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

Consider a weather balloon filled with helium gas having some initial pressure and volume rising and expanding adiabatically to a final volume under decreasing atmospheric pressure. What is the work done by the gas?
If the initial and final temperatures are known, then, for an adiabatic process, the work done is obtained from its internal energy, expressed in terms of temperature change.
Another way is using the condition for the adiabatic process, from which the gas&#39;s initial and final pressures and volumes can be related. The terms are rearranged for simplification.
Recall the work during the volume change and substitute the obtained pressure expression in it.
By integrating this expression with the volume change, the work done during an adiabatic process can be determined.
If the initial gas pressure in the helium balloon is 1 atm, and the balloon&#39;s volume changes from 25 m3 to 100 m3, then by substituting the known quantities in the derived expression, the work done by the gas can be calculated.

work done in an adiabatic process

Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 &#176;C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not quasi-static, although we are making that assumption here. What are the pressure and temperature of the mixture after the compression? What is the work done during the compression?
Solution:
For an adiabatic compression process the expression for pressure is written as
<img alt="Adiabatic process formula: \( p_2 = p_1 \left( \frac{V_1}{V_2} \right)^\gamma \), thermodynamics equation." src="/files/ftp_upload/13689/13689_Equation_1.svg" style="text-align: center; height: 34px;" data-altupdatedat="1754904545000" data-alt="Adiabatic process formula, \(p_2 = p_1(V_1/V_2)^\gamma\), thermodynamics equation." />
Using the molar heat capacity ratio of air as 1.4 and by substituting the known quantities in the expression (1), the pressure of the mixture after the compression is calculated.
<img alt="Adiabatic process equation showing pressure-volume relationship in thermodynamics." src="/files/ftp_upload/13689/13689_Equation_2.svg" style="text-align: center; height: 34px;" data-altupdatedat="1754904545000" data-alt="Ideal gas law equation example with pressure and volume calculations." />
From the ideal gas law and using the obtained pressure value, the temperature of the mixture after the compression is also calculated.
<img alt="Thermodynamics equation, T2=(p2V2/p1V1)T1, shows temperature-pressure-volume relation." src="/files/ftp_upload/13689/13689_Equation_3.svg" style="text-align: center; height: 34px;" data-altupdatedat="1754904545000" data-alt="Thermodynamic process equation, T2 as a function of pressure, volume, diagram, ideal gas law." />
<img alt="Ideal gas law equation, pressure-volume relation, diagram, educational use." src="/files/ftp_upload/13689/13689_Equation_4.svg" style="text-align: center; height: 34px;" data-altupdatedat="1754904545000" data-alt="Pressure-volume-temperature equation, ratio formula, scientific calculation diagram." />
<img alt="Temperature conversion formula, equation showing value of 328&#176;C." src="/files/ftp_upload/13689/13689_Equation_5.svg" style="text-align: center; height: 10px;" data-altupdatedat="1754904545000" data-alt='Equation of static equilibrium shown as "= 328&#176;C", representing temperature stability.' />
Thus, the pressure and temperature of the mixture after compression inside the cylinder of an automobile diesel engine are determined.
If the compression process is isothermal, then the value of pressure changes from the obtained value. This is because, in an adiabatic compression process, if the temperature increases, the pressure becomes greater. Hence, on injecting the fuel into the cylinder near the compression stroke, the air mixture attains a higher temperature, resulting in spontaneous ignition of the fuel without any need for spark plugs.
By knowing the initial and final pressure, the work done during the compression can be obtained using
<img alt="Thermodynamic work formula W=1/(1-&#947;)(p2V2-p1V1), equation in energy transfer studies." src="/files/ftp_upload/13689/13689_Equation_6.svg" style="text-align: center; height: 34px;" data-altupdatedat="1754904545000" data-alt="Thermodynamics formula, W=1/(1-&#947;)(p&#8322;V&#8322;-p&#8321;V&#8321;) calculation for work in adiabatic process." />
Substituting the known and the obtained quantities in the above expression, the work done equals -1.63 J. Here, the negative sign indicates that the work is done by the piston on the air-gas mixture.

Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an ...

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JoVE Core

Physics

Unit 1

The First Law of Thermodynamics

KEY TERMS AND CONCEPTS

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

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-3.

Energy Basics

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SC.912.P.10.1

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In the case of a ...

Isothermal Processes

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Isochoric and Isobaric Processes

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SC.912.P.10.4

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SC.912.P.10.5

Chemical Reactions

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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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