At which of the following temperature would the molecules of a gas have twice the average kinetic energy they have at 20°C

The correct option is 313° C.

The average kinetic energy of the molecules of a gas is directly proportional to its absolute temperature measured in Kelvin. This relationship is defined as:

$KE\propto T$

First, we convert the initial temperature from Celsius to Kelvin:

$T_1=20+273=293\text{K}$

For the molecules to have twice the average kinetic energy, the absolute temperature must also double:

$T_2=2\times T_1$

Substituting the initial temperature value:

$T_2=2\times 293\text{K}=586\text{K}$

Finally, we convert the final temperature back into Celsius:

$T_2\text{(°C)}=586-273=313\text{°C}$