Question

On the basis of the kinetic theory of gases, derive an expression for the pressure exerted by a gas.​

Answer 1

Answer:

But by assumptions of the kinetic theory of gases the average kinetic energy of a molecule is constant at a constant temperature. Thus the right-hand side of the equation is constant. Thus, PV = constant i.e. P ∝ 1 / V . This is Boyle's Law.

Explanation:

hope it helps you

Answer 2

$P = \frac{1}{3}p (c)^{2}$ is called the kinetic energy per unit volume of the gas.

Explanation:

• Consider a cubical vessel (of side l) with walls perfectly elastic as in the figure.  Let the vessel have one gram molecule of a gas with its molecules in random motion.
• Consider a molecule (mass m) moving with a velocity c, that can be resolved into three components u, v, and w in the direction of the edges of the cube along x, y ,z axes.
• $c^{2} = u^{2}+ v^{2} +w^{2}$
• Let us consider two faces of the cube, say P and Q, normal to x−axis. When the molecule collides with the side Q with a velocity u, it rebounds with −u, while its other components remain unchanged.
• Change in momentum of the molecule due to this collision =−2mu, which is imparted to the wall per collision.
• This equation gives the pressure exerted by the gas on the walls of the vessel .It has the same value in any direction because the molecules have no preference for direction.
• We have $p = \frac{mN}{v}$,
• Therefore, =$P= \frac{1}{3}p (c)^{2}$.