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JEE Main20236 Apr 2023Evening ShiftPhysicsKinetic Theory of GasesActual

The temperature of an ideal gas is increased from 200 K to 800 K . If r.m.s. speed of gas at 200 K is v 0 . Then, r.m.s. speed of the gas at 800 K will be:

Options

  1. Av 0 4
  2. Bv 0
  3. C4 v 0
  4. D2 v 0

Correct answer

D. 2 v 0

Step-by-step solution

At 200   K , the rms speed is given by v 0 = 3 R × 200 M       . . . ( 1 ) At 800   K , the rms speed is given by v ' = 3 R × 800 M       . . . 2 Divide equation (2) by equation (1) and solve to calculate the required speed. v ' v 0 = 3 R × 800 M 3 R × 200 M = 800 200 =   2 ⇒ v ' = 2 v 0

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