According to Charles's Law, volume of an ideal gas is directly proportional to temperature at constant pressure,
V₁/ T₁ = V₂/T₂
where V₁ and V₂ are the initial and final volume respectively and T₁ and T₂ are initial and final temperature respectively.
Given, initial volume of balloon = 200 L
Initial temperature of balloon = 100 K
Final temperature of balloon = 400 K
Plugging the given data in Charles’s law we can calculate the final or new volume of the balloon,
V₂ = V₁/T₁ x T₂
= (200 L/ 100 K) x 400 K = 800 L