AP Physics C Mechanics Questions on Heat Engines and Refrigerators

📚 Quick Study Guide

• 🔥 Heat Engines: Convert thermal energy into mechanical work. They operate in cycles.
• ⚙️ Efficiency ($e$): The ratio of work done ($W$) to heat absorbed ($Q_H$). Formula: $e = \frac{W}{Q_H} = 1 - \frac{Q_C}{Q_H}$, where $Q_C$ is the heat exhausted.
• 🧊 Refrigerators: Transfer heat from a cold reservoir to a hot reservoir, requiring work input.
• 🌡️ Coefficient of Performance (COP): The ratio of heat removed from the cold reservoir ($Q_C$) to the work done ($W$). Formula: $COP = \frac{Q_C}{W} = \frac{Q_C}{Q_H - Q_C}$.
• 🔄 Carnot Cycle: A theoretical thermodynamic cycle that gives the maximum possible efficiency for a heat engine or COP for a refrigerator operating between two temperatures.
• ☀️ Carnot Efficiency: $e_{Carnot} = 1 - \frac{T_C}{T_H}$, where $T_C$ and $T_H$ are the absolute temperatures (in Kelvin) of the cold and hot reservoirs, respectively.
• ❄️ Carnot COP (Refrigerator): $COP_{Carnot} = \frac{T_C}{T_H - T_C}$

Practice Quiz

1. A heat engine operates between a hot reservoir at 400 K and a cold reservoir at 300 K. What is the maximum possible efficiency of this engine?

   1. 25%
   2. 33%
   3. 50%
   4. 75%

2. A refrigerator has a coefficient of performance (COP) of 4.0. How much work (in Joules) must be supplied to remove 1200 J of heat from the cold reservoir?

   1. 300 J
   2. 400 J
   3. 600 J
   4. 4800 J

3. A Carnot engine operates with an efficiency of 40% when the temperature of the cold reservoir is 300 K. What is the temperature of the hot reservoir?

   1. 400 K
   2. 420 K
   3. 500 K
   4. 750 K

4. Which of the following statements is true regarding the Carnot cycle?

   1. It is a reversible cycle.
   2. It has the lowest possible efficiency for any heat engine.
   3. It violates the second law of thermodynamics.
   4. It can only operate with ideal gases.

5. A heat engine absorbs 800 J of heat from a hot reservoir and exhausts 600 J of heat to a cold reservoir. What is the efficiency of the engine?

   1. 25%
   2. 33%
   3. 75%
   4. 80%

6. A refrigerator maintains a freezer compartment at -13°C while exhausting heat into a room at 27°C. What is the maximum possible coefficient of performance (COP) of this refrigerator?

   1. 0.23
   2. 6.5
   3. 7.0
   4. 7.5

7. Which of the following processes is NOT part of the Carnot cycle?

   1. Isothermal expansion
   2. Adiabatic expansion
   3. Isobaric compression
   4. Isothermal compression