Download App

Kinetic Theory — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsKinetic Theory5 Marks
Question
State the assumptions of the kinetic theory of gases. The density of carbon dioxide gas at $0^{\circ} \mathrm{C}$ and at a pressure of $1.0 \times 10^5$ newton/ metre ${ }^2$ is $1.98 \mathrm{~kg} / \mathrm{m}^3$. Find the root mean square velocity of its molecules at $0^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$. Pressure is constant.
✓

Answer

The entire structure of the kinetic theory of gases is based on the following assumptions which were first stated by Classius.
  1. A gas consists of a very large number of molecules (of the order of Avogadro's number, $10^{23}$), which are perfect elastic spheres. They are identical in all respects for a given gas and are different for different gases.
  2. The molecules of a gas are in a state of incessant random motion. They move in all directions with different speeds, (of the order of 500m/s) and obey Newton's laws of motion.
  3. The size of the gas molecules is very small as compared to the distance between them. If typical size of a molecule is $2\mathring{\text{A}},$ average distance between the molecules is $\geq20\mathring{\text{A}}.$ Hence volume occupied by the molecules is negligible in comparison to the volume of the gas.
  4. The molecules do not exert any force of attraction or repulsion on each other, except during collision.
  5. The collisions of the molecules with themselves and with the walls of the vessel are perfectly elastic. As such the momentum and the kinetic energy of the molecules are conserved during collisions, though their velocities change.
  6. There is no concentration of the molecules at any point inside the container i.e., molecular density is uniform throughout the gas.
  7. A molecule moves along a straight line between two successive collisions and the average straight distance covered between two successive collisions is called the mean free path of the molecules.
  8. The collisions are almost instantaneous, i.e., the time of collision of two molecules is negligible as compared to time interval between two successive collisions.
Numerical: We know that$\text{P}=\frac{1}{3}\rho\text{v}^2$
$\therefore\text{v}_{\text{rms}}=\sqrt{\big(\text{v}^2\big)}=\sqrt{\Big(\frac{3\text{P}}{\rho}\Big)}$
Given that $\text{P}=1.0\times10^5\text{newton/metre}^2$$\rho=1.98\text{kg/metre}^3$
$\therefore\text{v}_{\text{rms}}=\sqrt{\Big[\Big\{\frac{3\times(1.0\times10^5)}{1.98}\Big\}\Big]}$
$=389\text{metre/sec}.$
From kinetic theory of gases, the root mean square speed is directly proportional to the square root of absolute temperature$\text{v}_{\text{rms}}\propto\sqrt{\text{T}}$
$\therefore\frac{(\text{v}_{\text{rms}})_{30}}{(\text{v}_{\text{rms}})_0}=\sqrt{\Big[\Big(\frac{273+30}{273+0}\Big)\Big]}$
$=\sqrt{\Big[\Big(\frac{303}{273}\Big)\Big]}=1.053$
$(\text{v}_{\text{rms}})_{30}=(\text{v}_{\text{rms}})_0\times1.053$
$=389\times10.53=410\text{ metre/sec}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Kinetic Theory→Kinetic Theory — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A particle A having a charge of $2.0 \times 10^{-6} \mathrm{C}$ and a mass of 100 g is placed at the bottom of a smooth inclined plane of inclination $30^{\circ}$. Where should another particle $B$, having same charge and mass, be placed on the incline so that it may remain in equilibrium?
→
The P-V diagram for a cyclic process is a triangle ABC drawn in order. The co-ordinates of A, B, C are $(4,1),(2,4)$ and $(2,1)$. The co-ordinates are in the order ( $\mathrm{P}-\mathrm{V}$ ). Pressure is in $\mathrm{Nm}^{-2}$ and volume is in litre. Calculate work done during the process from A to $\mathrm{B}, \mathrm{B}$ to C and C to A . Also, calculate work done in the complete cycle.
→
Gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter 14). Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s.
→
Define impulse and establish its relation with momentum change. Explain the importance of impulse. Or Define impulse of a force and prove that the impulse of a force on a body is equal to change in momentum. Or State the momentum impulse theorem. Explain its physical importance with examples.
→
One end of a $10cm$ long silk thread is fixed to a large vertical surface of a charged nonconducting plate and the other end is fastened to a small ball having a mass of $10g$ and a charge of $4.0 \times 10^{-5}C$. In equilibrium, the thread makes an angle of $60°$ with the vertical. Find the surface charge density on the plate.
→
A and B are two particles having the same mass 'm'. A is moving along x-axis with a speed of $10ms^{-1}$ and B is at rest. After undergoing a perfectly elastic collision with B, particle A get scattered through an angle of $30°$. What is the direction of the motion of B and the speeds of A and B after the collision?
→
A geostationary satellite is orbiting the earth at a height of 6R above the surface of earth. Here R is the radius of the earth. What is the time period of another satellite at a height of 2.5R from the surface of the earth?
→
A metallic rod of length $1m$ is rigidly clamped at its midpoint. Longitudinal stationary waves are set up in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is $2 \times 10^{-6}m$. Write the equation of motion at a point $2cm$ from the midpoint and those of the constituent waves in the rod. (Young's modulus = $2 \times 10^{11}Nm^{-2}$ and density = $8000kg m^{-3}$)
→
Explain the difference between static friction, kinetic friction and rolling friction.
→
A 1kg block is executing simple harmonic motion of amplitude 0.1m on a smooth horizontal surface under the restoring force of a spring of spring constant 100N/m. A block of mass 3kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, find the frequency and the amplitude of the motion.
→