this post was submitted on 22 Nov 2023
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Your criticism is accurate in terms of thermodynamic efficiency, where we have to account for all energy entering and leaving the system.
But we are talking about economic efficiency, where we only count the energy passing through the wires. In the context of a thread on heat pump water heaters, the distinction is important: heat pumps use a small amount of electrical energy to scavenge a large amount of thermal energy from the environment. Thermodynamically, we have to count that energy; economically, that energy is "free" for the taking.
I have never heard of a "heat pump dishwasher"; the dishwasher is using a resistive heat source, and not the "free" energy from the environment.
When you understand why heat pumps are commonly 200% to 300% economically efficient (without breaking the laws of thermodynamics or becoming perpetual motion machines), you will understand why heating cold water in a dishwasher can be less efficient than heating it in a water heater.