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NEETPhysicsKinetic Theory of Gases

The pressure ( P ) versus temperature ( T in Kelvin) graph for a fixed mass of an ideal gas shows two straight lines passing through the origin, corresponding to two different constant volumes V₁ and V₂ . The line for V₁ is steeper than the line for V₂ . Two states of the gas, A and B , are marked on the lines for V₁ and V₂ respectively, such that both states have the exact same pressure P₀ . If v_A and v_B are the r

Options

  1. Av_A < v_B
  2. Bv_A > v_B
  3. Cv_A = v_B
  4. Dv_A = 2v_B

Correct answer

A. v_A < v_B

Step-by-step solution

From the ideal gas equation, PV = nRT P = ( nR V )T . For a P-T graph, the slope is nR V . Since the line for V₁ is steeper than the line for V₂ , its slope is greater, which means V₁ States A and B are at the same pressure P₀ . From the graph equation T = PV nR , at a constant pressure P₀ , the temperature is directly proportional to the volume. Since V₁ The rms speed of gas molecules is given by v_ rms = 3RT M . Since v_ rms T and T_A Answer: v_A < v_B

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