Final answer:
The total kinetic energy of the gas increases as the temperature doubles from T to 2T, despite some moles converting from diatomic to monatomic form with fewer degrees of freedom.
Step-by-step explanation:
The question asks what is the change in the total kinetic energy of a gas when N1 moles of a diatomic ideal gas is heated from temperature T to 2T and during the process N2 moles of the gas become monatomic.
For an ideal gas, the kinetic energy of the molecules is directly proportional to the temperature. In the given scenario, because the temperature is doubled from T to 2T, the kinetic energy of the remaining diatomic molecules will also double. Additionally, for monatomic gases, as they have fewer degrees of freedom than diatomic gases, each mole of diatomic gas which becomes monatomic loses some energy. However, because the temperature is doubled, the kinetic energy of the converted monatomic moles will also be increased, albeit not as much as if they had remained diatomic. The net effect is a complex interplay of the increase in temperature and the change in degrees of freedom, but generally, there will be an increase in the total kinetic energy of the gas.
Therefore, the correct answer to the given question is (a) Increased.