Question

Statement - I : The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume because.
Statement - II : The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

• A. 1) Statement - I is true, Statement - II is true; statement - II is a correct explanation for statement - I
• B. 2) Statement - I is true, statement - II is true; statement - II is NOT a correct explanation for statement - I
• C. 3) statement - I is true, statement - II is false
• D. 4) statement - I is false, statement - II is true

Answer 1

The correct option is B 2) Statement - I is true, statement - II is true; statement - II is NOT a correct explanation for statement - I

The rms velocity is given as $v_{rms}=\sqrt{\frac{3RT}{M}}$, where M is the molecular weight of the given gas. Thus the kinetic energy is given as $\frac{1}{2}M{v}_{rms}^2=\frac{3}{2}RT$. Using gas equation PV=RT we get the kinetic energy as $\frac{3}{2}PV$.
Both the statement are correct but 2 is not the correct explanation of 1.