Equipartition Specific Heats & Mean Free Path — Practice Questions

Free NEET Physics multiple-choice questions on Equipartition Specific Heats & Mean Free Path. Attempt each question and reveal the answer with a full explanation.

The mean free path of a gas molecule depends on the molecular diameter d and number density n as: 1 nd 2 1 n 2d 1 nd nd 2 What is the value of the ratio of specific heats for a gas with 6 degrees of freedom? 1.33 1.40 1.67 1.25 The mean free path of molecules of a gas (radius r ) is inversely proportional to: r 2 r r r 3 If the mean free path of a gas molecule is , and the diameter of the molecule is d , then the mean free path is proportional to: 1/d 2 1/d d 2 d The mean free path of a gas molecule is l . If the number density of molecules is increased to 4 times, the mean free path becomes: l/4 4l 2l l/2 The diameter of a gas molecule is d . The mean free path of the gas molecules is proportional to: d -2 d -1 d d 2 The mean free path of a gas molecule is related to the number density n as: 1/n n n 2 n A rigid diatomic molecule has f degrees of freedom. The ratio of specific heat at constant pressure to specific heat at constant volume ( ) is: 1 + 2 f 1 + f 2 f 2 f+1 f At very high temperatures, a diatomic molecule like H 2 has how many degrees of freedom? 7 5 3 6 The mean free path for a gas, with molecular diameter d and number density n can be expressed as: 1 2 n d 2 1 2 n 2 d 2 1 2 n d 1 n d 2 The ratio of the average translational kinetic energy of He atom to that of H 2 molecule at the same temperature is: 1:1 2:1 1:2 4:1 The ratio of average kinetic energy of a H 2 molecule to that of a CH 4 molecule at the same temperature is: 1:1 1:8 2:16 1:16 The number of degrees of freedom for a linear triatomic molecule like CO 2 (at room temperature) is: 5 6 3 7 If C P and C V denote the specific heats of unit mass of nitrogen at constant pressure and constant volume respectively, then which of the following is correct? C P - C V = R/28 C P - C V = R/14 C P - C V = R C P - C V = 28R A gas mixture contains 2 moles of He and 1 mole of H 2 . The ratio of specific heats = C P/C V for the mixture is: 1.58 1.67 1.40 1.33 If the mean free path of a gas is at pressure P , what will be the mean free path if the pressure is increased to 4P at constant temperature? /4 4 /2 2 A mixture of 2 moles of Helium ( He ) and 4 moles of Nitrogen ( N 2 ) is kept at a constant temperature. The ratio of the average translational kinetic energy per molecule of He to that of N 2 is: 1:1 1:7 2:7 4:1 The molar specific heat at constant volume C V for a mixture of 1 mole of a monoatomic gas and 1 mole of a diatomic gas (rigid) is: 2R 3R 1.5R 2.5R A rigid triatomic linear molecule has how many degrees of freedom at room temperature? 5 3 6 7 The number of degrees of freedom of a diatomic gas molecule at very high temperature (where vibrational modes are active) is: 7 3 5 6 The mean free path of a gas molecule depends on the molecular diameter d as: d -2 d -1 d 2 d A cylinder contains 1 mole of Neon gas (monoatomic) and 1 mole of Oxygen gas (diatomic). The ratio of specific heats for the mixture is: 1.5 1.4 1.67 1.33 If the collision frequency of a gas molecule is , the mean time between collisions (relaxation time) is: 1/ 2 A diatomic gas molecule has translational, rotational and vibrational degrees of freedom. The ratio of C P/C V is: 9/7 7/5 5/3 1.4 If the mean free path of a molecule is at temperature 27 C , what will be the mean free path at 327 C if the pressure is kept constant? 2 2 2 4 If the volume of an ideal gas is reduced to half its original value at constant temperature, the mean free path of the molecules will: Be halved Double Remain the same Quadruple If both the pressure and the absolute temperature of a gas are doubled, the mean free path of the gas molecules will: Remain unchanged Become double Become half Become four times If the diameter of gas molecules is doubled, the mean free path will: Decrease by a factor of 4 Decrease by a factor of 2 Increase by a factor of 4 Remain the same The mean free path of molecules of a gas, with diameter d and number density n , is given by = 1 2 n d 2 . If the pressure is kept constant, how does vary with absolute temperature T ? T T 1/T T 2 If the volume of a gas is decreased by 10 % at constant temperature, the percentage increase in its pressure will be approximately: 11.1 % 10 % 9 % 20 % If the mean free path of a gas molecule is 2 10 -7 m at a pressure of 10 5 Pa , what will be its mean free path at 0.5 10 5 Pa pressure if temperature remains constant? 4 10 -7 m 1 10 -7 m 2 10 -7 m 8 10 -7 m If the mean free path of a molecule is at pressure P , what is its value at pressure 2P if the temperature is also doubled? 2 /2 4 The mean free path of a gas molecule at a pressure P and temperature T is . If the temperature is kept constant and the pressure is reduced to P/2 , the new mean free path will be: 2 /2 4 2 A cylinder contains a mixture of 1 mole of Helium and 1 mole of Argon. The average kinetic energy per molecule of the mixture at temperature T is: 3 2 k B T 3k B T 1 2 k B T 5 2 k B T If the mean free path of a gas is l at 27 C , its mean free path at 127 C at constant pressure is: 4l/3 3l/4 16l/9 2l If the volume of an ideal gas is doubled at constant temperature, the collision frequency of molecules with the walls of the container will: Decrease Increase Remain same Become zero The mean free path of a gas molecule is . If the pressure of the gas is kept constant while the absolute temperature is doubled, the new mean free path will be: 2 /2 2 Which of the following factors does not affect the mean free path of a gas molecule? Mass of the molecule Molecular diameter Number density Pressure The mean free path of a gas molecule depends on the absolute temperature T at constant volume as: T 0 T T 1/T A molecule of a gas has a diameter of 2 10 -10 m . Calculate the order of magnitude of the mean free path if the number density is 10 25 m -3 . 10 -7 m 10 -9 m 10 -5 m 10 -11 m The mean free path of a gas molecule depends on the absolute temperature T and pressure P as: T P P T PT 1 PT The mean collision time between molecules of an ideal gas depends on the absolute temperature T as: 1/ T T T 1/T The mean free path of molecules in an ideal gas A is half that of another ideal gas B . The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B . If number densities of the gases A and B are n A and n B , respectively, the correct option is: n A=n B n A=2n B n A= 1 4 n B n A= 1 2 n B An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and f number of vibrational modes. If the ratio of heat capacities C P/C V of the gas is 8/7 , then the value of f is: 4 3 2 1 The molar specific heat at constant pressure C P of a gas is 5R/2 . The number of degrees of freedom f is: 3 5 6 2 The molar heat capacity of a certain gas is found to be C V = 3R . The ratio of specific heats is: 1.33 1.40 1.67 1.25 The average distance traveled by a gas molecule between two successive collisions is called: Mean free path Mean velocity Collision diameter Relaxation time A rigid molecule consists of 3 atoms at the vertices of an equilateral triangle. Neglecting vibrational modes, the number of degrees of freedom for this molecule is: 6 5 3 7 The molar heat capacity at constant pressure ( C P ) for a monoatomic gas is: 5 2 R 3 2 R 7 2 R R 2