No, the kinetic energy of a gas does not double when the temperature is doubled with constant pressure and volume. According to the ideal gas law, the relationship between temperature (T), pressure (P), and volume (V) is given by:
PV = nRT
Where: P = pressure V = volume n = number of moles of gas R = ideal gas constant T = temperature
From this equation, we can see that temperature (T) is directly proportional to the product of pressure (P) and volume (V), given a constant number of moles (n) and the ideal gas constant (R).
The kinetic energy (KE) of a gas is related to temperature through the equation:
KE = (3/2)kT
Where: KE = kinetic energy k = Boltzmann constant T = temperature
As we can see, the kinetic energy (KE) is directly proportional to the temperature (T). So, if the temperature is doubled, the kinetic energy of the gas will also double.