20.14
Adiabatic Processes for an Ideal Gas
When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expans…
A thermodynamic process with no heat transfer inside or outside the system is termed adiabatic.
Thus, according to the first law of thermodynamics, the change in internal energy is the negative of the work done in an adiabatic process.
For instance, a fire piston consisting of a thermally insulated tube has one end closed, and the other end has a movable plunger.
If a small piece of cotton ball is placed inside the tube and the plunger is allowed to push down rapidly at room temperature, the cotton ball catches fire despite no heat being applied. This happens due to adiabatic compression.
Here, as the volume decreases, the work done becomes negative; hence, the internal energy change is positive, with a corresponding increase in gas temperature.
Conversely, when opening a bottle of cooled carbonated drink, the gas trapped in the bottle undergoes adiabatic expansion, resulting in the work done being positive.
As a result, the internal energy decreases with a corresponding temperature drop, condensing the evaporated vapor into a visible cloud.
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Q1: What happens to temperature when an ideal gas undergoes adiabatic compression?
During adiabatic compression, work is done on the gas without heat transfer. According to the first law of thermodynamics, this work increases the internal energy, raising the gas temperature significantly. For example, in a fire piston, rapid compression of air heats it enough to ignite cotton without external heat application.
Q2: Why does a gas cool down during adiabatic expansion?
In adiabatic expansion, the gas does work on its surroundings without receiving heat. This work reduces internal energy, lowering the gas temperature. When opening a carbonated drink bottle, trapped gas expands adiabatically, cooling enough to condense water vapor into a visible cloud.
Q3: How does adiabatic compression relate to engine knock in automobiles?
In car cylinders, gas-air mixtures compress so rapidly that heat exchange with the environment cannot occur, making the process adiabatic. The resulting temperature rise can cause uncontrolled explosions before spark ignition, creating engine knock. Higher-octane gasoline raises the ignition temperature, preventing premature detonation.
Q4: What is free expansion and why does temperature remain constant?
Free expansion occurs when a gas expands into a vacuum without external pressure. No work is done, and the thermally insulated container prevents heat transfer. With both work and heat equal to zero, internal energy remains unchanged. For an ideal gas, constant internal energy means constant temperature.
Q5: How does the first law of thermodynamics apply to adiabatic processes?
In adiabatic processes, heat transfer is zero, so the first law simplifies to: change in internal energy equals negative work done. During compression, negative work increases internal energy and temperature. During expansion, positive work decreases internal energy and temperature. This relationship governs all adiabatic behavior.
Q6: What distinguishes an adiabatic process from other thermodynamic processes?
An adiabatic process involves no heat transfer between the system and surroundings, making it thermally isolated. Unlike isothermal processes where temperature stays constant, or isobaric processes where pressure remains fixed, adiabatic processes allow temperature and pressure to change based solely on work done.
Q7: Why is the fire piston experiment a practical demonstration of adiabatic compression?
The fire piston demonstrates adiabatic compression by rapidly compressing air in a thermally insulated tube. The work done in an adiabatic process increases the gas internal energy and temperature so dramatically that cotton ignites without external heat. This clearly shows the relationship between work, internal energy, and temperature.