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NEET2026PhysicsChapterActual

A closed container holds a sample of an ideal gas at 127^ C . To what temperature must the gas be heated so that the root mean square (rms) speed of its molecules increases by 150 % ?

Options

  1. A627^ C
  2. B727^ C
  3. C2227^ C
  4. D2500^ C

Correct answer

C. 2227^ C

Step-by-step solution

The initial temperature of the gas is T₁ = 127^ C = 127 + 273 = 400 K . The root mean square speed of an ideal gas is given by v_ rms = 3RT M , which implies v_ rms T . Let the initial rms speed be v₁ . Since the rms speed increases by 150 % , the new rms speed v₂ is given by: v₂ = v₁ + 1.5v₁ = 2.5v₁ Using the relation v_ rms T , we have: v₂ v₁ = T₂ T₁ Substituting the values: 2.5 = T₂ 400 Squaring both sides: 6.25 = T₂ 400 T₂ = 6.25 400 = 2500 K Converting the temperature back to Celsius: T₂ = 2500 - 273 = 2227^ C

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