Physics Part Ii Chapter 13 Kinetic Theory

State Boyle's Law?

Calculate the degrees of freedom for monoatomic, diatomic and triatomic gas?

what do you mean by mean free path and write the formula?

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

• 650  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

• kinetic energy changes but the momentum is 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

• 1.54

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

• 4/3

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

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_A, K_B and K_C, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then

• K_A < K_B < K_C

• K_A > K_B > K_C

• K_B > K_A > K_C

• K_B < K_A < K_C

A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio Kt: (K_t+ K_r) for the sphere is

• 7:10

• 5:7

• 2:5

• 10:7

A graph between pressure P (along with the y-axis) and absolute temperature, T (along with the x-axis) for equal moles of two gases have been drawn. Given that the volume of the second gas is more than the volume of first gas. Which of the following statement is correct?

• Slope of gas 1 is less than gas 2

• Slope og gas 1 is more than gas 2

• Both have some slopes

• None of the above

A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity u = 0.5 mls. The kinetic energy of the sphere is

• 0.1 J

• 0.3 J

• 0.5 J

• 0.42 J

Pressure of an ideal gas is increased by keeping temperature constant. What is the effect on kinetic energy of molecules?

• increase

• Decrease

• No change

• Can't be determined

Pressure of an ideal gas is increased by keeping temperature constant. What is effect on kinetic energy of molecules?

• Increase

• Decrease

• No change

• Cannot be determined

For a gas $\frac{\mathrm{R}}{{\mathrm{C}}_{\mathrm{v}}}$= 0.67. This gas is made up of molecules which are

• monoatomic

• polyatomic

• mixture of diatomic and polyatomic molecules

• diatomic

A horizontal tube of length l closed at both ends, contains an ideal gas of molecular weight M. The tube is rotated at a constant angular velocity ω about a vertical axis passing through an end. Assuming the temperature to be uniform and constant. If p₁ and p₂ denote the pressure at free and the fixed end respectively, then choose the correct relation

• $\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1} = {\mathrm{e}}^{\frac{{\mathrm{M\omega }}^2 {\mathrm{l}}^2}{2^{\mathrm{RT}}}}$

• $\frac{{\mathrm{p}}_1}{{\mathrm{p}}_2} = {\mathrm{e}}^{\frac{\mathrm{M} {\mathrm{\omega l}}^2}{\mathrm{RT}}}$

• $\frac{{\mathrm{p}}_1}{{\mathrm{p}}_2} = {\mathrm{e}}^{\frac{\mathrm{\omega } \mathrm{l} \mathrm{M}}{3\mathrm{RT}}}$

• $\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1} = {\mathrm{e}}^{\frac{{\mathrm{M}}^{2 }{\mathrm{\omega }}^{2 }{\mathrm{l}}^2}{3\mathrm{RT}}}$

Two rigid boxes containing different ideal gases are placed on table. Box A contains one mole of nitrogen at temperature T₀ , while box B contains 1 mole of helium at temperature 7/3 T₀. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes) then the final temperature of gases, T_f in terms of T₀ is

• $\frac{2\hspace{0.17em}{\mathrm{T}}_0}{5}$

• $\frac{3 {\mathrm{T}}_0}{5}$

• $\frac{5 {\mathrm{T}}_0}{3}$

• $\frac{9 {\mathrm{T}}_0}{7}$

The temperature of the cold junction of thermocouple is 0°C and the temperature of hot junction is T^o C. The emf is E = 16T - 0.04T² µV. The inversion temperature T_f is

• 300^o C

• 200^o C

• 500^o C

• 400^o C

The temperature of a gas is raised from 27° C to 927° C. The root mean square speed

• gets halved

• gets doubled

• is $\left(\sqrt{\frac{927}{27}}\right)$ times the earlier value

• remains the same

Two different isotherms representing the relationship between pressure p and volume V at a given temperature of the same ideal gas are shown for masses m₁ and m₂ , then

• Nothing can be predicted

• m₁ < m₂

• m₁ = m₂

• m₁ > m₂

1 mole of H₂ gas is contained in a box of volume V  = 1.00 m³  at  T = 300 K. The gas is heated to a temperature of  T = 3000 K  and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)

• same as the pressure initially

• 2 times the pressure initially

• 10 times the pressure initially

• 20 times the pressure initially