Concept:Pressure is generated on container walls strictly by the linear momentum transfer of molecules impacting and bouncing off the walls.
Formula:$$ P = \frac{2}{3} \left( \frac{N}{V} \right) \langle K.E._{\text{trans}} \rangle $$
Solution:- The equation states that Pressure (\( P \)) depends on the number density of the gas and the average kinetic energy of linear motion.
- Linear motion corresponds to "translational" kinetic energy.
- Therefore, pressure is directly proportional to the average translational kinetic energy.
Why other options are incorrect:Vibrational and rotational kinetic energies contribute to the gas's internal heat capacity but do not contribute to momentum transfer (pressure) against the walls. Physical size is assumed to be zero in ideal gases.
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