No heat engine, either actual or ideal, operating in a cycle can convert all the heat supplied into mechanical work.

No heat engine, either actual or ideal, operating in a cycle can convert all the heat supplied into mechanical work.

• A. True
• B. False
• C. Sometimes
• D. Not Applicable

Answer: (A)

In a cyclic heat engine, not all the heat drawn from the hot source can be turned into work because some heat must be rejected to the cold sink to close the cycle. The energy balance for a cycle says work output equals the heat in minus the heat out: W = Q_in − Q_out. Since the heat rejected to the cold reservoir (Q_out) is always greater than zero for finite temperatures, the work produced is always less than the heat absorbed. Even the most efficient reversible cycle between two finite temperatures—the Carnot cycle—has an efficiency η = 1 − T_cold/T_hot, which is always less than 1 unless the cold reservoir is at absolute zero or the hot reservoir is infinite—both impossible in practice. Therefore, no heat engine operating in a cycle can convert all the heat supplied into mechanical work.

In a cyclic heat engine, not all the heat drawn from the hot source can be turned into work because some heat must be rejected to the cold sink to close the cycle. The energy balance for a cycle says work output equals the heat in minus the heat out: W = Q_in − Q_out. Since the heat rejected to the cold reservoir (Q_out) is always greater than zero for finite temperatures, the work produced is always less than the heat absorbed. Even the most efficient reversible cycle between two finite temperatures—the Carnot cycle—has an efficiency η = 1 − T_cold/T_hot, which is always less than 1 unless the cold reservoir is at absolute zero or the hot reservoir is infinite—both impossible in practice. Therefore, no heat engine operating in a cycle can convert all the heat supplied into mechanical work.