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A liter of water IS a kilogram. Since oil is lighter, it's about .625 kg
Yes, it is.
1 litre of furnace oil will have a mass of 0.998 kg. The temperature of the oil is irrelevant.
1020m3/kg
Oil is slightly less dense than water and a litre of water weighs a kilogram. It would be less than a kilogram, but by how much depends on the type of oil.