Thermodynamics — Practice Quiz
A Physics cheat sheet for Thermodynamics — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.
Formulas & key concepts
First Law of Thermodynamics: Change in internal energy \(\Delta U\) equals heat \(Q\) added minus work \(W\) done by the system.
Heat Engine Efficiency: Efficiency \(e\) is work \(W\) divided by input heat \(Q_H\). Also related to rejected heat \(Q_C\).
Carnot Engine Efficiency: Maximum theoretical efficiency depends only on temperatures of hot \(T_H\) and cold \(T_C\) reservoirs.
Entropy Change: Change in entropy \(\Delta S\) for a reversible process at constant temperature \(T\).
Refrigerator Coefficient of Performance: Ratio of heat removed \(Q_C\) to work input \(W\).
Heat Pump Coefficient of Performance: Ratio of heat delivered \(Q_H\) to work input \(W\).
Practice quiz
A system absorbs $500 \text{ J}$ of heat and does $200 \text{ J}$ of work on its surroundings. What is the change in its internal energy?
- A) $300 \text{ J}$
- B) $700 \text{ J}$
- C) $-300 \text{ J}$
- D) $-700 \text{ J}$
Answer: A) $300 \text{ J}$
If a system does $150 \text{ J}$ of work and its internal energy decreases by $200 \text{ J}$, what is the heat exchange?
- A) $50 \text{ J}$ of heat is absorbed by the system.
- B) $50 \text{ J}$ of heat is rejected by the system.
- C) $350 \text{ J}$ of heat is absorbed by the system.
- D) $350 \text{ J}$ of heat is rejected by the system.
Answer: B) $50 \text{ J}$ of heat is rejected by the system.
A heat engine performs $1200 \text{ J}$ of work while absorbing $4000 \text{ J}$ of heat from a hot reservoir. What is its efficiency?
- A) $25\%$
- B) $30\%$
- C) $35\%$
- D) $40\%$
Answer: B) $30\%$
A heat engine operates with an efficiency of $40\%$. If it absorbs $2500 \text{ J}$ of heat from the hot reservoir, how much heat does it reject to the cold reservoir?
- A) $1000 \text{ J}$
- B) $1250 \text{ J}$
- C) $1500 \text{ J}$
- D) $2000 \text{ J}$
Answer: C) $1500 \text{ J}$
A Carnot engine operates between a hot reservoir at $227 \text{ \textdegree C}$ and a cold reservoir at $27 \text{ \textdegree C}$. What is its efficiency?
- A) $20\%$
- B) $30\%$
- C) $40\%$
- D) $50\%$
Answer: C) $40\%$
Which of the following statements about heat engine efficiency is true?
- A) The efficiency of a real heat engine can be greater than the Carnot efficiency.
- B) The Carnot efficiency depends on the type of working fluid used.
- C) A heat engine operating between two reservoirs can achieve $100\%$ efficiency if the cold reservoir temperature is $0 \text{ K}$.
- D) The Carnot efficiency represents the maximum possible efficiency for any heat engine operating between two given temperatures.
Answer: D) The Carnot efficiency represents the maximum possible efficiency for any heat engine operating between two given temperatures.
$1000 \text{ J}$ of heat is reversibly added to a system at a constant temperature of $27 \text{ \textdegree C}$. What is the change in entropy of the system?
- A) $3.33 \text{ J/K}$
- B) $33.3 \text{ J/K}$
- C) $333 \text{ J/K}$
- D) $3333 \text{ J/K}$
Answer: A) $3.33 \text{ J/K}$
A refrigerator removes $300 \text{ J}$ of heat from its cold compartment for every $100 \text{ J}$ of work input. What is its coefficient of performance?
- A) $1$
- B) $2$
- C) $3$
- D) $4$
Answer: C) $3$
A heat pump delivers $5000 \text{ J}$ of heat to a warm space while consuming $1250 \text{ J}$ of electrical energy (work). What is its coefficient of performance?
- A) $2$
- B) $3$
- C) $4$
- D) $5$
Answer: C) $4$
A heat pump has a $COP_{hp}$ of $3.5$. If it extracts $2500 \text{ J}$ of heat from the cold reservoir, how much work input is required?
- A) $714 \text{ J}$
- B) $1000 \text{ J}$
- C) $1750 \text{ J}$
- D) $2500 \text{ J}$
Answer: B) $1000 \text{ J}$
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