AP Physics C Questions on Thermodynamic Processes

📚 Quick Study Guide

• 🔥 Thermodynamic Processes: These involve changes in a system's state variables (pressure $P$, volume $V$, temperature $T$).
• 🌡️ Isothermal Process: Constant temperature ($T$ is constant). $PV = constant$. Work done: $W = nRT \ln(V_2/V_1)$.
• ⚙️ Adiabatic Process: No heat exchange with the surroundings ($Q = 0$). $PV^\gamma = constant$, where $\gamma = C_P/C_V$. Work done: $W = (P_2V_2 - P_1V_1)/(1 - \gamma)$.
• ⚖️ Isobaric Process: Constant pressure ($P$ is constant). Work done: $W = P(V_2 - V_1)$.
• 🔒 Isochoric Process: Constant volume ($V$ is constant). Work done: $W = 0$.
• 🔄 First Law of Thermodynamics: $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.
• 📈 Efficiency of a Heat Engine: $e = W/Q_H = 1 - (Q_C/Q_H)$, where $Q_H$ is the heat absorbed from the hot reservoir and $Q_C$ is the heat rejected to the cold reservoir.
• 🧊 Carnot Engine: The most efficient engine possible operating between two temperatures: $e_{Carnot} = 1 - (T_C/T_H)$.

🧪 Practice Quiz

1. A gas expands isothermally from a volume of $V_1$ to $V_2$. The work done by the gas is:
   1. $P(V_2 - V_1)$
   2. $nRT \ln(V_2/V_1)$
   3. $0$
   4. $(P_2V_2 - P_1V_1)/(1 - \gamma)$
2. In an adiabatic process, which of the following is true?
   1. Temperature remains constant.
   2. Pressure remains constant.
   3. No heat is exchanged with the surroundings.
   4. Volume remains constant.
3. For an isochoric process, the work done by the system is:
   1. $P(V_2 - V_1)$
   2. $nRT \ln(V_2/V_1)$
   3. $0$
   4. $(P_2V_2 - P_1V_1)/(1 - \gamma)$
4. The first law of thermodynamics states:
   1. $\Delta U = Q + W$
   2. $\Delta U = Q - W$
   3. $Q = \Delta U - W$
   4. $W = Q + \Delta U$
5. A Carnot engine operates between temperatures of 500 K and 300 K. Its efficiency is:
   1. 20%
   2. 40%
   3. 60%
   4. 80%
6. During an isobaric process, 500 J of heat are added to a gas, and the gas expands by 0.05 $m^3$ at a constant pressure of $10^4$ Pa. The change in internal energy is:
   1. 0 J
   2. 200 J
   3. 300 J
   4. 500 J
7. What is the value of work done in a cyclic process?
   1. Positive
   2. Negative
   3. Zero
   4. Depends on the Process