Name: adiabatic compression in an engine cylinder
Uploaded: 2025-05-22T09:05:49.000Z
Duration: 1 min 20 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.10

SC.912.P.10.2

Work Done in an Adiabatic Process

Si consideri un pallone meteorologico riempito di gas elio con una certa pressione iniziale e volume che sale e si espande adiabaticamente fino a un volume finale sotto pressione atmosferica decrescente. Qual è il lavoro svolto dal gas?
Se si conoscono le temperature iniziale e finale, quindi, per un processo adiabatico, il lavoro svolto si ottiene dalla sua energia interna, espressa in termini di variazione di temperatura.
Un altro modo è quello di utilizzare la condizione per il processo adiabatico, da cui è possibile mettere in relazione le pressioni e i volumi iniziali e finali del gas. I termini sono stati riorganizzati per semplificazione.
Richiamare il lavoro durante il cambio di volume e sostituire in esso l'espressione di pressione ottenuta.
Integrando questa espressione con la variazione di volume, è possibile determinare il lavoro svolto durante un processo adiabatico.
Se la pressione iniziale del gas nel palloncino ad elio è di 1 atm e il volume del pallone varia da 25 m3 a 100 m3, sostituendo le quantità note nell'espressione derivata, è possibile calcolare il lavoro svolto dal gas.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Fisica universitaria con fisica moderna. San Francisco, CA: Pearson. Pagine 641, 642</li>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. Estratto da <a href="https://openstax.org/books/university-physics-volume-2/pages/3-6-adiabatic-processes-for-an-ideal-gas">https://openstax.org/books/university-physics-volume-2/pages/3-6-adiabatic-processes-for-an-ideal-gas</a></li>
</ol>

lavoro svolto in un processo adiabatico

Consideriamo la compressione adiabatica di un gas ideale nel cilindro di un motore diesel di un'automobile. Il vapore di benzina viene iniettato nel cilindro di un motore di automobile quando il pistone si trova nella sua posizione espansa. La temperatura, la pressione e il volume del miscuglio gas-aria risultante sono rispettivamente di 20 °C, 1,00 x 105 N/m2 e 240 cm3. Il miscuglio viene quindi compresso adiabaticamente a un volume di 40 cm3. Notare che, nell'effettivo funzionamento di un motore d'automobile, la compressione non è quasi statica, anche se facciamo quell'assunzione qui. Quali sono la pressione e la temperatura del miscuglio dopo la compressione? Quanto lavoro viene fatto durante la compressione?

Soluzione:

Per un processo di compressione adiabatica, l'espressione per la pressione è scritta come:

<img alt="Equation1" src="/files/ftp_upload/13689/13689_Equation_1.svg" style="text-align: center; height: 34px;" />

Utilizzando il rapporto delle capacità termiche molari dell'aria come 1,4 e sostituendo le quantità note nell'espressione (1), si calcola la pressione del miscuglio dopo la compressione.

<img alt="Equation2" src="/files/ftp_upload/13689/13689_Equation_2.svg" style="text-align: center; height: 34px;" />

Dalla legge dei gas ideali e usando il valore di pressione ottenuto, si calcola anche la temperatura del miscuglio dopo la compressione.

<img alt="Equation3" src="/files/ftp_upload/13689/13689_Equation_3.svg" style="text-align: center; height: 34px;" />

<img alt="Equation4" src="/files/ftp_upload/13689/13689_Equation_4.svg" style="text-align: center; height: 34px;" />

<img alt="Equation5" src="/files/ftp_upload/13689/13689_Equation_5.svg" style="text-align: center; height: 10px;" />

Di conseguenza, la pressione e la temperatura del miscuglio dopo la compressione all'interno del cilindro di un motore diesel di un'automobile vengono determinate.

Se il processo di compressione è isoterico, allora il valore della pressione cambia dal valore ottenuto. Ciò avviene perché, in un processo di compressione adiabatica, se la temperatura aumenta, la pressione diventa maggiore. Pertanto, iniettando il carburante nel cilindro vicino alla fase di compressione, il miscuglio di aria raggiunge una temperatura più elevata, risultando nell'accensione spontanea del carburante senza alcun bisogno di candele.

Conoscendo la pressione iniziale e finale, il lavoro compiuto durante la compressione può essere ottenuto utilizzando:

<img alt="Equation6" src="/files/ftp_upload/13689/13689_Equation_6.svg" style="text-align: center; height: 34px;" />

Sostituendo le quantità note e ottenute nell'espressione sopra, il lavoro compiuto è pari a -1,63 J. Qui, il segno negativo indica che il lavoro viene svolto dal pistone sul miscuglio aria-gas.

Lavoro svolto in un processo adiabatico

Si consideri la compressione adiabatica di un gas ideale nel cilindro di un motore diesel di un'automobile. Il vapore di benzina viene iniettato nel cilindro di un ...

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adiabatic compression in an engine cylinder

Adiabatic compression in an engine cylinder changes the pressure, temperature, and volume of a gas-air mixture. In this setup, gasoline vapor is injected into the cylinder when the piston is in its expanded position. The mixture starts at 20 °C, 1.00 x 10^5 N/m^2, and 240 cm^3.

The mixture is then compressed adiabatically to 40 cm^3. Adiabatic means no heat is exchanged with the surroundings during the process. For this calculation, the compression is treated as quasi-static, even though real automobile engine compression is not quasi-static.

Using the adiabatic pressure relation and the molar heat capacity ratio for air, 1.4, the final pressure is found from the initial conditions and the volume change. The ideal gas law is then used with that pressure to calculate the final temperature of the mixture. The result shows that the compressed gas reaches a higher pressure and temperature than it had before.

If the compression were isothermal, the pressure would be different from the value found here. In an adiabatic compression, the temperature rises, so the pressure becomes greater. This helps explain why fuel injected near the compression stroke can ignite on its own in a diesel engine, without spark plugs.

The work done during compression is found from the initial and final pressure values. The calculated work is -1.63 J. The negative sign means the piston does work on the air-gas mixture during compression.

Adiabatic Compression in an Engine Cylinder

adiabatic-compression-in-an-engine-cylinder

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Adiabatic compression in an engine cylinder changes the pressure, temperature, and volume of a gas-air mixture. In this setup, gasoline vapor is injected into the cylinder when the piston is in its expanded position. The mixture starts at 20 °C, 1.00 x 10^5 N/m^2, and 240 cm^3. The mixture is then compressed adiabatically to 40 cm^3. Adiabatic means no heat is exchanged with the surroundings during the process. For this calculation, the compression is treated as quasi-static, even though real...

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See how adiabatic compression changes pressure, temperature, and work in an engine cylinder, using ideal gas relations and a diesel engine example.

Adiabatic Compression in an Engine Cylinder | JoVE K12

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SC.912.P.10.3

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New York State Science Learning Standards

HS. Energy

HS-PS3-3.

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SC.912.P.10.5

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SC.912.P.10.6

A. Energy is involved in all physical and chemical processes. It is conserved, and can be transformed from one form to another and into work. At the atomic and nuclear levels energy is not continuous but exists in discrete amounts. Energy and mass are related through Einstein's equation E=mc2.

B. The properties of atomic nuclei are responsible for energy-related phenomena such as radioactivity, fission and fusion.

C. Changes in entropy and energy that accompany chemical reactions influence reaction paths. Chemical reactions result in the release or absorption of energy.

D. The theory of electromagnetism explains that electricity and magnetism are closely related. Electric charges are the source of electric fields. Moving charges generate magnetic fields.

E. Waves are the propagation of a disturbance. They transport energy and momentum but do not transport matter.

Adiabatic Compression in an Engine Cylinder

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