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Consider an ideal gas at pressure p , volume V and temperature T . The mean free path for molecules of the gas is L . If the radius of gas molecules, as well as pressure, volume and temperature of the gas are doubled, then the mean free path will be

Options

  1. A5 L 2
  2. BL 4
  3. CL 8
  4. D2 L

Correct answer

B. L 4

Step-by-step solution

Given, initial values of pressure, volume, temperature, radius of molecule of gas and mean free path are P p, V, T, r and L , respectively. Mean free path, aligned & = 2 2 R T r^2 N p L & = 2 2 R T r^2 N p aligned According to question if the radius of gas molecules, as well as pressure, volume and temperature of gas are doubled then aligned ^ & = 2 2 R 2 T 4 r^2 N 2 p & = 1 4 2 2 R T r^2 N p = L 4 aligned (From Eq. (i)) Hence, the mean free path will be L 4 .

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