Kinetic Interpretation Of Pressure

Central to this problem is the kinetic theory expression for pressure given in NCERT Class 11, Chapter 13 (Kinetic Theory), which can be written as $P=\frac{1}{3}\rho \overline{v^2}$, where $\rho$ is the mass density of the gas and $\overline{v^2}$ is the mean square molecular speed. Pressure is therefore directly proportional to the product of density and mean square speed. If the density is doubled, that alone doubles the pressure, and if the mean square speed is also doubled, that contributes another factor of two. Multiplying the two independent factors gives $2\times 2=4$, so the pressure becomes four times its original value. The option claiming pressure only doubles accounts for just one of the two changes. The option that pressure is unchanged ignores both effects entirely. The option that pressure halves reverses the proportionality. This form is simply the standard pressure relation rewritten using density, since the mass per unit volume already folds together molecular mass and number density into a single measurable quantity. A plausibility check confirms the outcome: since $P$ scales linearly with each quantity independently, doubling both must multiply the pressure by their product, and a fourfold rise is dimensionally and physically consistent with a denser, faster-moving gas.