Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEETPhysicsKinetic Theory of Gases

Consider a linear polyatomic gas having f active vibrational modes. If is the ratio of specific heat capacities ( C_p C_v ) for this gas, the correct expression for the number of vibrational modes f in terms of is:

Options

  1. A4 - 3 - 1
  2. B7 - 5 2( - 1)
  3. C7 - 5 - 1
  4. D5 - 3 2( - 1)

Correct answer

B. 7 - 5 2( - 1)

Step-by-step solution

For a linear polyatomic gas, there are 3 translational degrees of freedom and 2 rotational degrees of freedom. Let the number of active vibrational modes be f . Each vibrational mode contributes R to the molar heat capacity at constant volume ( C_v ). The total C_v is given by: C_v = 3 2 R + 2 2 R + fR = 5 2 R + fR = ( 5 + 2f 2 )R The molar heat capacity at constant pressure ( C_p ) is: C_p = C_v + R = ( 5 + 2f 2 )R + R = ( 7 + 2f 2 )R The ratio of specific heats is: = C_p C_v = 7 + 2f 5 + 2f Rearranging to solve f

Practice Kinetic Theory of Gases on Quantrex Academy →

More from Kinetic Theory of Gases

Pressure exerted by an ideal gas on the walls of the container is equal to a) mean kinetic energy per unit volume. b) half of mean kinetic energy per unit volume. c) one-third of m 2026Two litre of an ideal gas at 42^ C is heated at a constant pressure to 357^ C . Then the final volume is 2026The temperature at which the mean kinetic energy of the molecules of gas is ( 1 4 )^ th of the mean kinetic energy of its molecules at 147^ C is 2026There are two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and volume are P_A , T_A and V in the vessel A and P_B , T_B and V in vessel B. The 2026The pressure P , volume V and temperature T of a gas in the jar A and the other gas in the jar B is at pressure 2P , volume V/4 and temperature 2T , then the ratio of the number of 2026The temperature at which the root-mean-square speed of carbon dioxide molecules becomes just sufficient for escaping Earth's atmosphere is approximately (Mass of carbon dioxide mol 2026If the ratio of specific heat of gas = C_p C_v , then the value of C_p in terms of and gas constant R is 2026The internal energy per molecule for a diatomic (non-rigid) gas is (where k_B is Boltzmann's constant and T is absolute temperature). 2026 Full Kinetic Theory of Gases list All NEET PYQs