The second law of thermodynamics imposes what limit on the efficiency of a heat engine? the second law of thermodynamics imposes what limit on the efficiency of a heat engine? a heat engine must deposit some energy in a cold reservoir. the energy a heat engine must deposit in a cold reservoir is greater than or equal to the energy it extracts from a hot reservoir. the energy a heat engine must deposit in a cold reservoir is greater than or equal to the energy extracted as useful work.