Final answer:
Based on Charles's Law, the volume of a gas is directly proportional to temperature. Setting up a proportion reveals that the original volume should be 7 liters when considering the temperature increase and volume increase provided, which is not one of the provided options.
Step-by-step explanation:
According to Charles's Law, the volume of a gas is directly proportional to its temperature when pressure is held constant. In the scenario where the balloon increased in size by 0.5 liters upon a temperature increase from 280 Kelvin to 300 Kelvin, we can set up a proportion to find the original volume of the balloon at the fair.
Let V1 be the original volume of the balloon at 280 K and V2 be the increased volume at 300 K. Since V2 = V1 + 0.5 L and Charles's Law is given by V1/T1 = V2/T2, we have V1/280 K = (V1 + 0.5 L)/300 K.
By solving for V1, we get V1 × 300 K = V1 × 280 K + 140 L. Simplifying, we find that 20 K × V1 = 140 L, and thus V1 = 140 L / 20 K, which results in V1 = 7 L.
However, this is not one of the options provided, which indicates a possible mistake in the given choices or in the calculation. Re-examining the calculations shows that the correct calculation should result in V1 = 7 liters, which suggests an error in the question since none of the answer options match. A proper answer based on the calculation is 'None of the above'.