If I built a computer as heavy as my first Thinkpad using a modern processor and filling the rest of the machine with batteries, I'd have a month of continuous use ;-)
Up to 100 Wh / battery, up to 160 Wh with airline approval. All laptops I know of have a 100 Wh battery at most. Macbook pro's used to have that size, but the latest gen has a smaller capacity. You can carry spare batteries, as long as they are for "personal use".