Looking at the equation for Carnot efficiency, I notice that as the temperature of the heat sink approaches zero, the efficiency approaches unity:
$$ \eta_{rev} = 1 - \frac{0}{T_H} = 1 $$
Seeing as the efficiency of a heat engine is the ratio between the heat it is absorbing and the work it outputs, an efficiency of 1 indicates that all heat absorbed is output as work. By first law, this implies that the engine is rejecting no heat to the low temperature sink.
This result doesn't make any sense to me. Why would a decreasing heat sink temperature result in less heat rejected?
To explain my confusion somewhat hand-wavily: if the temperature of the two reservoirs is equal, we end up with no heat transfer, and therefore $Q_L$ is zero. As we deviate from this case of reservoirs with equal temperature (which is what happens if you decrease $T_L$ while holding $T_H$ constant), why is it that we once again approach the case of $Q_L$ equals zero?
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