Kinetic Interpretation Of Pressure

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Nitrogen gas of density 1.25 kg/m^3 has molecules whose root-mean-square speed is 500 m/s; calculate the pressure exerted by this gas.

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Expressing gas pressure in terms of molecular motion, the kinetic theory gives $P=\frac{1}{3}ho\, v_{rms}^{2}$, where $ho$ is the mass density and $v_{rms}$ is the root-mean-square speed. This follows from averaging the momentum that molecules transfer to the walls during elastic collisions, with the factor $\frac{1}{3}$ coming from the equal sharing of mean-square speed among the three spatial directions. Substituting $ho=1.25$ kg/m	extsuperscript{3} and $v_{rms}=500$ m/s gives $P=\frac{1}{3}	imes1.25	imes(500)^{2}=\frac{1}{3}	imes1.25	imes2.5	imes10^{5}\approx1.04	imes10^{5}$ Pa. The value $3.13	imes10^{5}$ Pa omits the factor $1/3$. The value $0.52	imes10^{5}$ Pa mistakenly uses $\frac{1}{6}$ instead of $\frac{1}{3}$. The value $2.08	imes10^{5}$ Pa doubles the correct result by misreading the density. This is the NCERT kinetic interpretation of pressure linking the microscopic and macroscopic descriptions, and it shows pressure rises with both density and the square of molecular speed. As a plausibility check, the result is close to one atmosphere ($1.013	imes10^{5}$ Pa), which is exactly what we expect for a gas at ordinary laboratory density and molecular speed.

Kinetic Interpretation Of Pressure

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