We can use the combined gas law equation to solve this problem:
(P₁V₁)/T₁ = (P₂V₂)/T₂
Where P is pressure, V is volume and T is temperature.
Assuming the pressure stays constant, we can rewrite the equation as:
(V₁/T₁) = (V₂/T₂)
Substituting the given values, we get:
(V₁/303 K) = (V₂/271 K)
Solving for V₂, we get:
V₂ = (V₁/303 K) x 271 K
V₂ = (18.2 L/303 K) x 271 K
V₂ = 16.28 L
Therefore, the balloon will occupy a volume of 16.28 L at 271 K.