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NEET PHYSICSKinetic TheoryMedium

Question

For a gas, R/CV=0.67R/C_V = 0.67. This gas is made up of molecules which are:

A

Diatomic

B

Mixture of diatomic and polyatomic molecules

C

Monoatomic

D

Polyatomic

Step-by-Step Solution

We are given the ratio RCV=0.6723\frac{R}{C_V} = 0.67 \approx \frac{2}{3}. Rearranging this, we get CV=32RC_V = \frac{3}{2}R. For an ideal gas, the molar heat capacity at constant volume (CVC_V) depends on the degrees of freedom (ff) according to the relation CV=f2RC_V = \frac{f}{2}R. Comparing the values:

  • For a monoatomic gas, f=3f=3, so CV=32RC_V = \frac{3}{2}R .
  • For a diatomic gas, f=5f=5, so CV=52RC_V = \frac{5}{2}R.
  • For a polyatomic gas, f6f \ge 6, so CV3RC_V \ge 3R. Since the calculated CVC_V matches that of a monoatomic gas, the gas is monoatomic. Alternatively, using the adiabatic index γ\gamma: CPCV=R    γ1=RCV=0.67C_P - C_V = R \implies \gamma - 1 = \frac{R}{C_V} = 0.67. Thus γ=1.67\gamma = 1.67, which corresponds to a monoatomic gas.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Kinetic Theory. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSKinetic Theorymolecules

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