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.

$$\Delta U = Q - W$$

Heat Engine Efficiency: Efficiency \(e\) is work \(W\) divided by input heat \(Q_H\). Also related to rejected heat \(Q_C\).

$$e = \frac{W}{Q_H} = 1 - \frac{Q_C}{Q_H}$$

Carnot Engine Efficiency: Maximum theoretical efficiency depends only on temperatures of hot \(T_H\) and cold \(T_C\) reservoirs.

$$e_{Carnot} = 1 - \frac{T_C}{T_H}$$

Entropy Change: Change in entropy \(\Delta S\) for a reversible process at constant temperature \(T\).

$$\Delta S = (\frac{Q}{T})_R$$

Refrigerator Coefficient of Performance: Ratio of heat removed \(Q_C\) to work input \(W\).

$$COP_{ref} = \frac{Q_C}{W}$$

Heat Pump Coefficient of Performance: Ratio of heat delivered \(Q_H\) to work input \(W\).

$$COP_{hp} = \frac{Q_H}{W}$$

Practice quiz

  1. 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) $300 \text{ J}$

  2. 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.

  3. 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) $30\%$

  4. 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) $1500 \text{ J}$

  5. 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) $40\%$

  6. 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.

  7. $1000 \text{ J}$ 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) $3.33 \text{ J/K}$

  8. 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) $3$

  9. 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) $4$

  10. 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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