Answer
(a) Less than
(b) III
Work Step by Step
(a) We know that the temperature of an ideal gas is doubled from $100C^{\circ}$ to $200C^{\circ}$. Doubling the Celsius temperature from $100C^{\circ}$ to $200C^{\circ}$ changes the Kelvin temperature from $373.15K=(100+273.15)$ to $473.15K=(200+273.15)$ and this increase is less than a factor of $2$.
(b) We know that the best explanation is option (III) -- that is, doubling the Celsius temperature form $100C^{\circ}$ to $200C^{\circ}$ changes the Kelvin temperature from $373.15K$ to $473.15K$, which is an increase of less than a factor of 2.
