Kinetic Theory

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

Degree of freedom for polyatomic gas

• ≥ 4

• ≥5

• ≥6

• ≥7

Assertion: Vibrational energy of diatomic molecule corresponding to each degree of  freedom is  k_B T.

Reason:  For every molecule, vibrational degree of freedom is 2.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.