= Solution
Extraction <energy> is $6000\ \mathrm{kg}\times2500\ \mathrm{kWh\,kg^{-1}}=15$ GWh per year. A continuously operating 2 GW electrical plant generates 17.5 TWh per year, so lithium extraction consumes about $\boxed{0.086\%}$ of its output under the stated estimate. This is energetically favorable even before claiming anything about capital costs or extraction feasibility.
For an ocean <mass> about $1.4\times10^{21}$ kg, concentration 0.17 ppm implies about $2.4\times10^{14}$ kg lithium. At the specified consumption/output ratio, a hypothetical 20 TW electric world would use $6\times10^7$ kg annually, giving roughly $4\times10^6$ years. For 3 TW the corresponding scale is $3\times10^7$ years. State the assumed demand: “power the world” does not uniquely specify electric demand versus primary-energy use. These are inventory quotients ignoring growth, accessible fraction, ecological constraints and processing throughput.
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