

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Path Dependence in Gas Work | JoVE K12

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Path Dependence in Gas Work

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