The parameter that remains the same for molecules of all gases at a given temperature is :

We need to identify which parameter remains the same for molecules of all gases at a given temperature. According to the kinetic theory of gases, the average kinetic energy of a gas molecule depends only on the absolute temperature: $$ \overline{KE} = \frac{3}{2}k_B T $$. This expression is independent of the mass or nature of the gas.

The average speed, given by $$\bar{v} = \sqrt{\frac{8k_BT}{\pi m}}$$, depends on the molecular mass $$m$$, so different gases have different speeds at the same temperature. The average momentum, calculated as $$m\bar{v} = m\sqrt{\frac{8k_BT}{\pi m}} = \sqrt{\frac{8mk_BT}{\pi}}$$, also depends on $$m$$ and therefore varies between gases. Mass itself obviously differs for different gas molecules. In contrast, the average kinetic energy, given by $$\frac{3}{2}k_BT$$, depends only on temperature and is thus the same for all gases at a given temperature, regardless of their mass or chemical identity.

The correct answer is Option (1): kinetic energy.