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Your question is not very specific, as 'oil' is a very broad term.

Crude oil is never burned straight, it is always processed. I will assume gasoline is what is being used.

Gasoline produces 36.6 kWh of power per one US gallon. Therefore:

(36.6 kWh/ 1 gal) = ( 1 kWh/ X gal)

(1 * 1) / 36.6 = X

X ~= 0.0273 gallons

So it takes about 0.0273 gallons of gasoline to produce one kWh of power.

Some digging on various sites tells me that about 55% of crude oil (per gallon) gets processed into gasoline. So we take our number of gallons and multiply it by 155%:

0.0273 gal/gas * 1.55 ~= 0.0423 gal/oil

So it takes 0.0423 gallons of oil to generate one kWh of power.

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