AP Physics 2 Questions on Adiabatic Processes: Exam Prep

📚 Quick Study Guide

• 🔥 Definition: An adiabatic process is one in which no heat is transferred into or out of the system ($Q = 0$).
• 🌡️ First Law of Thermodynamics: For an adiabatic process, the first law simplifies to $\Delta U = -W$, where $\Delta U$ is the change in internal energy and $W$ is the work done by the system.
• 💨 Ideal Gas Law Relation: For an ideal gas undergoing an adiabatic process, $PV^\gamma = constant$, where $P$ is the pressure, $V$ is the volume, and $\gamma = \frac{C_p}{C_v}$ is the adiabatic index (ratio of specific heats).
• ⚙️ Work Done: The work done during an adiabatic process is given by $W = \frac{P_2V_2 - P_1V_1}{1 - \gamma}$, where $P_1$ and $V_1$ are the initial pressure and volume, and $P_2$ and $V_2$ are the final pressure and volume.
• 🧊 Free Expansion: A free expansion (also called a Joule expansion) is an adiabatic process where no work is done, and the internal energy remains constant.
• 💡 Quasi-static Process: An adiabatic process is quasi-static if it occurs slowly enough to maintain internal equilibrium within the system.
• ✏️ Important Note: Remember to use consistent units for all calculations!

Practice Quiz

1. A gas expands adiabatically. What happens to its temperature?

   1. It increases.
   2. It decreases.
   3. It remains constant.
   4. It depends on the type of gas.

2. In an adiabatic process, which of the following is true?

   1. $\Delta U = 0$
   2. $Q = 0$
   3. $W = 0$
   4. $\Delta T = 0$

3. For an ideal gas undergoing an adiabatic process, which relationship holds true?

   1. $PV = constant$
   2. $P/V = constant$
   3. $PV^\gamma = constant$
   4. $P^\gamma V = constant$

4. What is the work done in an adiabatic free expansion of an ideal gas?

   1. $P\Delta V$
   2. $\Delta U$
   3. Zero
   4. Infinite

5. The adiabatic index ($\gamma$) is the ratio of:

   1. Specific heat at constant volume to specific heat at constant pressure.
   2. Specific heat at constant pressure to specific heat at constant volume.
   3. Pressure to volume.
   4. Volume to pressure.

6. Which of the following processes is most likely to be adiabatic?

   1. Slow compression of a gas in a cylinder.
   2. Rapid expansion of a gas from a container.
   3. Boiling water in a kettle.
   4. Melting ice in a glass.

7. In an adiabatic process, if the volume of a gas is compressed, what happens to the pressure?

   1. It decreases.
   2. It increases.
   3. It remains the same.
   4. It becomes zero.