Suppose the absolute temperature of an ideal gas is doubled from 100 K to 200 K.

(a) Does the average speed of the molecules in this gas increase by a factor that is greater than, less than, or equal to 2?

(b) Choose the best explanation from among the following:

I. Doubling the Kelvin temperature doubles the average kinetic energy, but this implies an increase in the average speed by a factor of (2 = 1.414....., which is less than 2.

II. The Kelvin temperature is the one we use in the ideal-gas law, and therefore doubling it also doubles the average speed of the molecules.

III. The change in average speed depends on the mass of the molecules in the gas, and hence doubling the Kelvin temperature generally results in an increase in speed that is greater than a factor of 2?