Kinetic Theory

Cp and Cv are specific heats at constant pressure and constant volume respectively. It is observed that
Cp – Cv = a for hydrogen gas
Cp – Cv = b for nitrogen gas
The correct relationship between a and b is

• a = 14 b

• a = 28 b

• a = 1/14b

• a = 1/14b

The speed of sound in oxygen (O₂) at a certain temperature is 460 ms⁻¹. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

• 1420 ms⁻¹

• 550 ms⁻¹

• 375 ms⁻¹

• 375 ms⁻¹

A charged particle moves through a magnetic field perpendicular to its direction. Then

• the momentum changes but the kinetic energy is constant

• both momentum and kinetic energy of the particle are not constant

• both, momentum and kinetic energy of the particle are constant

• both, momentum and kinetic energy of the particle are constant

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio c_p/c_v of the mixture is

• 1.59

• 1.62

• 1.4

• 1.4

One mole of ideal monoatomic gas (γ = 5/30) is mixed with one mole of diatomic gas(γ = 7/5). What is γ for the mixture? γ denotes the ratio of specific heat at constant pressure, to that at constant volume.

• 3/2

• 23/15

• 35/23

• 35/23

The mass of a hydrogen molecule is 3.32 x 10^-27 kg. If 10²³ hydrogen molecules strike, per second, a fixed wall of area 2cm² at an angle of 45° to the normal, and rebound elastically with a speed of 10³ m/s, then the pressure on the wall is nearly:

• 4.70 x 10² N/m²

• 2.35 x 10³ N /m²

• 4.70 x 10³ N/m²

• 2.35 x 10² N /m²

A particle is moving in a circular path of radius a under the action of an attractive potential U = -k/2r². its total energy is:

• $-\frac{3}{2}\frac{k}{a^2}$

• $\frac{-k}{4a^2}$

• $\frac{k}{2a^2}$

• zero

For an ideal gas, the specific heat at constant pressure C_p is greater than the specific heat at constant volume C_v. This is because

• There is a finite work done by the gas on its environment when its temperature is increased while the pressure remains constant

• There is a finite work done by the gas on its environment when its pressure is increased while the volume remains constant

• There is a finite work done by the gas on its environment when its pressure is increased while the temperature remains constant

• The pressure of the gas remains constant when its temperature remains constant

The difference between the specific heats of a gas is 4150 Jkg^-1 K^-1. If the ratio of specific heat is 1.4, then the specific heat at constant volume of the gas (in J kg^-1 K^-1) is

• 1037.5

• 2037.5

• 8300

• 10375

For a monoatomic gas, the molar specific heat at constant pressure divided by the molar gas constant R is equal to

• 2.5

• 1.5

• 5.0

• 3.5