Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20265 April 2026Morning ShiftPhysicsKinetic Theory of GasesActual

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Statement I: Change in internal energy of a system containing n mole of ideal gas can be written as U = n C_v (T_f - T_i) = nR - 1 (T_f - T_i) , where = C_p C_v , T_i = initial temperature, T_f = final temperature. Statement II: Relation between degree of freedom f and (= C_p/C_v) is ( = 1 + 2 f ) Choose the correct a

Options

  1. ABoth A and R are true and R is the correct explanation of A
  2. BBoth A and R are true but R is NOT the correct explanation of A
  3. CA is true but R is false
  4. DA is false but R is true

Correct answer

B. Both A and R are true but R is NOT the correct explanation of A

Step-by-step solution

Statement I is true because for an ideal gas, the change in internal energy is given by U = n C_v T . Using Mayer's relation C_p - C_v = R and the ratio of specific heats = C_p C_v , we can write C_v = R - 1 . Substituting this, we get U = nR - 1 (T_f - T_i) . Statement II is true because according to the law of equipartition of energy, the molar heat capacity at constant volume is C_v = f 2 R and at constant pressure is C_p = ( f 2 + 1 )R . Therefore, = C_p C_v = 1 + 2 f . Statement II does not explain Statement I

Practice Kinetic Theory of Gases on Quantrex Academy →

More from Kinetic Theory of Gases

If 2 mole of an ideal monoatomic gas at temperature T , is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is : 2026Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If the average kinetic energy of H₂ and O₂ molecules, kept in two 2026One gas of n₁ mole of molecules at temperature T₁ , volume V₁ , and pressure P₁ , and another gas of n₂ mole of molecules at temperature T₂ , volume V₂ , and pressure P₂ , are mixe 2026A mixture of carbon dioxide and oxygen has volume 8310 cm ^3 , temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mi 2026The mean free path of a molecule of diameter 5 10⁻¹⁰ ~m at the temperature 41^ C and pressure 1.38 10⁵ ~Pa , is given as _ _ _ _ m. (Given k_ B =1.38 10⁻²³ ~J / K ). 2026A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50^ C . The gas is now heated to double its temperature. The modified pressure is _ _ _ 2026Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of mo 2026The volume of an ideal gas increases 8 times and temperature becomes (1 / 4)^ th of initial temperature during a reversible change. If there is no exchange of heat in this process 2026 Full Kinetic Theory of Gases list All JEE Main PYQs