Adiabatic Ideal-Gas Processes: Energy Changes and Quasi-Static Relations

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What is an adiabatic process?

A thermodynamic process in which no heat is transferred between the system and its surroundings; its heat transfer is $Q=0$.

How does the first law apply to an adiabatic process?

With work $W$ defined as work done by the system, $Delta E_{\text{int}}=Q-W$ becomes $Delta E_{\text{int}}=-W$ when $Q=0$.

What happens to an ideal gas's temperature during free expansion into a vacuum?

It remains unchanged. In an insulated free expansion, both $Q$ and $W$ are zero, so internal energy is unchanged; for an ideal gas, internal energy depends only on temperature.

Why does adiabatic compression heat a gas?

The surroundings do work on the gas. With no heat transfer, that work increases the gas's internal energy and, for an ideal gas, its temperature.

How can higher-octane gasoline help with engine knocking?

Higher-octane gasoline is more resistant to premature ignition, helping prevent the fuel-air mixture from igniting due to the temperature rise during compression before the timed spark.

Quiz questions

1. For a fixed amount of ideal gas, which relation holds along a quasi-static adiabatic path?Answer: $pV^\gamma=\text{constant}$.
2. For an ideal gas, how is the heat-capacity ratio $\gamma$ defined?Answer: $\gamma=C_P/C_V$.
3. At the same state, how does the pressure-volume slope of an adiabatic curve compare with that of an isotherm for an ideal gas?Answer: Its magnitude is $\gamma$ times greater.
4. During adiabatic compression, what sign does $W$ have if it denotes work done by the gas?Answer: Negative, because work is done on the gas.
5. An ideal diatomic gas is compressed adiabatically from $293\,\text{K}$ and $240\,\text{cm}^3$ to $40\,\text{cm}^3$, with $\gamma=1.4$. Approximately what is its final temperature?Answer: $600\,\text{K}$.