JEE Main · PhysicsEasy

$According to the kinetic theory of gases, the pressure P exerted by an ideal gas of density ρ and mean square speed v^{2} is given by which expression?$

A. $\frac{1}{3} ρ \overline{v^{2}}$
B. $\frac{2}{3} ρ \overline{v^{2}}$
C. $\frac{1}{2} ρ \overline{v^{2}}$
D. $ρ \overline{v^{2}}$

Show correct answer & step-by-step solution

Correct answer: A — $\frac{1}{3} ρ \overline{v^{2}}$

Solution

$The kinetic theory pressure formula is P = \frac{1}{3} \frac{N m}{V} \overline{v^{2}} .$
$The density ρ is defined as \frac{N m}{V} .$
$Substituting ρ into the pressure equation gives P = \frac{1}{3} ρ \overline{v^{2}} .$
$Hence the answer is (A).$

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