Which statement correctly describes Q_H and Q_C in a heat engine?

• A. Q_H is the heat expelled to the cold reservoir.
• B. Q_C is the heat absorbed from the hot reservoir.
• C. Q_H is the heat absorbed from the hot reservoir.
• D. Q_H equals Q_C in a reversible cycle.

Answer: (C)

In a heat engine, heat flows into the system from the hot reservoir and some of that energy is converted into work while the rest is dumped to the cold reservoir. The symbol Q_H represents the heat absorbed from the hot reservoir, while Q_C represents the heat expelled to the cold reservoir. The energy balance Q_H = Q_C + W shows that the engine must take in more heat than it dumps to the cold reservoir, because some of that energy goes into doing work (W > 0). Therefore Q_H is the heat absorbed from the hot reservoir.

The other statements mix up the directions of heat flow or imply zero work. The heat expelled to the cold reservoir is Q_C, not Q_H. The heat to the cold reservoir is not the heat absorbed from the hot reservoir, and in a functioning engine Q_H does not equal Q_C because there is always some work produced.