* Temperature and Kinetic Energy: You're right that temperature is directly proportional to the average kinetic energy of the particles in a substance. So, if you double the temperature of a gas, you'll double the average kinetic energy of its particles.

* The Problem with Steam: The issue is that steam is already in its gaseous phase. While heating it from 100°C to 200°C will increase its temperature and average kinetic energy, it's not a simple doubling.

* Heat Capacity and Phase Changes: The relationship between temperature change and kinetic energy change is influenced by the substance's heat capacity. Steam has a specific heat capacity, meaning it takes a certain amount of energy to raise its temperature by a specific amount. This heat capacity is not constant and can vary with temperature.

* Further Complication: Phase Changes: You need to consider that the temperature range of 100°C to 200°C for steam also includes the potential for phase changes. If you are heating steam from 100°C to 200°C, you are potentially increasing the energy beyond just kinetic energy. You might be adding energy that goes towards increasing the potential energy of the molecules, leading to a change in the intermolecular distances or even a transition to a plasma state at very high temperatures.

In summary:

While doubling the temperature of a gas generally leads to doubling the average kinetic energy of its particles, this doesn't always apply to steam due to its heat capacity and the possibility of phase changes.